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Full text of "Stellar chromospheres"



Si>^il7 



o 1 Jc/JLLd/iJV 

CHROMOSPHERES 



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A colloquium held at 

GODDARD SPACE FLIGHT CENTER 

February 21-24, 1972 




NATIONAL AERONAUTICS AND SPACE ADMINISTRATION 



§ 



NASA SP-317 



STELLAR 
CHROMOSPHERES 



The proceedings of the International Astronomical Union Colloquium 

held at NASA Goddard Space Flight Center 

February 21-24, 1972 



Edited by 
S. D. Jordan and E, H. Avrett 



Prepared by Goddard Space Flight Center 




Scientific and Technical Injormation Office 1973 

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION 

Washington, D.C. 



For sale by the Superintendent of Documents, 

U.S. Government Printing Office, Washington, D.C. 20402 

Library of Congress Catalog Card Number 70-604567 



CONTENTS 

Part I. Spectroscopic Diagnostics of Chromospheres and the 

Chromospheric Energy Balance 1 

"Temperature Distribution in a Stellar Atmosphere, 

Diagnostic Basis," John T. Jefferies, Nancy D. 

Morrison 3 

Discussion following the introductory talk by Jefferies 24 

"Stellar Chromospheric Models," Eugene H. Avrett 27 

Discussion following the introductory talk by Avrett 41 

Part II. Observational Evidence for Stellar Chromospheres 77 

"Evidence for Stellar Chromospheres Presented by 
Ground-based_Spectra of the Sun and Stars," 
Francoise Praderie 79 

"Evidence for Stellar Chromospheres Presented by Ultra- 
violet Observations of the Sun and Stars," Lowell 
Doherty 99 

Discussion following talks by Praderie and Doherty 124 

Part III. Mechanical Heating and its Effect on the Chromo- 
spheric Energy Balance , 179 

"Mechanical Heating in Stellar Chromospheres Using 

the Sun as a Test Case," Stuart D. Jordan 181 

Discussion following the introductory talk by Jordan 201 

"Theoretical Understanding of Chromospheric Inhomo- 

geneities," Philippe Delache 207 

Discussion following the introductory talk by Delache 218 

Part IV. Variation of Chromospheric Properties with 

Stellar Mass and Age 263 

"Chromospheric Activity and Stellar Evolution," 

Rudolf Rippenhahn 265 

Discussion follpwing the introductory talk by Kippen- 

.hahn 279 

Summary, O.C. Wilson 305 

Concluding remarks following the Summary 312 



m 



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PREFACE 

lAU Colloquium 19 on "Stellar Chromospheres" was a natural extensiori 
of its predecessor "Spectrum Formation in Stars with Steady State 
Extended Atmospheres," held during April, 1969, in Munich, Germany. 
The present colloquium was co-sponsored by Commissions 36 and 29 of 
the International Astronomical Union. The official organizing committee 
comprised Y. Fujita, J. C. Pecker, F. Praderie, R. N. Thomas, and A. 
Underhill, with Uriderhill chairing a local, east coast organizing committee 
consisting of, besides herself, E. Avrett, S. Heap, S. Jordan, and D. 
Leckrone. The Colloquium honored Professor Cecilia Payne-Gaposhkin of 
the Smithsonian Astrophysical Observatory for her many outstanding 
contributions to astronomy. The aim of the organizers was to bring 
together experts on the complex radiative, hydrodynamical, and observa- 
tional problems which the outer layers of stars provide, in the hope of 
clarifying both our present knowledge as well as where to go in the 
future. It is hoped that, to this end, these Proceedings will be helpful for 
students entering the field as well as research workers who were unable to 
attend. 

There were no contributed papers other than the eight summary papers 
listed in the Contents. However, we would like to acknowledge, with our 
appreciation, the many participants who carefully edited their remarks 
and returned to us finished manuscripts complete with bibliographies, etc. 
We have attempted to retain the spirit and format of these manuscripts 
where they appear, while always being guided by the need to preserve the 
open, informal atmosphere of the discussions which did, in fact, prevail 
during the Colloquium. The final responsibility for editing is ours and, if 
minor changes have confused or obscured meaiiing, we offer the authors 
our apologies. 

Several organizations participated in sponsoring, planning, financing, and 
running the Colloquium. In addition to official sponsorship by the lAU, 
the Goddard Space Flight Center and the Smithsonian Astrophysical 
Observatory were co-hosts, Goddard providing the site and direct support 
and the Smithsonian providing assistance in planning and a grant to 
defray expenses. Additional financial support was provided by a National 
Science Foundation Grant, and the cost of publishing the Proceedings was 
borne by Goddard. 

Finally, it might be appropriate to point out a few salient features of the 
Colloquium which will certainly have bearing on future developments. 
The entire question of what, exactly, constitutes a chromosphere, both 



conceptually, in definition, and in physical actuality, as inferred from 
spectral diagnostics, was discussed avidly and ardently during the sessions. 
The final summary and the subsequent discussion illustrate how varied are 
the experiences and opinions of two highly respected experts in this area. 
In general, the difficulties, both theoretical and observational, of studying 
chromospheres in detail still leave open many important questions which 
await not only improved research techniques, but improved communica- 
tions between the researchers. We hope these Proceedings wiU serve that 
function for all concerned. 

The Editors 

Greenbeh, Sept. 18, 1972 



VI 



VISITING PARTICIPANTS 

L. H. ALLER, UCLA, Dept. of Astronomy, Los Angeles, Cat. 

R. G. ATHAY, High Altitude Observatory, Boulder, Cot. 

L. H. AUER, Yale University, New Haven, Conn. 

E. H. AVRETT, Smithsonian Astrophysical Observatory, Cambridge, Mass. 

J. M. BECKERS, Sacramento Peak Observatory, Sunspot, N. Mex. 

H. A. BEEBE, New Mexico State, Las Cruces, N. Mex. 

R. A. BELL, Univ. of Maryland, College Park, Md. 

A. M. BOESGAARD, Univ. of Hawaii, Inst, for Astronomy, Honolulu, Hawaii 
K. H. bOhM, Univ. of Washington, Astronomy Dept., Seattle, Wash. 

E. bOHM-VITENSE, Univ. of Washington, Astronomy Dept., Seattle, Wash. 

R. M. BONNET, Laboratoire de Physique Stellaire et Planetaire, 91- Verrieres-Le- 

Buisson, France 
J. P. CASSINELLI, Joint Inst. For Laboratory Astrophysics, Boulder, CoL 
J. L' CASTOR, Joint Inst. For Laboratory Astrophysics, Boulder, Col. 
R. CAYREL, Observatoire de Meudon, 92 Meudon, France 
P. C. CHEN, State Univ. of New York, Stony Brook, N. Y. 
E. G. CHIPMAN, Laboratory For Atmospheric and Space Physics, Boulder, CoL 
P. S. CONTI, Joint Inst. For Laboratory Astrophysics, Boulder, CoL 
Y. CUNY, Observatoire de Meudon, 92 Meudon, France 
R. J, DEFOUW, Harvard College Observatory, Cambridge, Mass. 
P. DELACHE, Observatoire de Nice, Nice, France 
L. R. DOHERTY, Univ. of Wisconsin, Washburn Observatory, Madison, Wis. 

B. DURNEY, National Center For Atmospheric Research, Boulder, CoL 
T. L. EVANS, Royal Observatory of Edinburgh, Edinburgh, Scotland 

R. A. E. FOSBURY, Royal Greenwich Observatory, Greenwich, England 
H. FRISCH, Observatoire de Nice, Nice, France 

C. FROESCHLE, Observatoire de Nice, Nice, France 

C. GAPOSHKIN, Smithsonian Astrophysical Observatory, Cambridge, Mass. 

K. B. GEBBIE, Joint Inst. For Laboratory Astrophysics, Boulder, CoL 

R. T. GIULI, NASA Manned Spacecraft Center, Houston, Texas 

M. GROS, Observatoire de Meuden, 92 Meudon, France 

M. HACK, Trieste Observatory, Trieste, Italy 

J. P. HARRINGTON, Univ. of Maryland, College Park, Md. 

S. S. HILL, Michigan State Univ., East Lansing, Mich. 

J. T. JEFFERIES, Univ. of Hawaii, Inst, for Astronomy, Honolulu, Hawaii 

M. C. JENNINGS, Univ. of Arizona, Steward Observatory, Tucson, Ariz. 

H. R. JOHNSON, High Altitude Observatory, Boulder, CoL 

W. KALKOFEN, Smithsonian Astrophysical Observatory, Cambridge, Mass. 

R. S. KANDEL, Boston University, Dept. of Astronomy, Boston, Mass. 

R. KIPPENHAHN, Universitats-Stemwarte Gottingen, Gottingen, West Germany 

Y. KONDO, NASA Manned Spacecraft Center, Houston, Texas 

R. A. KRIKORIAN, Inst. d'Astrophysique, Paris, France 

L. V. VXim,Univ. of California, Berkeley, CaL 

J. W. LEfBACHER, Joint Inst, for Laboratory Astrophysics, Boulder, CoL 

J. R. LESH, Joint Inst, for Laboratory Astrophysics, Boulder, CoL 

J. LINSKY, Joint Inst, for Laboratory Astrophysics, Boulder, CoL 

S. -Y. LIU, Univ. of Maryland, College Park, Md. 

C. MAGNAN, Institute d'Astrophysique, Paris, France 

R. W. MILKEY, Kitt Peak Nat. Observatory, Tucson, Arizona 

vii 



J. L. MODISETTE, Houston Baptist College, Houston, Texas 

H. W. MOOS, Johns Hospkins Univ., Baltimore, Md. 

N. D. MORRISON, Univ. of Hawaii, Inst for Astronomy, Honolulu, Hawaii 

D. J. MULLAN, The Observatory, Armagh, Northern Ireland 

S. A. MUSMAN, Sacramento Peak Observatory, Sunspot, N. Mex. 

G. NESTERCZUK, Wolf Research, College Park, Md. 

K. NICHOLAS, .Wi/v. of Maryland, College Park, Md. 

G. K. H. OERTEL, NASA Headquarters, Washington, D. C. 

J. M. PASACHOFF, California Inst, of Technology, Dept. of Astronomy, Pasadena, 

Cal. 
J. C. PECKER, Inst. d'Astrophysique, Paris, France 
D. P. PETERSON, State Univ. of New York, Stony Brook, N. Y. 
J. PEYTREMANN, Harvard College Observatory, Cambridge, Mass. 
A. I. POLAND, High Altitude Observatory, Boulder, Col. 

F. PRADERIE, Inst dAstrophysique, Paris, France 

N. G. ROMAN, NASA Headquarters, Washington, D. C. 

J. D. ROSENDAHL, Univ. of Arizona, Steward Observatory, Tucson, Ariz. 

G. ROTTMAN, John Hopkins Univ., Baltimore, Md. 

D. SACOTTE, Laboratoire de Physique Stellaire et Planetaire, 91-Verrieres-Le- 
Buisson, France 

J. SCHMID-BURGK, University of Heidelberg, Heidelberg, West Germany 
R. SCHWARTZ, New York Univ., Dept of Physics, New York, N Y. 

E. SEDtMAYR, University of Heidelberg, Heidelberg, West Germany 
N. R. SHEELEY, Kitt Peak Nat. Observatory, Tucson, Ariz. 

T. SIMON, Univ. of Hawaii, Inst, for Astronomy, Honolulu, Hawaii 

E. V. P. SMITH, Univ. of Maryland, College Park, Md. 

A. SKUMANICH, High Altitude Observatory, Boulder, Col 

P. SOUFFRIN, Observatoire de Nice, Nice, France 

R. STEIN, Brandeis University, Boston, Mass. 

R. STEINITZ, Joint Inst, for Laboratory Astrophysics, Boulder, Col. 

H. H. STROKE, New York Univ., New York, N. Y. 

R. N. THOMAS, Joint Inst, for Laboratory Astrophysics, Boulder, CoL 

P. ULMSCHNEIDER, Univ. of Wuerzburg,,Astronomische Institut, Wuerzburg, 

West Germany 
R. ULRICH, UCLA, Dept. of Astronomy, Los Angeles, Cal. 
W. UPSON, Univ. of Maryland, College Park, Md. 
J. C. VALTIER, Observatoire de Nice, Nice, France 
J. E. VERNAZZA, Harvard College Observatory, Cambridge, Mass. 
O. C. WILSON, Hale Observatories, Pasadena, Cal. 
G. L. WITHBROW, Harvard College Observatory, Cambridge, Mass. 
K. O. WRIGHT, Dominion Astrophysical Observatory, Victoria, B. C, Canada 



\m 



PARTICIPANTS FROM GODDARD 

P. L. BERNACCA S. KASTNER R. E. SAMUELSON 

J. C. BRANDT D. A. KLINGLESMITH K. H. SCHATTEN 

R. D. CHAPMAN M. LAGET S. SOBEISKI 

L. DUNKELMAN D. S. LECKRONE W. M. SPARKS 

W. A. FEIBELMAN S. P. MARAN D. WEST 

D. FiscHEL c. Mccracken a. m. wilson 

S. R. HEAP J. M. MEAD C. L. WOLFF 

S. D. JORDAN K. W. OGILVIE A. B. UNDERHILL 



IX 



PARTI 

SPECTROSCOPIC DIAGNOSTICS OF CHROMOSPHERES 

AND THE CHROMOSPHERIC ENERGY BALANCE 

Chairman: Roger Cayrel 



INTRODUCTORY COMMENTS BY SESSION CHAIRMAN CAYREL 

I would like to define the topic for today and then turn to John Jefferies 
for the first introductory paper. I understand that today's topic is 
twofold. First, if there is a temperature rise in a layer of optical thickness 
of a few hundredths in the visible, what are the features of the spectrum 
which are most able to detect it? That I would say is the first point. The 
second point is how such a temperature rise can be driven either by a 
radiative mechanism or by dissipation of mechanical energy. 



Page intentionally left blank 



TEMPERATURE DISTRIBUTION IN A STELLAR 
ATMOSPHERE-DIAGNOSTIC BASIS 

John T. Jefferies 

Nancy D. Morrison 

Institute for Astronomy 

University of Hawaii 

Presented by John T. Jefferies 

INTRODUCTION 

As is well known, the word "chromosphere" was coined to denote the 
bright, thin, colored ring seen as the solar limb was obscured by the 
Moon at the time of a total eclipse. This region of the Sun's atmosphere 
was found to be the source of many strong emission lines — the flash 
spectrum — some persisting to such heights as to leave no doubt that 
their cores originated quite high in the chromosphere. The presence of 
such an emission line region is not unexpected; however, what gives the 
solar chromosphere special interest is the fact that its observed spectro- 
scopic properties cannot be explained on the basis that it is a simple 
extension of a "classical" atmosphere for which radiative, hydrostatic, and 
local thermodynamic equihbrium all apply. Thus, the height above the 
limb to which most ecUpse Unes persist is inconsistent with the predicted 
density scale height. The observation of neutral and ionized heUum lines 
in the flash spectrum demands temperatures far in excess of those 
predicted for a radiative equilibrium model. Further difficulty is encoun- 
tered in attempting to explain in classical terms the shapes and strengths 
of certain chromospheric lines in the disk spectrum, notably the self 
reversals in the cores of H and K. Such observations, coupled with the 
recognition that the coronal temperature is in the range of millions of 
degrees and the discovery of the peculiar inhomogeneities in the chromo- 
spheric gas, e.g., the spicules and the supergranular flow pattern and such 
transitory phenomena as surges, flares and prominences, all contributed to 
the recognition that the properties of the chromosphere are controlled by 
factors that Ue outside the scope of a classical atmosphere. Thus, the 
partitioning of the Sim into photosphere, chromosphere, and corona is 
seen to be far more fundamental than the simple geometrical division 
based on eclipse observation. It appears that there are different mech- 
anisms at work in these layers, especially in the way energy is transferred. 

We recognize now that some, at least, of the spectroscopic features of the 
solar chromosphere are consistent with the hypothesis that the tempera- 
ture increases outward above some minimum value found a few hundred 



kilometers above the limb. The temperature rise is thought to be a result 
of the dissipation of mechanical energy generated in the photosphere, and 
if this is so we will naturally expect this process to take place in other 
stars, leading to the formation of stellar chromospheres. A direct 
approach to the study of these layers might be to concentrate on the 
kinematic motion of the line-forming layers as deduced from the shapes, 
strengths, and wavelength shifts of spectral lines. It is also fruitful, 
however, to consider the symptom of the dissipation of energy, namely 
the temperature rise, as a basis for comparison between solar and stellar 
chromospheres and this is the approach we shall adopt here. Thus, we 
shall consider a stellar chromosphere as a region where the temperature 
increases outward, and we shall examine spectroscopic methods for 
inferring the existence and properties of a temperature rise . 

The following section sets out the physical basis for the discussion with 
some general considerations on how (or whether) the temperature struc- 
ture of a gas controls the shapes of spectral lines. In particular, we shall 
discuss why some lines are very sensitive temperature indicators while 
others are much less so. Following that, we shall consider emission lines 
and what they can tell us about the atmosphere of the star, and we shall 
discuss methods for determining the temperature structure of the atmos- 
phere from the analysis of Une profiles. The final section contains a brief 
discussion of the information in the stellar continuum, together with 
some miscellaneous indicators. 

THE INFLUENCE OF TEMPERATURE STRUCTURE 
ON LINE PROFILES 

The monochromatic flux Fj, emerging from a plane,parallel semi-infinite 
gas is given by 

P. = 2 f S^(^.)E2(r,)dT^ , (1) 

"'ft 



where r„ is the monochromatic optical depth, E2 is the second exponen- 
tial integral, and S^ is'the source function, defined as 



V 

where e^ and k„ represent respectively the monochromatic volume 
emissivity and the absorption coefficient per unit length in the gas. In 



general, both e^ and k^ will contain components from continuum and line 
processes; however we are here primarily interested in the cores of strong 
lines formed in the outer atmospheric layers, and we shall neglect the 
continuum contribution. 

Clearly, the emergent flux will reflect the temperature distribution only 
to the extent that Sj^ (or e^ and k^) depends on the temperature. For a 
spectral line it is well known — see, e.g., Jefferies (1968) - that 



S = 






Ht^ , (3) 



where ni , nj are the concentrations of atoms in the lower and upper 
levels of the line gi , gj are the statistical weights of the levels and \j/(i/) is 
a function which we shall set equal to unity, following Jefferies (1968) 
and Hummer (1969). This latter approximation implies that the line 
source function is independent of frequency over the core of the Une, and 
we shaU therefore drop the subscript f. The physical basis of bur 
arguments remains unchanged if we neglect stimulated emission, in which 
case equation (3) reduces to 

2hp3 gj n 
Sp = — . (4) 

Thus, the dependence of the emergent flux on the temperature structure 
of the gas is fixed by the temperature dependence of the population 
ratio. Now this ratio can be expressed, formally, as 

where Ry is the rate of. all transition paths, direct and indirect, which 
carry the atom from level i to level j. Recognizing that there are, in 
general, two mechanisms (collisional and radiative) by which transitions 
can take place, we can write, equivalently, _ 



roo 






(6) 



where the C*s are direct collisional rates and the first terms in numerator 
and denominator are respectively the direct radiative absorption and 
spontaneous transition rates, while the terms ly represent the rates of 
indirect transitions taking the atom from level i to level j. In this 
formulation, the "source" terms C^^ and I^ represent the creation of 
fresh photons into the radiation field, while the sink terms C21 and In 
represent the destruction of absorbed photons by de-excitation of the 
atom. The source terms thus represent the ultimate source of the 
radiation in the gas. 

Thomas (1957) distinguished two classes of lines according to whether 
direct collisional transitions or indirect processes are chiefly responsible 
for creation and destruction of photons. If C12 > I12 and C21 ^ Iji, 
equation (3) reduces to 



f 

J (1 



. ,J,0,dv^eB^(T) 
Sg - 1 + e ' ^^^ 

where By(T) is the Planck function at the local kinetic temperature T, 0^ 
is a normalized profile of the absorption coefficient and the important 
parameter e is defined as 

e ^ -H (8) 

A21 

Thus, e measures the importance of direct collisional relative to radiative 
de-excitations of an atom in the upper level of the line. In this case, 
therefore, the gas temperature enters directly into the line source 
function; the physical reason is that the collisions then control the 
production of new photons in the line, and the rate of these collision 
transitions depends on the kinetic temperature, through the Boltzmann 
distribution. Thus, for such a "collisionally controlled" line, the atmos- 
pheric temperature structure should be reflected in the Une profile. The 
essential questions of interest to us here are, can we know a priori 
whether a line is "coUisionally controlled," and, if so, exactly how is the 
temperature structure reflected in the profile of the observed Une? 

Thomas (1957) gave a partial analysis of the first question. In particular, 
he showed that, for stars of solar type and later, one would expect strong 
resonance lines of non-metals, and of ionized nietals, to be coUisionally 
controUed. The dichotomy depends on the atomic level structure and on 
the color temperature of the steUar continuum; as particularly important 



cases In this category, we identify the resonance Unes of Ca+, Mg+, H, C, 
N,^and O when formed in stars of solar type and later. Thomas also 
showed that the ratio of the populations of the levels of the resonance 
lines of neutral metals should be controlled less by coUisions than by 
indirect processes, which should, in turn, be controlled by the strength of 
the cohtiniium radiation field streaming through the gas. As a conse- 
quence, the source functions of such lines should not reflect the local 
temperature distribution in the region where the lines are formed, but 
rather the temperature in the region where the continua originate. 
Thomas' corresponding partitioning of lines into "collisional" and "photo- 
electric" control is important to keep in mind when designing observa- 
tional programs, but it must be appUed with an inteUigent understanding 
of its basis. Thus, whether a given line falls into one or the other of the 
classifications depends on the gas temperature, the stellar continuum flux, 
and the local density; the classification is not- an immutable property of 
the line. For example, the cooler the star, the closer a given Une will be 
to coUisional control. 

Considerable insight into the question of just how sensitively the tempera- 
ture structure is reflected in the line profile has been obtained over the 
past ten to fifteen years. For a collisionally controUed line, for which Sgis 
given by equation (7), we can compute the emergent radiation for a given 
temperature model by solving (with appropriate boundary conditions) the 
transfer equation 



^1^ = \-h = K- (l-'^)Jo \1>v^'' - %(T) , (9) 

V 



where X = Cji/CAji + Cji) is the probability of a collisional de- 
excitation of an atom in the upper state of the line. We consider solutions 
of equation(9) for two general cases, an isothermal semi-infinite layer of 
gas, and secondly, a model in which the temperature increases outward. 

ISOTHERMAL LAYER 

Schematic results for an isothermal layer are illustrated in Figures I-l and 
1-2 for a set of values of the scattering parameter X. Two aspects of these 
figures should be particularly noted. Firstly, the line source function 
saturates to the Planck function at an optical depth of X"* as measured in 
the line center. This characteristic distance is known as the "thermaliza- 
tion length," corresponding physically to the average optical distance 
which a photon will travel from its point of creation as a new photon, 



S/B 




Figure I-l The ratio of the line source function to the Planck function, for an iso- 
thermal gas, as a function of optical depth at the line center. The differ- 
ent curves refer to different values of the scattering parameter \. 



-<| ^ 

o> 
o 




Figure 1-2 The logarithm of the ratio of the emergent flux in the line to the Planck 
function, for an isothermal gas, as a function of wavelength. The profiles 
refer to different values of the scattering parameter \. 



following collisional excitation, to its point of destruction by collisional 
de-excitation; this occurs, on the average, after X'* successive absorptions 
and reemissions. Detailed discussions of the thermalization length are 
given, e.g., by Finn and Jefferies (1968a, *) and by Hununer and Rybicki 
(1971a). It is important in the present context to point out that an 
equivalent interpretation of the thermalization length is the distance to 
which a change in atmospheric conditions will be reflected in the 
radiation field. Thus, for example, a discontinuous jump in temperature at 
some point in the gas would be reflected in the radiation field up to an 
optical distance (measured in the line center) of X^' away. Clearly, 
therefore, the degree of line scattering in the gas has a profound effect on 
the depth distribution of intensity in the line and so, via equation (7), on 
the line source function and on the profile of the emergent flux. 

This fact is reflected in the second point we wish to emphasize, which is 
illustrated in Figure 1-2. The line profiles shown there are obviously 
different, yet they are computed for atmospheres with identical tempera- 
ture structure; in fact, the gas is isothermal in the kinetic temperature 
(although the profiles are in absorption). The differences among the 
profiles arise from the differences in X(or e), not from any differences in 
temperature structure. Only in the case of LTE (for which X = 1) is the 
temperature uniquely reflected in the profile; the line is then completely 
filled in. From the definition (8) it can be shown that e '^ ICT' * n for a 
strong line in the visible, where n is the electron density in cm"' . In the 
solar chromosphere where Ca II H and K are formed, n 'v 10" cm~^ 
consequently, X 'v e '^' 10"^, a value assuring a major departure from 
local thermodynamic equilibrium. Since X is proportional to the density 
the profiles of coUisionally controlled lines certainly reflect the gas 
density. In a more general case of a non-isothermal gas, we shall show 
that both the temperature and density distributions determine the profile; 
evidently, the problem of separating these two effects from the line 
profile will not be straightforward. 

THE CHROMOSPHERIC CASE 

CollisionaUy Controlled Lines 

Jefferies and Thomas (1959) studied the formation of a coUisionally con- 
trolled line in a gas whose temperature increases towards the top of the 
atmosphere. Their temperature model is shown in Figure 1-3 as the full line; 
the source functions derived by solving equation (9) are shown schemat- 
ically as broken curves; the conesponding emergent line profiles are shown 
in Figure 1-4. It is immediately clear that the temperature structure is cer- 
tainly reflected in the profiles but to a degree which is controlled by the 



10 



to 

o 



1 
1 




1 1 1 1 
1 1 II 




1 





12 3 4 5 6 

Log To 

Figuie 1-3 The line source function as a function of optical depth in the line center . 
The solid curve represents the Planck function according to the model of 
Jefferies and Thomas (1958). The dashed curves are solutions of the 
equation of radiative transfer for this model, for different values of \. 




Figure 1-4 Emergent line profiles predicted by the model 
of Jefferies and Thomas (1958) for different values of \. 



11 

parameter X, as would be expected from the arguments given above. There 
is a striking qualitative agreement between the computed line profiles and 
those observed in late type stars, particularly for Ca II H and K, and the Fe 
II (3100 A) lines (cf. Weymann 1962, Boe^aard 1972), as well as in solar 
Lya and Mg II H and K. The general consistency of the predictions is evi- 
dence that these self-reversed lines do arise in a gas with a positive tempera- 
ture gradient. 

The shape of the profile depends not only on the amplitude of the 
temperature rise, but also on the relative values of the optical depth t^^ 
where this rise begins and the thermaUzation depth t*(=X''). The K-line 
reversals should be or absent if t^, < r* and strong if t^ > t*. Thus, 
emission features should go with high densities and deep chromospheres, 
and weak or no emissions should accompany low densities and thin 
chromospheres. 

In summary, the observation of self -reversed emission cores in H and K 
give direct evidence of the existence of an outward temperature rise in 
the stellar atmosphere. Their absence in these Unes is not, however, 
necessarily an indication of the absence of such a temperature rise since 
the density and temperature characteristics of the gas may be such that a 
temperature rise could not be reflected in the Kline profile. It may be 
relevant in this regard that observations of some F stars show deep 
normal K line profiles and others show reversals (e.g., Warner 1968). 

Photoelectrically Controlled Lines 

Thomas' arguments also give us some insight into the reason why lines 
like Ha, which are as "strong" as K, do not normally show an emission 
reversal. We shaU not go into detail here, but merely note, with 
Stromgren (1935), that certain lines, of which solar Ha is in fact a good 
example, derive their excitation mainly through indirect transitions which 
transfer atoms from the lower to the upper state via an intermediate 
state, commonly the continuum. Such processes are governed by absorp- 
tion of radiation generated lower in the atmosphere, which is essentially 
present as a background illumination. As a result, the local temperature in 
a chromospheric region where the line is formed plays little or no role in 
determining the emergent line shape (although it may control the Doppler 
width and so set a scale to the profde). In that case, the line source 
function takes the form 



Sg = (1-n) J^^^di. -Htj B* , (10) 



12 

both 17 and B* being controlled by the strength and "color" of the 
continuous and weak line radiation streaming through the chromosphere, 
and so being constant with depth in line forming regions. Thus, independ- 
ently of the kinetic temperature structure in the chromosphere, emergent 
profiles of photoelectrically controlled lines will have the same form as 
those shown in Figure 1-2 since the source and sink terms for the cases 
illustrated there are also constant with depth. Such lines will then appear 
in absorption even when H and K show strong emission cores. This is not 
to say that Ha must always be in absorption; e.g., at high densities direct 
collisions can become more important than indirect photoelectric 
processes and such a shift to collisional control is probably the reason 
that Ha goes into emission in solar flares and in flare stars. 

INFLUENCE OF INCLUDING MORE LEVELS 

The simple physical arguments presented above give great insight into the 
response of line profiles to the temperature and density structure of a gas. 
For a quantitative discussion, however, greater detail is needed in the 
specification of the atomic level structure, particularly the incorporation 
of more than the two levels (plus continuum) to which earUer treatments 
were confined. Many calculations of multi-line problems have beeri carried 
out - cf. e.g., Avrett (1966), Finn and Jefferies (1968fe, 1969), Cuny 
(1968), Athay et al. (1968) - but they change the above physical picture 
Uttle if at all. One significant general conclusion from such calculations, 
however, is that the source functions of multiple lines (such as H and K) 
share an essentially common depth dependence over much of the gas. 
Waddell (1962) showed that this equality is required by a comparison of 
solar center-to-limb observations of Dj and D2 . If generally correct, the 
conclusion is of great importance for the analysis of stellar spectra. 

SUMMARY 

We have seen that profiles of certain spectral lines should be sensitive to 
the temperature distribution in a gas and so can presumably be considered 
indicators of the presence of chromospheres. We have seen that these lines 
are, in fact, observed to have profiles which indicate the presence of an 
outward temperature rise, and have seen why others, comparably strong, 
should not, and do not, show the same features. For the temperature- 
sensitive lines, we have seen that the profiles reflect both temperature and 
density structure, but it is not clear that we can disentangle these 
dependences in a unique way. 

The basic physical ideas seem clear and give self -consistent (if qualitative) 
results. Their application to stellar problems will demand more 



13 

SE^histicated computations, particularly taking into account many atomic 
levels in order to allow predictions on a nimiber of lines formed in the 
same atom or ion. 

The theoretician also faces the fact that the inhomogeneous structure seen 
in the solar chromosphere may be expected to be present in other stars, 
and he must seek to compute its influence on the space averaged profiles 
observed from a star. The averaged spectriim from a multidimensional 
medium does not necessarily reflect average temperature or density 
conditions, but the extent of this failure is not yet clear. The techniques 
for studying such questions are available in Monte Carlo programs or in 
the more conventional solution of three-dimensional transfer problems, 
and it seems that only by model calculations can we obtain some idea of 
the sensitivity of different lines in stellar spectra to inhomogeneities. Such 
data are essential if we are ever to develop sound methods of analysis, or 
even to design meaningful observation programs. 

DO EMISSION LINES IMPLY A CHROMOSPHERE? 

The problem of what the presence of an emission line implies about the 
structure of a stellar atmosphere is still unsolved. Following Gebbie and 
Thomas (1968), we can characterize the problem in the following specific 
terms: The observed flux is given as 

F„ = / I„Mdco , (11) 



and the central question is whether the emission line is intrinsic, over all 
or some of the star's surface (i.e., 1„ > I^), or whether it has a 
geometrical origin because the area of integration is much greater for the 
line than for the continuum. It is of basic importance to try to develop a 
diagnostic tool to discriminate between these two possible sources of 
emission lines. Although we have no concrete ideas to suggest here, a 
reasonable first step would be to study some model problems to clarify 
the consequences of postulating a geometrical origin for emission lines. 
The theoretical tools for handling such problems are available, especially 
since the development (cf. Hummer and Rybicki, 1971 b ) of simpler 
methods for handling transfer problems in spherical atmospheres. A model 
problem based on a pure hydrogen atmosphere could greatly clarify this 
question. 

A line will be intrinsically in emission if the line and continuum source 
functions are related according to the inequaUty, 



14 

SfiC'-o = 1) > Sc (^c = 1) . (12) 

where the optical depths are measured along the direction of observation, 
and Tq refers to the line center, t^ to the continuum at a neighboring 
wavelength. We may obviously satisify this inequaUty either by reducing 
Sg or by increasing Sg. The latter possibility occurs most naturally, at 
least for a collisionally controlled line, if the temperature increases 
outwards. This mechanism explains the fact that, in the solar atmosphere, 
emission lines are abundant below '\/1600 A (and present up to 'v2000 
A). To some extent, their appearance is favored by the increasing 
continuum opacity below about 1800 A which places the region of 
formation of the continuum near the temperature minimum, while that of 
the lines Ues in the chromosphere. 

The alternative notion that S(, is depressed below Sg was originally 
explored by Schuster (1905), later by Underbill (1949) and more recently 
by Gebbie and Thomas (1968). In its simplest form, and the one most 
favorable for emission line formation in a "classical" atmosphere, 
Schuster's mechanism supposes that the line is formed in LTE so that Sg 
= By, while the continuum is formed partly by thermal and partly by 
scattering processes so that S^ is given as 

Sc = -V J, + ^By(T) , (13) 

with X„ < 1 . 

For an isothernwl gas, Sg/By(T) will be less than unity near the front of 
the atmosphere because the escape of photons from the surface reduces 
Jy below By. Consequently, inequaUty (12) is satisfied and the line 
appears in emission. For a normal radiative equiUbrium gradient, however, 
the continuum intensity J^ increases substantially and it becomes much 
more difficult to satisfy the inequality (12). Gebbie and Thomas (1968) 
concluded that, except perhaps in the infrared, the Schuster mechanism 
would be ineffective in a classical atmosphere. Their conclusion, sup- 
ported by the work of Harrington (1970), is only strengthened if the line 
source function is represented by the more physically correct expression 
(7). In this case, the emergent central intensity drops below its LTE 
value, making it still more difficult for the line to appear in emission. The 
appUcability of the Schuster mechanism is further reduced by the fact 
that it requires that the continuum not be formed in LTE; for most stars, 
however, LTE is believed to hold in the continuum. Still , exceptions 
exist, especially for hot stars, where electron scattering is significant 



15 

while, even for the Sun. LTE fails below the Lyman limit. Hence, the 
possibility that S^ is reduced by some departure from LTE in the 
continuous spectrum needs to be kept in mind in connection with the 
appearance of emission lines in a stellar spectrum. 

We believe that a rich field of investigation of great potential to stellar 
spectroscopic diagnostics is to be found in a concentrated attack on the 
appearance of emission lines in stars. So far, the confusion between 
processes forming intrinsic emission lines and those arising from extended 
envelopes (stationary or expanding) has limited our ability to use these 
lines for diagnostic purposes. The sophistication of present-day computa- 
tional methods is sufficient, and the rewards sufficiently attractive, to 
merit a full-scale attack on the problem of differentiating between these 
two entirely different origins for emission lines. 

ANALYSIS OF SPECTRAL LINES 

OPTICALLY THICK GASES 

We saw above that certain lines are expected to contain information in 
their profiles on, among other things, the distribution of temperature with 
depth in the gas. We now wish to discuss briefly the problem of using the 
information in an observed line profile to infer the temperature distribu- 
tion in the gas; in a sense, this is the inverse of the problem, discussed 
above, of computing the Une profile given the atmospheric structure. 

The best starting point currently available is the expression 

K = ^l ^(UE^cgdt^ , (14) 



which already restricts the scope of our analysis to a homogeneous 
semi-infinite plane — parallel layer. A more complicated expression 
suitable for spherically symmetric geometry could no doubt be obtained; 
an extension to more general expressions incorporating stochastic spatial 
variations is beyond the present development of the subject. 

From equation (14), the first part of the analysis consists in determining 
from the observed profile F^ the run of Sy(ty) for each point on the Une 
profile. As it stands, however, infinitely many possible distributions Sy(tp) 
will satisfy the integral equation (1 4). Some limitation of these solutions 
can be obtained if we restrict attention to those parts of the profile where 
continuum processes are negligible compared to those in the line, so that S„ 



16 

and ty refer only to the spectral line. However, even in that case, the depth 
distribution of Sj, is not uniquely determined. In order to invert equation 
(14) uniquely, Jefferies and White (1967) have shown that it is necessary 
to have observational profiles of two or more lines whose source functions 
at all depths are related in some known way. Since, as mentioned above, 
studies of multiline transfer problems have indicated that the source func- 
tions of close-lying multiplet lines are essentially equal at all depths, except 
perhaps close to the surface, such lines should provide the necessary data for 
an analysis. This principle has been applied by Curtis and Jefferies (1967) 
to the solar D lines (for which the availability of center-to-limb data greatly 
simplifies the problem, and allows us to retrieve information on the con- 
tinuum parameters also). Wilson and Worrall (1969) have also attempted an 
analysis of the solar D lines, using data at one point on the disk; their pro- 
cedure is essentially equivalent, therefore, to that which would in practice 
be applied to stellar spectra, where no geometrical resolution is obtainable. 
It is not our purpose here to discuss in detail such analytical methods, or 
the closely related method of deJager and Neven (1967), but rather to 
draw attention to their existence, since they offer an alternative interpretive 
method to that based purely on model calculations. The theory of such 
analytical processes also allows a more incisive study of such important 
questions as the uniqueness of a particular derived model, a subject quite 
beyond the scope of this paper but one nevertheless deserving closer 
study than it has received. 

While the analytical method has promise, at least, of determining the 
depth variation of Sjj and the frequency and depth variation of the line 
absorption coefficient, its application so far (to solar data) has not been 
wholly satisfying. The difficulty may lie in inadequate data, in uncertain- 
ties in the inversion of the integral equation, in limitations in the basic 
formulation (14), or in the degree to which Sg is independent of 
wavelength within the line and the same from one line to another. 

If such problems can be resolved, the depth variation of Sg would still 
require interpretation in terms of the density and temperature structure 
of the gas. We can see no way of approaching this other than through a 
model calculation. At least, the depth and wavelength dependence of the 
line absorption coefficient that is yielded by the analysis would be helpful 
by setting constraints on the model. 

OPTICALLY THIN GASES ^ 

The specific intensity emitted from a gas in an optically thin line reflects 
the integral of the volume emissivity along the line of sight; in general, 
the line profile does not reflect the way in which emitting material is 



17 

distributed and an infinite number of geometrical rearrangements of the 
emitting material will yield the same emission in all optically thin lines. A 
satisfying technique for spectroscopic diagnosis of an optically thin line 
would therefore seek some way of specifying the physical state of the gas 
which is unique and so preserved under such geometrical rearrangement. 
This general problem has been studied by Jefferies, Orrall, and Zirker 
(1972). While their particular interest lay in its use for the analysis of 
coronal forbidden lines, the method is of general application, in particular 
to the optically thin lines of the solar chromosphere. 

For a transparent gas, the specific intensity I, integrated over the line 
profile, can be written 



I = ^ A nu(x)dx, (15) 

J 

where n„ is the population of the upper state of the line and x is the 
geometrical coordinate in the line of sight. The emissivity is controlled 
only by the local electron density and temperature, and the intensity of 
interacting radiation fields of known strength, provided that n^ is 
determined by electron collisions or by the absorption of radiation in 
spectral regions which are themselves thin. In the usual way, we expand 
the population nu in the form 



n 


"u 


"i 


""a 


"h 


u 


"i 


"a 


"h 


n 



(16) 



with n; the concentration of the ionization stage to which the line 
belongs, n^ and n^ the concentrations of the element and of hydrogen, 
and n the electron density. The ratios nj/n^, n„/ni, and njj/n are all 
fimctions of n and T only. If we define 

n 



a 



ei n 



^. (17) 

H 



as the abundance of the element with respect to hydrogen and define an 
ionization-excitation function 

"u "i "h 
x(n,T)= , (18) 

n^ n^ n 



18 



then equation (15) takes the form 



/*oo 



hv 

I = Aa 

4n 



el 



X(n,T)ndx. 



(19) 



Specific distributions n(x) and T(x) would, of course, characterize the gas 
uniquely and would yield straightfonvardly a value of I. However, as 
stated above, we could never determine such distributions uniquely from 
the observed intensities. We therefore abandon the geometrical distribu- 
tion as a characterization of the gas and instead transfer the analytical 
problem to an n, T space by introducing a distribution function M(n>T) 
through the definition 



dN(n,T) = Nju(n,T) dndT, 



(20) 



with dN(n,T) the number of electrons in the sampled column that are in 
neighborhoods where the electron temperature lies between T and T + dT 
and, simultaneously, the electron density lies between n and n + dn. The 
distribution dN is normalized to the total electron content N in the 
column so that )u(n,T) is normalized to unity. In these terms we can write 



= Ca„N 



x(n,T)M(n,T) dndT, 



(21) 



•'o«'o 



where C = (h>'/47r) A. Equation (21) is a double integral equation with 
kernel x(n.T) which may, in principle, be solved for the distribution 
function )u(n,T), given data on the number of lines for which the 
functions x are sufficiently different. 

While, in principle, we might hope to infer the bivariate function fJi(n,T), 
in practice we shall probably have to accept the more limited description 
of the gas implicit in the assumption that n and T are uniquely related 
everywhere along the line of sight. 

In that more restrictive case, equation (21) becomes 

I = Ca.. N I xfnfD. Tl 0(T) dT, (22) 



a^, N * x[n (T), T] 
•' 



19 
where the distiibution function 0(T) is given by 



*Cr) = 



M(n,T) dn (23) 



•'0 



and n(T) is the single valued function relating the electron density to the 
temperature. Clearly (T) dT is the fraction of all the electrons in the 
column whose temperatures Ue between T and T + dT. 

The finesse of an, analysis based on the above formulation will depend on 
the degree to which the excitation-ionization functions X(n,T) differ from 
one line to another. Since we can calculate x in advance once we know 
the cross sections for radiative and coUisional transitions;, we can decide in 
advance which set of lines of a particular ion will best suit our needs for 
analysis. 

ZETA AURIGAE-TYPE ECLIPSING BINARIES 

Because of their special geometry, a class of eclipsing binaries present 
favorable cases for the study of a stellar chromosphere. Of the bright stars 
of this type, the prototype f Aur is the best observed but the 
observational results are similar for 31 and 32 Cygni - cf. Wilson (1961), 
Wright (1970). These binary systems are composed of a K-type super- 
giant and an early B-type dwarf or subgiant which undergoes total ecUpse. 
As it passes behind the extended atmosphere of the supergiant absorption 
lines appear in the spectrum. Since the radiation field of the B star may 
affect the temperature structure of the chromosphere of the K giant it is 
not clear to what extent results from these systems apply to single stars. 
In the absence of any other way of obtaining direct detailed information 
about the temperature structure of a star other than the sun, the method 
nevertheless has great value. 

In spite of this fact, few observers have attempted to draw conclusions 
about the variation of temperature with height in the chromosphere. 
Those who have done so have used a curve-of-growth analysis for the line 
spectrum to derive values for the excitation and ionization temperatures 
at one or several heights in the chromosphere. In their study of f Aurigae, 
Wilson and Abt (1954) were able to reproduce their observations only by 
supposing the envelope to be slumpy. Otherwise, the B-type star ought to 
ionize the envelope of the supergiant to a greater degree than that 
observed. Wright (1959) concurred that the chromospheric spectrum ought 
to be produced mainly in small condensations where the density is much 



20 

greater than in the rest of the gas. Further evidence for the existence of 
condensations is given by the observation that the chromospheric K line 
usuaUy contains several components of different radial velocities. As in the 
Sun, then, a correct analysis must take into account the inhomogeneity of 
the medium. 

MISCELLANEOUS INDICATORS 

SYMBIOTIC FEATURES 

Unambiguous indications of the presence of a temperature rise are given 
by what we will call symbiotic spectral features: features whose behavior 
in a stellar spectrum yields, through elementary analysis, values of 
temperature or abundance that are anomalous or disagree with the values 
derived from other spectral features in the same star. For example, 
calculation of the population of the lower level for conditions expected in 
stars yields an estimate for the strength of the line at a given temperature. 
If the line has a large excitation potential and is stronger than expected, 
it must arise in a hot layer above the photosphere. For example, the 
Balmer lines in some M-type giants are anomalously strong, indicating 
overpopulation of the second level by a large factor (Deutsch 1970). For 
a Ononis, Spitzer (1939) showed that the great strength of Ha impUes a 
radiation density of Lyathat corresponds to a temperature of 17000°K. 
This value contrasts sharply with the effective temperature of the star, 
which is near 3300°K. Another example of this type of indicator is a 
group of lines near 1 micron wavelength due to Si I and Mg I (Spinrad 
and Wing 1969). Since they have excitation potentials of about 6 eV, 
their presence is favored by temperatures of 5000° or 6000°K. Neverthe- 
less, they are as strong in a Ori as they are in the Sun. Finally, the most 
important symbiotic features are the lines arising from excited states of 
He I. Though X10830 is the most prominent of these lines, others, such 
as X5876, may be observable in cool stars also. Vaughn and Zirin (1968) 
calculated the population of the lower level of the line at 10830 A and 
found that, for all densities considered, it is negligible for T < 20000 °K 
and large for all higher temperatures. This line must therefore be regarded 
as a clear indicator of a large rise in temperature in the upper atmosphere 
of any star whose effective temperature is substantially less than this 
value. 

CONTINUOUS SPECTRA 

For a region of a stellar continuous spectrum where the opacity is known 
as a function of wavelength, the wavelength variation of the emergent 



21 

flux wfll contain information gbout the temperature gradient. In some 
regions of the g)ectrum, the opacity may be so high that even the 
continuous radiation arises effectively in the chromosphere; in the sun 
this happens for millirnetre radiowaves, and again in the near UV at about 
700 A. If the color temperature, or the brightness temperature, of the 
radiation increases as the opacity increases, an outward temperature rise is 
indicated. 

An exaniple of such a case is found in the ultraviolet below about 0.3 
fxm, where a high opacity is provided by the bound-free continua of 
hydrogen and the metals. The opacity generally increases toward shorter 
wavelengths, and, at some wavelength, the continuous radiation originates 
effectively at the height in the atmosphere where the temperature has a 
minimunj. Naturally, this wavelength is shorter than the wavelength at 
which the chroinp^here begins to influence the cores of the lines and 
where, consequeiitly, emission lines begin to appear. Since the transition 
of the line ^ectrum from absorption to emission occurs at longer and 
loiiger wavelengths for later and later spectral types, it is reasonable that 
the influence of the chroinosphere on the continuum should also extend 
to longer wavelengths for later spectral types. Doherty (1970) has studied 
the ultraviolet continua of K and M stars near 3000 A as observed by 
OAO-2. In particular, he considered the wavelength dependence of the 
color temperature of the continuum, which should reflect the variation of 
the electron temperature with height. For stars of spectral type earlier 
than about K5, the flux below 0.28 nm decreases rapidly toward shorter 
wavelengths. For a Tauri and a Orionis, however the flux decreases much 
more slowly in this region, and both stars show a minimum in the color 
temperature at about 0.30 /im. Whether this minimum indicates a 
temperature minimum in the stellar atmosphere or only a maximum in 
the opacity is not clear. 

Another source of continuous opacity that may be important to this 
discussion is the H-ion. Beyond 1 .6 nm, the free-free opacity of this ion 
increases monotonically, in a known manner (Geltman, 1965). If, in the 
chromosphere of a cool star, the temperature is low enough and the 
electron density is high enough, the H-ions might produce enough opacity 
so that the continuous radiation in the observable infrared would arise in 
the chromosphere. Thus, limb brightening or even an infrared excess 
might be observable at wavelengths shorter than 20 (im. Noyes, Gingerich, 
and Goldberg (1966) searched unsuccessfully for limb brightening at 24 
/im in the Sun. From a model of the solar chromosphere, they predicted 
that the Sun should show an infrared excess at 50 /im. They suggested 
further that other stars, in which there is an additional opacity source in 
the infrared or in which the temperature minimum lies at greater optical 



22 . 

depth than in the Sun, might show an infrared excess at shorter 
wavelengths. 

Another source of excess radiation at long wavelengths might be free-free 
emission from hydrogen. If the characteristics of the long-wave radiation 
were to require that the source have an electron density lower than that 
expected in the photosphere, the radiation would have to arise in an 
extended envelope surrounding the star. If, in addition, the temperature 
required for the source is substantially higher than the effective tempera- 
ture of the star, a temperature rise above the photosphere is indicated. 
For example, Wallerstein (1971) has considered whether the excess at 10 
Hm of the KO supergiant W Cephei could be produced by free-free 
emission. He found that the size (but not the wavelength dependence) of 
the infrared excess could be produced by free-free emission in a sphere 
with radius 15 A.U. if the electron density is 2 - 4 x 10' cm'^and the 
electron temperature is 50O0-6000°K. Since the effective temperature of a 
KO supergiant is only about 4000°K (Allen 1963, p. 201), the star 
presumably has a chromosphere, but the free-free emission, which comes 
from a very extended region, apparently does not originate there. 

In the Sun, free-free emission at radio frequencies arises in the corona. 
From a simple model of a stellar corona, Weymann and Chapman (1965) 
have predicted that free -free emission should be detectable in~the 
microwave region, and this emission has been detected in cool stars 
(Kellermann and Pauliny-Toth 1966; Seaquist 1967). 

CONCLUSION 

In this review, we have tried to indicate areas where further theoretical 
work would improve the present understanding of stellar chromospheres. 
In several places, we have emphasized that calculations of line profiles 
need to take into account inhomogeneities in the gas. This necessity arises 
from the fact that all stars that can be observed with spatial resolution 
over the disk — the Sun and the f Aur variables — show inhomogeneities 
in the chromosphere. Past work on the f Aur variables has shown that the 
effect of inhomogeneities can be striking. 

We have also considered the problem of obtaining the distribution of 
temperature with height from an observed line profile. Although we 
pointed out that such methods exist and should be applied to stellar 
spectra, we also noted that the methods carmot yet be applied with 
complete success. Not only are better line profiles needed than are usually 
obtainable from stars, but further improvements in the theory are also 
required, from improvements in the basic formulation to refinements in 
numerical techniques. 



23 

The most general area of research that we have suggested is, however, the 
question of what emission Unes mean. We mentioned three situations that 
are thought capable of producing emission lines in a stellar atmosphere: a 
temperature rise, the Schuster mechanism, and the case where the 
effective emitting area is larger in the line than in the continuum. Of 
these suggestions, only the first is thought to exist generally; still, the 
others cannot be entirely ruled out. It would be desirable to know in 
detail what conditions would permit the Schuster mechanism or the 
geometrical mechanism to operate. This area of research promises to be 
one of the most fruitful in the area of stellar chromospheres. 

The work described here was partially supported by Grant #GP 31750X 
■from the National Science Foundation. 

REFERENCES 

Men, C.W., 1963 , Astrophysical Quantities, 2nd. ed., (The Athlone Press, 

London). 

Athay, R.G., Avrett, EH., Beebe, HA., Johnson, H.R., Poland, AJ., and 

Cuny, Y., 1968, Resonance Lines in Astrophysics NCAR, Boulder, 

Colo., p. 169. 
Avrett, EH., 1966, Ap. J. 144, 59. 
Boesgaard, AM., 1972 (This Symposium). 
Cuny, Y., 1968, Solar Phys. 3, 204. 
Curtis, G.W. and Jefferies, J.T., 1967, Ap. J. 150, 1961. 
de Jager, C. and Neven, L. 1967, Solar Phys. 1, 27. 
Deutsch, A.J., 1970, lAU Symposium No. 36, eds. Houziaux and Butler 

(Springer-Verlag, New York), p. 199. 
Doherty, L.R. 1970, paper presented at the meeting on Solar Studies 

With Special Reference to Space Observations held at the Royal 

Society, London, Apr. 21-22, 1970. 
Fmn, G.D., and Jefferies, J.T., 1968 a, J. Quant. Spectrosc. Radiat. 

Transfer 8, 1675. 

^, \968b ibid, 8, 1705. 

, 1969 ibid, 9, 469. 

Gebbie, K.B. and Thomas, RJSf., 1968, Ap. J. 154, 285. 

Geltman, S., 1965, Ap. J. 141, 376. 

Harrington, JP., 1970, Ap. J., 162, 913. 

Hummer, D.G., 1969, Man. Not. R. Astr. Sac. 145, 95. 

Hummer, D.G., and Rybicki, G.B., 1971a, Ann. Rev. Astron. Ap. 9, 237. 

,19716 Mon. Not. R. Astr. 

Sbc. 152, 1. 
Jefferies, J.T., 1968, Spectral Line Formation, (Blaisdell Pub. Co. 

Waltham, Mass). 



24 

Jefferies, J.T., Orrall, F.Q. and Zirker, 3B., 1972, Solar Phys. (in press) 

Jefferies, J.T. and Thomas, RJ^J., 1959, Ap. J. 129, 401. 

Jefferies, J.T. and White, O.R., 1967, Ap. J. 150, 1051. 

KeUermann, K.I. and Pauliny-Toth, IJ.K., 1966, ^p. /. 145, 953. 

Noyes, R. W., Gingerich, 0., and Goldberg, L., 1966, AP- J- 145, 344. 

Schuster, A., \905, Ap. J. 21, 1. 

Seaquist, E.R., 1961, Ap. J. 148, 123. 

Spinrad, H. and Wing, R.F., 1969, Ann. Rev. Astron. Astrophys. 7 249. 

Spitzer, L., 1939, Ap. J. 90, 494. 

Stromgren, B., 1935, Z. Astrophys 10, 237. 

Thomas, RJ^J., \9Sl,Ap. J. 125, 260. 

Underhill, A.B., 1949, yip. J., 110, 340. 

Vaughan, AH. and Zirin, H., 1968, Ap. J. 152, 123. 

Waddell, JH., 1962, Ap. J. 136, 231 . 

Wallerstein, G., 1971, yip. /. 166, 725. 

Warner, B. 1968, Observatory 88, 217. 

Weymann, R., 1962, Ap. J. 136, 844. 

Weymann, R. and Chapman, G., 1965, Ap. J. 142, 1268. 

Wilson, AM. and Worrall, G., 1969, Astr. Astrophys. 2, 469. 

Wilson, O.C. 1961, Stellar Atmospheres, ed. Greenstein, vol. 6, Stars and 

Stellar Systems (Chicago U of Chicago Press), p. 436. 
Wilson, O.C. and Abt, H., 1954, Ap. J. Suppl. 1,1. 
Wright, K.O., 1959, PmW. Dominion Astrophys. Obs. 11, 77. 
Wright, K.O., 1970, Vistas in Astronomy 12, 147. 

DISCUSSION FOLLOWING THE INTRODUCTORY 
TALK BY JEFFERIES 

Skumanich - There is a hidden parameter in Jefferies' curves which I 
think should be brought out, namely, the thickness of the chromosphere 
or, conversely, the scale height. If the optical thickness of the chromo- 
sphere is held constant and there are changes in the density, then the 
physical thickness must change. Such a change is governed by the 
momentum equation (e.g. hydrostatic equilibrium). 

Jefferies — You are quite right. I should have mentioned that for 
illustration I took a constant optical thickness for the chromosphere and 
varied X independently. 

Skumanich — This makes three parameters not two, and we should worry 
about the variations of all thrge. 

Jefferies — Yes, that's correct, and the relationship of the thickness of the 
chromosphere to the density is of fundamental importance. In point of 
fact, if the optical depth where the chromospheric temperature rise begins 



25 

is greater than the thennaUzation length then you'll have strong chromo- 
^heric emission, and if it's less the emission will be weak. 

Athay — There is another aspect of the uncertainty coming into the 
profile, and that is the opacity of the atmosphere. Even the photoelec- 
trically controlled lines depend on temperature due to the temperature 
dependence of the line opacities. 

Scumanich — One more parameter is that-which describes the kinematic 
situation, and this brings the number of basic parameters to four. 

Poland — In reference to the statement that an increasing source function 
is the result of a chromosphere, it should be mentioned that Auer and 
Mihalas have obtained results that show it is possible to get emission lines 
due to optical pumping without a chromosphere. For example Hell lines 
can be pumped by hydrogen lines if the overlap is sufficient. 



Page Intentionally Left Blank 



STELLAR CHROMOSPHERIC MODELS 

Eugene H. Avrett 

Smithsonian Institution 
Astrophysical Observatory 



ABSTRACT 

In "Types of Theoretical Models" we describe two basic types of 
theoretical models — radiative equilibrium and empirical — that are used 
to represent stellar chromospheres. The next Section is a summary of 
recent work on the construction of radiative-equilibrium model atmos- 
pheres that show an outward temperature increase in the surface layers. 
Also, we discuss thcchromospherlc cooUng due to spectral Unes. In 
"Solar Empirical Models" we describe the empirical determination of 
solar-type chromospheric models that, in order to match observations, 
imply a temperature rise substantially greater than that predicted by 
radiative equilibrium. Such a temperature rise must be largely due to 
mechanical heating. An attempt is made in the concluding Section to 
apply a scaled solar chromospheric model to a star with a different 
surface gravity. The results suggest that the chromospheric optical thick- 
ness is sensitive to gravity and that the width of chromospheric line 
emission increases with stellar luminosity, in quaUtative agreement with 
the width-luminosity relationship observed by Wilson and Bappu. 

TYPES OF THEORETICAL MODELS 

Current research on chromospheric models can be described in terms of 
two. different approaches. The first involves calculating a theoretical 
spectrum on the basis of a set of a priori assumptions that includes the 
assumption of radiative equilibrium. Often a grid of such models is 
constructed for different values of effective temperature, surface gravity, 
and composition. The calculation of radiative-equilibrium models has 
reached a new level of sophistication recently with the detailed inclusion 
of non-LTE effects (Auer and Mihalas, 1972) and line blanketing (Kurucz, 
Peytremann, and Avrett, 1972). 

These models may account for most of the observed features in normal 
stellars spectra, but they do not account for the chromospheric spectra of 
late-type stars such as the Sun. As discussed in the following section, the 



27 



28 

only point of controversy in the solar case is whether or not radiative 
equilibrium plays even a minor role in the initial chromospheric tempera- 
ture rise. 

The second approach is the same as the first except that in place of the 
radiative-equilibrium assumption, which fixes the temperature distribution, 
we adjust the temperature versus depth by trial and error until the 
computed spectrum ^rees with the observed one. An empirical model for 
the solar chromosphere is obtained in this way, as discussed below. The 
solar spectrum has been observed throughout different wavelength regions 
in such detail that we can test our theoretical models for consistency: 
Typically, we have a greater number of spectral features to match than 
parameters to adjust. 

Once a detailed empirical chromospheric model is obtained for the Sun, 
or for any well-observed star, it is possible to calculate the mechanical 
energy flux as a function of depth, i.e., the amount that must be added 
to the radiative flux to make the total flux constant with depth. A 
knowledge of the mechanical flux distribution should lead us to an 
understanding of the nonradiative heating mechanism, and then perhaps 
to a method by which this flux distribution can be calculated for any 
star. As a result, we would be able to construct realistic chromospheric 
models based on the assumption of radiative equilibrium with mechanical 
heating. Despite the work still to be done, this goal seems within reach. 

RADIATIVE-EQUILIBRIUM MODELS 

Here we summarize recent work on the construction of model atmos- 
pheres in radiative equilibrium that show an outward temperature increase 
in the surface layers. 

Auer and Mihalas (1969a, b, 1970) have calculated non-LTE radiative- 
equilibrium model atmospheres for hot stars with effective temperatures 
of 12500° and 15000°K. They examine the heating of the outer layers 
caused by a positive flux derivative in various continuum wavelength 
intervals when J^ exceeds the continuum source function. They find that 
the main source of heating is due to photoionization in the Balmer 
continuxmi and that this is mostly a population effect: The Ha line 
provides an efficient channel for 3 to 2 transitions causing a greater level 
2 population, greater heating, and a surface temperature rise. The line 
itself tends to cool the atmosphere, but by an amount smaller than the 
heating caused by the change of level populations. 

Feautrier (1968) also computed non-LTE model atmospheres in radiative 
and hydrostatic equilibrium with effective temperatures 15000° and 



29 

25000°K and log g = 4, and with a solar effective temperature together 
with both log g ^ 2 and solar gravity. He includes departures from LTE in 
H^as well as in hydrogen. In the higher effective-temperature atmos- 
pheres, he finds surface-temperature increases of as much as 1000° or 
2000°K in agreement with Auer and Mihalas, but in the solar effective- 
tempeiatuie cases, he finds inaeases of oidy a few hundred degrees. 

The physical mechanism lesponable for the surface-temperature rise was 
pointed out by Cayrel (1963); it is an extension of the classical 
radiative-equilibrium model of a planetary nebula, as discussed, for 
example, by Baker, Menzel, and Aller (1938). Essentially, there is a shift 
from LTE in the underlying star to unbalanced radiative equilibrium in 
the low -density outer atmosphere, where the temperature is close to the 
color temperature of the star, rather than to the lower classical boundary 
temperature. 

Skumanich (1970) has recently discussed the validity of the Cayrel 
mechanism in response to an earlier suggestion by Jordan (1969) that 
radiative equilibrium is incompatible with a departure of the continuum 
source function from the Planck function for atmospheres of large H" 
concentration. 

Gebbie and Thomas (1970, 1971) discuss the role that collisions play in 
the energy balance. They find that the low chromospheric densities are 
too high to be neglected in calculating the temperature and atomic 
populations. Hence, the planetary-nebula type of calculation does not give 
correct results for the low chromosphere. They discuss the determination 
of the temperature distribution in terms of transfer effects and population 
effects and, as a measure of population effects, introduce a quantity they 
call the "temperature control bracket," defined as the photoionization 
rate divided by the corresponding integral containing the monochromatic 
source function instead of J^ . 

Most of the above studies are concerned with heating due to photoioniza- 
tion. A number of other recent studies have been made of radiative- 
energy losses and of cooling due mainly to lines. 

Dubov (1965) emphasizes that the main factor responsible for the cooling 
of the chromosphere is radiation in separate spectral lines. Athay (1966) 
discusses the energy loss from the middle chromosphere due to the 
hydrogen Balmer lines. Frisch (1966) estimates the cooUng due to 
collisional excitation in various lines and finds that, in the vicinity of the 
temperature minimum, the energy losses due to the Ca and Mg H and K 
resonance lines together with the Ca infrared triplet are approximately 
half those due to radiative recombination. Athay and Skumanich (1969) 



30 

and Athay (1970) carry out extensive non-LTE line-blanketing calcula- 
tions and find that the tendency for the temperature to rise in the surface 
layers due to the Cayrel mechanism is strongly resisted by the effects of 
line blanketing; they also find that a chromospheric rise of 300° or more 
would require a substantial input of mechanical energy. 

Hence, it is by no means certain that even the initial temperature rise in 
the low solar chromosphere occurs as a consequence of radiative equilib- 
rium. 

SOLAR EMPIRICAL MODELS 

In this section we discuss the empirical determination of model chromo- 
spheres, such as that of the Sun, for which the temperature rise is 
substantially greater than that predicted by radiative-equilibrium calcula- 
tions. The results shown here are from the study of Linsky and Avrett 
(1970) of the solar H and K lines. The model has been chosen such that 
the predicted microwave spectrum lies within observed limits and the 
computed H- and K-line profiles resemble those observed from quiet 
regions near the center of the solar disk. This model is intended to be 
only a representative one. Empirical solar models that also match various 
features in the extreme ultraviolet have been constructed more recently 
by Noyes and Kalkofen (1970), Gingerich, Noyes, Kalkofen, and Cuny 
(1971), and Vernazza, Avrett, and Loeser (1972). 

Disk -center brightness temperatures observed in the region 10/x to 2 cm 
are shown in Figure 1-5. The solar continuous opacity increases with 
increasing wavelength in this region, so that radiation at longer wave- 
lengths is emitted by layers at greater heights in the atmosphere. The 
spectrum shortward of about 300ju originates in the photosphere, and that 
longward, in the chromosphere. 

The solid line in Figure 1-5 represents the brightness temperatures we 
computed based on the temperature -height distribution shown in Figure 
1-6. The abrupt temperature increase that begins at about 7500° has been 
introduced to account for the Lyman-continuum spectrum shortward of 
912 A and to keep the computed gas pressure above coronal values (see 
Athay, 1969, Noyes and Kalkofen, 1970). 

Unfortunately, there is a second function of height that must be 
introduced in order to specify the model. In our study of the calcium 
Unes, we need to introduce non-thermal Doppler broadening to explain 
the observed central line widths. The line absorption coefficient at the 
wavelength X for an atom of mass M has the Doppler width 



31 



10000 



9000 



8000 



'b 7000 



6000 - 



5000 - 



4000 - 



|ii I I I I — I — I [1 1 1 I I I — I — r- 

-BUHL a TLAMICHA (1968) 



n I I I I — I — r 



STAELIN , etol. (1964) 
-SALOMANOVICH (1962) 



TOLBERT a 
STRATTON 



BASTIN, etol, (1964) 




LOW a 

eiLLESPIE 
(ld6SI) 



J liii I I i i-^j 



Figure 1-5 Comparison of the observed aiid calculated brightness temperatures of 
the disk center. References to the papers indicated in the figure are 
given by Linsky and Avrett (1970). 



15000 


1 


1 1 1 1 1 1 1 r 1 1 1 1 r 1 1 1 1 1 


1 1 1 1 r 


12000 


- 


TEMPERATURE CK) 


- 


10000 


- 




- 


9000 


- 




- 


8000 


- 


V 


- 


7000 


- 


^*--.,,,.,^^ 


- 


6000 


- 


^^\ 


) 


5000 


- 


\ 


J 


4000 


_t 


HEIGHT (KM) ^^ 
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 


1 1 1 1 1 



2500 2000 1500 1000 500 

Figure 1-6 The assumed temperature-height distribution. 



32 






:acT 

M 



+ V2 



where T is the temperature at the given depth. We use the parameter V as 
a measure of any required nonthermal Doppler broadening. Central 
profiles of the Ca II infrared triplet lines, formed between 500 and 1000 
km, indicate values of V in the range 2 to 3 km/sec. Higher in the 
atmosphere, where the H- and K-line centers are formed, V must exceed 4 
km/sec. We have attempted to adjust V(h) to obtain good agreement 
between the calculated and the observed line profiles. The result is shown 
in F^re 1-7. 



12 


\ 


1 1 


1 I 




10 


A 






- 


8 


- 






- 


V 6 


- 






- 


4 


- 








2 


- 













1 1 


1 1 





2500 2000 



1500 1000 
h 



500 



Figure 1-7 The nontheimal velocity distribution 
used in line bioadening and in the pressure equation. 

We have chosen to use V(h) also to represent a nonthermal contribution 
to the total pressure P. We let 



p vP.-Tpv^ 



33 

where Pg is the gas pressue and p is the density. This added pressure term 
extends the model in height and gives better agreement with observed 
edipse scale heights. 

Given T(h) and V(h), we solve the equations of hydrostatic equilibrium, 
statistical equilibrium, and radiative transfer for atomic hydrogen, taking 
into account the ionization and excitation of other constituents as 
required. Figure 1-8 shows the resulting ground-state hydrogen number 
density n,, the electron and proton densities n^ and n^, the electron 
pressure Pg, the total pressure P, and the turbulent pressure P, = l/2pV^. 



2- 15- 



I - 14 - 



o 



0- 13- 




2500 



2000 



1500 



1000 



500 



Figure 1-8 Distributions of pressure and number density, including n^ the electron 
density, np the proton density, n^ the density of hydrogen atoms in the 
ground state, Pg the electron pressure, Pj the turbulent pressure, and P 
the total pressure. 

Having established the atmospheric model, we solve the transfer and 
statistical-equilibrium equations for Ca II. Figure 1-9 shows the computed 
frequency-independent source function for the K line plotted against 
height and against line-center optical depth. This source function is a 
measure of the ratio of upper and lower level number densities. If this 



34 

ratio were given by the Boltzmann equation, as in LTE, S would be equal 
to the Planck function B, which is also shown for comparison. 




2500 



2000 



Figure 1-9 The K-line source function, Planck function, and line-center optical 
depth. The computed line-intensity values at Kj, K2, and K3 are indi- 
cated by dashed lines. 

The computed H- and K-line intensity profiles for the center of the solar 
disk are shown in Figure I-IO, compared with those observed by White 
and Suemoto (1968). We plot the average of the red and violet halves of 
each observed profile. Residual intensities are plotted in Figure I-IO, but the 
absolute intensities of Ki , Kj , and K3 (the minimum, peak, and central 
values) are shown for reference in Figure 5. The K2 peak intensity is 
substantially less than the maximum of S because of the Doppler-width 
variation with height in this region. The agreement between calculated 
and observed profiles shown in Figure 6 is the best we obtained after 
many trial adjustments of T(h) and V(h). 



35 



0.12 



0.10- 



0.08- 



0.06- 



0.04 



0.02 




A\ 



Figure I-IO The computed disk-centei H- and K-line profiles (broken lines) compared 
with the corresponding observed profiles of White and Suemoto(1968), 
(solid lines). 

These emergent line profiles are calculated assuming that the mono- 
chromatic line source function S^ is equal to S throughout the line. This 
assumption is valid in the Une core, where Doppler redistribution takes 
place, and in the far wings, where S = S^ = B. In the intermediate wings, 
several Doppler widths from line center, the situation is unclear. In this 



region the coherent-scattering approximation 



S. = 



J„ may be more 



accurate; if so, the computed line profile may have a different shape 
between K2and K^. 

The quiet-Sun Kj emission peaks are weak and subject to various 
fluctuations from point to point on the disk. It may be that we should 



36 



try to match not the spatially averaged profiles shown in Figure MO, but 
the ones observed with high spatial resolution. 

It is of interest to note the difference in shape between the quiet-Sun H 
and K profiles shown in Figure Ml and the plage profiles in Figure 1-12. 
The question of whether S^ is closer to S or J^ in the intermediate line 
wings might be answered by a theoretical study of plage profiles. The 
published research on coherence and noncoherence in the K-line wings is 
discussed in Section III .2 of the review by Linsky and Avrett (1970). 




Figure I-l 1 Low-spatial-resolution residual intensities of the H and K lines for quiet 
regions near the disk center, as obtained by Linsky (1970). Although the 
K line exhibits a distinct double reverssd, the H line exhibits only a 
plateau in the violet wing and no reversal at aU in the red wing. 




Figure 1-12 Low-spatial-resolution residual intensities of the H and K lines 
for a plage region, as obtained by Linsky (1970). 



37 



THE EFFECT OF GRAVITY ON CHROMOSPHERIC THICKNESS 



In this final section we attempt to apply a scaled solar chromospheric 
model to a star having a different surface gravity. Figure 1-13 shows the 
solar temperature distribution to be used for this purpose. This T(h) , 
differs somewhat from the earlier one shown in Figure 1-6 because we 
have made changes in the corresponding V(h). The photospheric tempera- 
ture distribution from zero height (tsooo ~ 1) to the temperature 
minimum is^ approximately in radiative equilibrium. The right-hand por- 
tion of Figure I-I4 shows the calculated photospheric temperature 
distribution for a star with a solar effective temperature but with log g = 
2. The log g = 2 photosphere is more extended in height by a factor of 
about 250, which is approximately the ratio of the two values of g. We 
have 'arbitrarily chosen a chromosphere for this star that is scaled from 
the solar model by roughly the same height factor. Note that the 
calculated chromospheric Tsooo scale is very different in the two cases. 
The computed number densities are shown in Figure I-l 5 : Those for log g 
= 2 are about a factor of 10 smaller than the corresponding solar values. 
However, the log g = 2 scale height exceeds that of the Sun by the much 
larger factor 250. Whenever the opacity is proportional to nj^, as it is for 
the K line, we expect the log g = 2 chromosphere to have a greater 
optical thickness. 

The K-line source function and line-center optical depth for the two cases 
are shown in Figure 1-16. In this figure and in the preceding one, the log 
g = 2 height scale appears at the top and the solar height scale at the 
bottom. Note that at the temperature minimum, t^ for log g = 2 is an 
order of niagnitude greater than TK(solar). This increased thickness leads 
to a greater width of that portion of the line that originates above the 
temperature minimum. When the thickness is greater, we need to look 
farther out in the line wings to see the photosphere. Figure 1-17 shows 
the two computed flux profiles. 

These results illustrate a plausible effect of a change in gravity: The 
lower-gravity atmosphere is less dense but geometrically extended to a 
greater degree. The outer layers then hav& greater optical thickness, which 
leads to a greater line-emission width and the geometrically extended 
atmosphere tends to have a greater luminosity. Hence, the width W 
increases with luminosity L. The degree to which these results appear 
consistent with the observed relationship Woe L' * found by Wilson and 
Bappu (1957) will be discussed later at this meeting by Dr. E. Peytre- 
mann. 

Further attention should be -given to the shape of the computed profiles 
shown in Figure 1-17. The observed stellar profiles appear to have a 



38 



8000 



7000- 



T(*K) 6000- 



5000 



4000L_l 



logr, 



2000 



sooo 

5 

r- 



T,|| » 5780 
log g'4.44 




-4 -3 -2 -1 

-I — I — I — I — n 



1600 



1200 



800 




h(km) 



Figure 1-13 The solai, log g = 4.44, temperature distribution used for 
compaiiosn wth another case for which log g = 2. 



log T, 



9000 







-9 


-4 


-3 


-2 -1 C 


1 


aooo 


r 


■\ 


1 


T^=5780 


1 1 




root) 


- 


\ 




log g «2 




- 


r(»K) 6000 


- 




^ 


s^ 


I 


- 


9000 


- 






\ 


/ 


- 


4000 






1 


. \y 


1 





9x10 4X10 3X10 2x10 ixlO 

Figure 1-14 The adopted log g = 2 temperature distribution. 



39 



(le«g-2) 




(Mior) 



Figure 15 A comparison of the number densities in the two cases. 



/ 

h(log«>2) 

5»I0* 4»loP SiiloP 2iloP I»ICP 



togr. 




2000 1600 



1200 800 

h(Mlor) 



togs^ 



Figure 16 The K line source function and line-center optical depth in the two cases. 



40 



2.5 

Sao 


- 


I 




1 1 1 / 1 
/ 

/ 
/ 

/ 
/ 

/ (5780, 4.44) 


- 


~6 '-5 
u 

a> 

«> 1.0 


- 




> 


/ K LINE 

/ 

/ 
/ 
/ 
/ 


- 


'g 


(5780, 2) 


X 

-J 0.5 


1 






K LINE 


- 





• 


1 




1 1 II 





0.5 



1.5 2.0 2.5 



3.0 



AX(A) 



Figure 1-17 The computed flux profile for the K line in the two cases. 

sharper transition between the Kj emission peak and the Ki minimum 
(see, for example, Griffin, 1968, and liller, 1968). Perhaps the transition 
between Doppler core and damping wings should occur farther out in the 
Une. Also, as noted in the last section, we should examine the effects of 
partial coherence in the region between Kj and K, . 



REFERENCES 

Athay, R.G. 1966, /Is/ropftj's. /., 146, 223. 

Athay, R.G. 1969, Solar Phys., 9, 51. 

Athay, R.G. \970,Astrophys. J.. 161, 713. 

Athay, R.G., Skumanich, A. 1969, Astrophys. J., 155, 273. 

Auer, LJH., Mihalas, D. 1969fl, Astrophys. J., 156, 157. 

Auer, LJi., Mihalas, D. 1969*, Astrophys. J., 156, 681. 

Auer, L.H., Mihalas, D. 1970, Astrophys. J.. 160, 233. 

Auer, LH. Mihalas, D. 1972, Astrophys. J. Suppl, 24, 193. 

Baker, J.G., Menzel, DJJ., Aller, LJI. 1938, Astrophys. J., 88, 422. 

Cayrel, R., 1963, Comptes Rendus, 257, 3309. 

Dubov, E.E., 1965, Soviet Astron. - A J., 9, 782. 



41 

Feautrier, P. 1968, Ann. D'Astrophys., 31, 257. 

Frisch, H. 1966,/. Quant. Spectrosc. Radiat. Transfer, 6, 629. 

Gebbie, K.B., Thomas, R2^. 1970, Astrophys. J., 161, 229. 

Gebbie, K.B., Thomas, RJ^. 1971 , Astrophys. J., 168, 461 . 

Gingerich, 0., Noyes, R.W., Kalkofen, W., Cuny, Y. 1971, Solar Phys., 

18, 347. 

Griffin, RP. 1968, A Photometric Atlas of the Spectrum of Arcturus, 

Cambridge Philosophical Society, Cambridge, England. 
Jordan, S.D. 1969, Astrophys. J., 157, 465. 
Kurucz, R.L., Peytremann, E., Avrett, EJi. 1972, Line Blanketed Model 

Atmospheres for Early Type Stars, U.S. Govt. Printing Office (in press) 
Liller, W. 1968, Astrophys. J., 151, 589. 
Linsky,J.L. 1910, Solar Phys., 11,355. 

Linslq^, J.L., Avrett, E.H. 1970, Pk/W. Astron. Soc. Pacific, 82, 169. 
Noyes, R.W., Kalkofen, W. 1970, Solar Phys., 15, 120. 
Skumanich, A. 1970, Astrophys. J., 159, 1077. 

Vemazza, JE., Avrett, EJI., Loeser, R. 1972, submitted to Astrophys. J. 
White, O.R., Suemoto, Z. 1968, Solar Phys., 3, 523. 
Wilson, O.C, Bappu, MJC.V. 1957, Astrophys. J., 125, 661 . 

DISCUSSION FOLLOWING THE INTRODUCTORY TALK BY AVRETT 

Aller - I should like to ask about the suggested theoretical one-sixth 
power relationship between calcium emission width and visual luminosity. 

Avrett — We find an increased width with decreasing gravity, which in 
turn is normally associated with an increased luminosity. In the session 
tomorrow Eric Peytremann wiU show the results we have to date and how 
they compare with the Wilson-Bappu relation. To summarize them, the 
log g = 2 case with a temperature similar to that of the sun turns out 
with a reasonable mass determination to fit the Wilson-Bappu relation 
within the error bars. The only other calculation we have done so far is 
for an effective temperature of 6000° with log g = 4; the error bars again 
include the Wilson-Bappu relationship but they are very large. At the 
moment these results are only schematic. Also our choice of a chromo- 
sphere in the non-solar cases was completely arbitrary. We have to see 
whether we just happened to select chromospheres which give the proper 
optical thickness for the calcium emission. 

Jefferies — This is more of a comment than a question. One of the things 
which bedevils comparison between observation and theory of model 
atmospheres is, of course, the question of the uniqueness of any derived 
model. In order to characterize an atmosphere fully one needs to 
introduce a substantial number of parameters. Because of this, one needs 



42 

to compare computed profiles for many lines and obtain good agreement 
with observation for all of them before one can have confidence in the 
model. Hence, while an observation of the K line is valuable, its value is 
greatly enhanced if it is accompanied by simultaneous observations of the 
other lines of ionized calcium. 

Lin^y — I should like to second what Jefferies has said concerning the 
need to observe many lines together. I have found from bitter experience 
that _ observations of the calcium K line contain insufficient information to 
define a unique model for a chromosphere or even a chromospheric 
structure in the Sun. One can always trade off temperatures against 
densities or broadening parameters at one height, or trade off properties 
at one height against those at another and obtain the same computed line 
profile. To surmount this problem we have obtained data, as we will show 
this afternoon, on the infrared triplet lines as well as the H and K lines of 
Ca II in a number of solar plages. These lines differ in opacity by about a 
factor of 200. One surprising thing that we have found is that it is not 
always true that chromospheric emission appears in the more opaque lines 
before it appears in the weaker lines. We find that the 8498 A line, the 
weakest of the infrared triplet lines of Ca II, shows emission before the 
more opaque 8542 A and 8662 A lines of the triplet. 

Underhill — The discussion up to now has necessarily concentrated on 
solar type objects. These objects can be used as an anchor to confirm the 
theory, and the development of theory is partly based on explaining solar 
observations. However, other stars have chromospheres. I should like to 
ask the theoreticians if there has been any attempt to examine how the 
theory of the classification of Unes into classes which are collision- 
dominated or into photo-electrically dominated classes must change as the 
temperature and the total radiation field changes. The density of stellar 
atmospheres changes from cooler to hotter stars — the atmosphere of a 
main-sequence B star is essentially the same as that of a G giant — so it 
seems to me to be possible that a coUision dominated line will change to 
a radiation dominated line as the peak density of the radiation field 
changes its wavelength range and the density of the atmosphere is 
reduced. Has anyone any views on this question? 

Thomas — The rules for that were set up when the original classification 
scheme was presented. You can calculate the coUision rate and the 
radiation rate or any of the other indirect rates. Recently there is the 
work of Auer and Mihalas in which the Ca lines and the Mg lines become 
photoionization dominated. 

Auer — I would like to comment on some of the work by Mihalas and 
myself on the atmospheres of very hot stars and to clarify the point 



43 

raised by Poland. The primary feature of the non-LTE atmospheres, 
which we constructed, is a temperature use at the surface caused by 
radiative he? ting. The models predict that the Paschen a line of hydrogen 
(and presumably the higher a transitions also) is an emission line. This 
effect is caused by a combination of the temperature use and the fact 
that the infrared lines are formed high in the atmosphere. In the region 
where these lines are formed the collision rates are low and the dominant 
way out of a state is a cascade to a lower state. The temperature rise 
aggravates the rate of recombination and, therefore, the rate of emission. 
The situation is somewhat similar to the planetary nebula case. 

This mechanism does not suffice to produceemission in the X4686 line of 
Hell, which is observed to be in emission in Of stars. We attempted to 
produce this emission by using the Bowen mechanism. The 2n to 2n 
transitions of Hell overlap the n to n' transitions of H, and therefore one 
might expect pumping of the 2n' levels of Hell. If the upper level of a 
transition is strongly overpopulated, an emission line will result. Such is 
the theory, but unfortunately the results are not in good agreement with 
the observations. There is a tendency for emission, but not nearly as 
much as the observations require and X10124 is predicted to be in 
absorption while it is observed to be in emission in f Pup. 

Cayrel — Is there any observation supporting the calculations of emission 
in Paschen a? 

Auer — Yes. There's another thing I should have mentioned. HeUum 5876 
and 6678 are also predicted to be weakly in emission at very high 
temperatures. It would appear that if you are looking for evidence of a 
temperature rise at the surface of an O star, you should look at the 
strong lines in the infrared. 

Praderie — Would you produce emission in H alpha also and could you 
say how it would vary as you change the gravity? 

Auer — The calculations that we have indicate that at the very highest 
temperatures the cores are beginning to go into emission, just very 
slightly. If you had an ecUpsing binary and you observed it just at ecUpse 
then you should see it strongly in emission. Unfortunately such binaries 
are few and far between and ofteri have structures complicated with 
circumstellar gas. NormaDy H alpha remains in absorption over the entire 
range. But to make definitive statements about a strong line like H alpha 
one really should know more about motions in the upper layers of the 
stellar atmosphere. 

Skumanich — I want to raise a word of caution about the broadening 
velocities Avrett used. There is observational evidence that velocities are 



44 

larger in the giants than in the main sequence stars, in which case the use 
of the scale of the main sequence ampUtudes is incorrect. I'm wondering 
whether, in fact, using constant energy relations for this broadening, like 
pv* = const, to go from main sequence stars to the giant stars may not be a 
better approximation. Then you might indeed find that you're not on the 
damping portion of the absorption coefficient curve but still in the 
Doppler part and you're not getting this kind of variation then. So it's 
not the actual thickness of the chromosphere that's changing with g but 
perhaps the broadening that is still changing. 

Cayrel — That's a very fundamental point. Can Dr. Olin Wilson perhaps 
comment on that? 

Wilson — I have always liked the velocity broadening but there is nothing 
sacred about that assumption. Ill wait until all the returns are in. 

Peterson — Along that line there is observational evidence that exists for 
turbulence following the mv* relationship. 

Pasachoff — May I remind the assemblage that for the Sun we have 
another way we can look at the surface of a star besides the methods 
used to produce the very lovely results we heard discussed this morning. 
We can look at the chromosphere sideways at the limb. Many people 
here, particularly the HAO, Sac Peak and Hawaii groups, have eclipse 
results that show the intensities of many lines at the limb very accurately. 
There are lines of many elements besides calcium. Even outside ecUpse we 
can also study the oxygen infrared triplet, the D3 Une of helium, and 
with a Uttle more difficulty the 10830 line of heUum. There are 
thousands of rare earth Unes. I recently made observations at the 
Sacramento Peak Observatory of the ionized titanium Lines near 3760 A, 
and the resonance Une of ionized strontium at 4077 A. Jacques Beckers, 
also at Sacramento Peak, has observed a whole sequence of ultraviolet 
chromospheric lines at the limb, which I am now studying. One can study 
outside of ecUpse much more than the relative intensities of the various 
lines, which all appear in emission. However, there are calibration and 
scattered light difficulties, and one can't study the height structure as well 
as at an eclipse. We have spoken of models of turbulent velocities varying 
with height; we should study the velocity variation with height by 
actually following the spectral lines out from the edge of the sun. 

Thomas — Could I just make a point of basic principle here. Sometime 
during this meeting maybe one should have a popularity vote on whether 
you want the chromosphere to begin where the temperature rises, or 
where you put the mechanical heating in which guarantees the rise above 
what you would have from a purely photospheric radiative equilibrium 



45 

model. It's a point one must carefully distinguish, particularly in view of 
Auer's remarks on the basic characteristics of chromospheres in hot and 
B stars referring to his and Mihalas' calculations of models with no 
mechanical heating. I have my own position which is that the mechanical 
energy input fixes the chromosphere. But that's something everybody has 
to decide for himself. So maybe we should think about it. 

Cayrel - Yes. In fact I have noted that nobody has really cared very 
much about the definition of the chromosphere which was involved in the 
topic of this morning. 

Kandel — I don't want to define a chromosphere, but I think we ought to 
be more specific about the temperature. We all understand that when we 
talk about the temperature structure we are talking about the electron 
temperature, and in some way the energy content of the electron gas. 
This is not the temperature of the atmosphere as a whole. When we get 
the source function of H and K, we have a measure of the excitation 
temperature of the Call gas, and when we talk about energetics we also 
have in mind some sort of temperature, but of the gas as a whole. We're 
interested in energetics which perhaps depend on electron temperature 
which, in principle, we get from continuum measurements and hydrogen 
ionization and excitation but which, in practice, we seem to have a hard 
time getting. What we want to do is find out how to determine these 
things, namely, the specific energy content of the gas in terms of the 
observables, the calcium populations, and other things. So perhaps we 
should keep in mind what we mean by a temperature. 

Thomas — Electron temperature is always the thing which one has in 
mind in all these kinds of calculations. I couldn't agree more with your 
premise and I'd like to know what partition of energy one has over all 
the energy levels. But so far we have again taken the theological position 
that there is an electron temperature that defines the velocity distribution 
of electrons, and that defines all collisional parameters. That's the only 
reason for doing it. 

Kandel - I think when we talk about a given temperature structure we're 
talking about an electron temperature structure. If we talk about an 
isothermal atmosphere this doesn't mean that the specific energy content 
does not vary through the atmosphere, and there is really no reason to be 
surprised at finding absorption lines coming from such an atmosphere . 

Pecker: I want to make a simple reply to the question of what is a 
chromosphere. Jefferies spoke at the beginning and said that the symp- 
toms of a chromosphere are an increase of the electron temperature This 
is a much too closed definition. You might have heating without having 



46 

heating _by mechanical energy, or you might have heating without an 
increase in temperature outward. I do not think that an outward 
temperature increase alone determines whether or not there is a chromo- 
sphere. 

Cayrel — I am not sure I have understood your point. If one star with no 
dissipation of mechanical energy at all has an outward rise in temperature, 
and if a second star has some dissipation, but not large enough to cause a 
temperature reversal would you say that the second star has a chromo- 
sphere but the first one does not? 

Pedcer' — Yes. 

Underhill — I think that the definition of a chromosphere should not 
consider the question of temperature, however defined. The chromosphere 
is that outer part of a stellar atmosphere where you have to consider the 
physical processes in detail. 

Thomas — I would really like to comment on this point. Suppose we 
divide the star into two parts: interior and exterior. Then our aim is to 
try to make general structural models of stars from the standpoint that 
the atmosphere is the transition region between the stellar interior and 
the interstellar medium. As a whole, a star is a non-equilibriuin, non- 
steady-state object. Basically it is a storage pot of energy and mass. The 
interior is characterized by the fact that the primary focus is on 
population of energy levels and concentrations of mass particles and you 
can compute all of these without caring at all about what the fluxes are, 
using standard LTE distribution functions. You compute the distribution 
of those TE parameters specifying the distribution functions by always 
using a diffusion approximation. This is a linear non-equilibrium thermo- 
dynamic equilibrium situation. Then consider the other part of the star, 
the atmosphere. There we are mainly concerned with propagation phe- 
nomena. We want to characterize the whole sweep of the atmosphere as a 
gradual unfolding from a completely degenerate aspect in the interior, 
which is locally in thermodynamic equilibrium in the broadest sense, to 
the interstellar medium, an almost completely non-degenerate configura- 
tion, not in LTE in any sense. Then we divide the atmosphere into a 
number of subregions. We characterize each subregion by the unfolding of 
some aspect of this kind of degeneracy which represents the general 
thermodynamic equiUbrium state. The reason I introduce this now was in 
answer to Anne Underbill's comment. It is not just the chromosphere 
where we begin to worry about the detailed physical characteristics, it is 
already in the photosphere. What is the basic point? In the sub- 
atmospheric regions we have a storage of electromagnetic energy and a 
storage of mass because we have a kind of diffusion approximation 



47 

characterizing the transfer of process in either case. The photosphere is 
characterized by an increasing direct escape of photons from the star. So 
we have in this region the gradual beginning of all those aspects of 
non-LTE which affect populations of energy levels associated with the 
fact that the photons can escape directly from the boundary and there is 
no longer, to a first approximation, an isotropic radiation field. Thq 
chromosphere we characterize as that region where we begin to have a 
departure from the storage properties of the mass flux. Go back to 
Eddington's old approximation in his representation of a Cepheid. He had 
a standing wave as far as the mass transfer and the kinetic energy transfer 
in the stars were concerned. Where did the model begin to lose energy? 
Only in the non-adiabatic part where one has a radiation field. The 
evolution from this thinking applied to a Cepheid atmosphere came in 
Schwarzschild's work where running waves were introduced in the upper 
part of the atmosphere. This is analogous to that thing which produces 
the chromosphere now — forget the details about convection, turbulence, 
etc. — producing acoustic waves that run out. In the Cepheid we have a 
system of standing waves in the interior. Suppose, for example, we had a 
zero minimum temperature at the top of the photosphere (which is the 
easiest way to look at it), then we'd have all the energy in trapped waves 
which leak a bit of energy at their top. This leakage is provided by 
"diffusion" through the system of standing waves in the subatmosphere. 
It's exactly in analogy with the storage of all the electromagnetic energy 
in the sub-atmosphere, with leakage from the diffusion approximation, 
balancing the surface loss, due to direct escape of photons at the 
boundary in the photosphere. So the photosphere is that part of the 
atmosphere which represents for electromagnetic energy, a transition from 
sheer storage with a little bit of leak in the sub -atmosphere to direct 
escape from the photosphere. The chromosphere is that region where I 
have a macroscopic escape of energy in the mechanical degrees of 
freedom, that is, progressive waves going out, as contrasted to the storage 
properties which hold at the bottom of the chromosphere . So I have then 
two distinct atmospheric regions: the photosphere and the chromosphere. 
We think we can do the same kind of thing in the corona in terms of 
direct mass loss from the star. I would just like you to focus on the- 
physics here: in the photosphere it's the photons, in the chromosphere 
it's the mechanical energy, in the corona it's the mass. All this should 
come after what Francoise Praderie is talking about tomorrow; she 
demonstrates it much more clearly than this. That's why I would buy the 
chromosphere as the place where we have a mechanical dissipation of 
energy, because a photospheric temperature rise, as Cayrel and Helene 
Frisch have very carefully pointed out, has nothing to do with anything 
except photons and the way in which they are linked to the interaction 



48 



with matter; namely, inelastic collisions are neglible, and we simply have 
photoionization for the opacity processes considered. 

Underhill — I want to make sure that we understand your definition of 
the chromosphere as the place where mechanical energy is dissipated. 
Also, we have to consider the end of this conference at the same time as 
the beginning. You say you are going to talk about a star where we have 
mass loss. I would like to say that many early type stars are known to 
have mass loss from direct observations. I don't think we can have mass 
loss following your types of arguments, which are physically logical to 
me, without also saying you have a chromosphere. Therefore, I'm going 
to say qflite happily that I can talk about chromospheres for stars of type 
A, B and O. Is that logic irrefutable? 

Thomas — I'll buy chromospheres for all types of stars. 

Linsky — This morning the subject came up of the Ca II H and K lines as 
indicators of stellar chromospheres. I think that it is relevant, therefore, 
to present some observations that Richard Shine and I at JILA have 
obtained in the calcium lines for solar plages and a sunspot. This work 
will be the basis of his thesis. At present we have reduced the observa- 
tions and are now in the process of building model chromospheres to 
explain the data. The data are all photoelectric and were obtained in a 
double pass at Kitt Peak. 

In Figure 1-18 we caU your attention to what the calcium lines look Uke 
in the average quiet solar chromosphere. Incidently, if the Sun were 



100 




Figure 1-18 



49 



observed as a point source, the profiles would be essentially the same as 
are seen in the quiet chromosphere. In this and subsequent figures we 
show the H and K resonance lines as well as the infrared triplet lines 
(8498, 8542, and 8662 A). As you recall the ratio of gf values and thus 
of opacity are 1:5:9 for the 8498, 8662, and 8542 Alines respectively. 
It is important to remember that the 8498 A line, is by far the weakest in 
the triplet. In these figures we give residual intensities for the lines 
relative to the interpolated continua at Line center as a function of 
wavelength measured from line center. In the quiet chromosphere the 
infrared triplet lines show no emission and H and K exhibit weak 
emission. Also the residual intensities in the cores of H and K are about 
the same. 

Figure 1-19 shows the five calcium lines in the weakest plage we observed. 
As has been known for some time, the cores of H and K show emission 



100 




and also broaden appreciably. K shows more emission than H with the 
ratio of residual intensities about 1 .1 instead of 1 .0. This ratio persists for 
all plages we observed. Also the residual intensities in the cores of the 
infrared triplet lines have increased significantly relative to the quiet 
chromosphere. What was unexpected in a weak plage was that the 8498 A 
line, the least opaque of the infrared triplet Unes, shows a definite double 
reversal in its core. In a slightly stronger plage, seen in Figure 1-20, there 



50 



100 



80 



60 



40 



20 



: 


1 1 


1 1 

84 


1 




98^^^~-'' — 


^ 


^^ 




/ ^^52/ 




^\l _ 


- 






'8542 




— 


s / 


V\ ^ 




— 




?^W 


W^ 






1 


1 1 


1 1 


1 





+1 



+2 



+3 



+4 



Figure 1-20 



is also a definite double reversal in 8498 but not in the other infrared 
triplet lines. This phenomenon is thus real and may place an important 
constraint upon acceptable models for weak solar plages. It also says that 
the 8498 A line may be a very sensitive indicator of stellar chromospheres 
of stars similar to the Sun. 

In the strongest plage we have observed, all five calcium lines, as shown in 
Figure 1-21, show emission features and K2V is 42% of the continuum. 
The double reversal in the 8662 A line is exaggerated by an iron line just 
to the violet of line center. Note that the 8498 A line shows a narrower 
and stronger emission feature than the other two infrared triplet lines. 

In a sunspot, shown in Figure 1-22, an entirely different set of profiles 
appear. The infrared triplet lines show no emission whereas the resonance 
lines show narrow eniission features in their cores. The emission feature in 
K is much brighter than that in H with the ratio about 1.6. I suspect that 
an explanation for the calcium line profiles in a sunspot will require a 
much thinner chromosphere as measured in K line center optical depth 
units and a much steeper temperature gradient for the chromosphere of a 
spot relative to a plage. 

Finally I would like to show an unexpected phenomenon in the wings of 
the calcium lines. In Figure 1-23 we show the calcium lines for the 
strongest and weakest plages and for the quiet chromosphere. Note that 
the wings of the lines for the strong and weak plages are identical and 



51 



100 




Figure 1-21 



100 



80 



60 



40 



20 - 



^^/N^- 


1 


1 1 


1 1 1 1 


'"^./^ 


■->. 




^. 




-A^- 


- 




vA 


/ /^ /^^2 


~ 


- 




V\\ 


/C^ 


- 


- 




\^ 


\M 


- 


- 






W r 


- 


- 




""i^ 




- 


- 


1 


1 


1 1 II 


- 



-2 -1 



+ 1 



+2 +3 



+4 



Figure 1-22 



52 



100 




+ 1 +2 +3 +4 



Figure 1-23 



significantly brighter than for the quiet profiles. This indicates that the 
plage phenomenon has an aspect which is photospheric and that the 
perturbation of the photosphere beneath a plage is independent of the 
chromospheric aspect of the plage. The sun thus exhibits two photo- 
spheres in addition to many chromospheres. 

The main reason why I show these data before they are analyzed is to 
emphasize that the Sun has many chromospheres and that the calcium 
lines are sensitive indicators of these chromospheres. Clearly any accept- 
able theory for how stellar chromospheres vary with spectral type, 
luminosity, and age must explain the vastrange of chromospheres on the 
Sun. To my mind this is an important example of why the study of 
stellar chromospheres and the solar chromosphere must be pursued 
together. 

Cayrel — These observations are very challenging, as theoretical predic- 
tions are most often compared to average spectra. Yet, these data show 



53 

that we obviously have a wide range of chromospheric activity. Are there 
comments on this? 

Underbill — This observation that the wings of these Unes formed in plage 
regions have more flux in them than the same lines in the photosphere 
makes one wonder. I would ask Linsky, or any other theoretician, would 
this heightening of the flux from the deeper layers of the photosphere 
correspond to a back warming? One comes back to the problem that you 
cannot logically separate a photosphere and a chromosphere. They 
overlap. They react back on one another. If you have dense material 
overlying a radiating region, its going to produce back warming. We've 
seen a difference of about 2 percent in the energy coming out, and that's 
a back warming to me. It has more implications that just being one of 
those oddities you observe on the Sun. You would expect to find this on 
any star where there is an overlay of dense material. The result might be 
a totally different combined atmosphere. We may not think of line 
blocking and back warming in interpreting many ground-based spectra 
from A stars, B stars, even early F, but when you go to shorter wave 
lengths, there are a lot more lines, so you are going to get lots of back 
warming. These are strong resonance Unes which are going to produce 
strong absorption in the outer fringes and which you might not even 
guess about by observing at 4000 A. Are any theoreticians able to make 
these ideas more precise? 

Pedcer — I would like to comment in a slightly different way. Linsky has 
given us some beautiful examples of what Jefferies told us this morning, 
that the source function and the flux in the line are extremely sensitive 
to such things as density effects. His results illustrate that the effect of 
very small terms, as shown by Thomas and Jefferies years ago, is 
sufficient to produce large emission differences in the cores of these lines. 
From the shape of the source function, you can infer the shape of the 
line. What is important in the source function, then, are the source terms, 
even when they are small. For example, consider the difference between 
the polarization in the case of isotropic scattering and of a small 
perturbation on the isotropy. The results are significantly different. This 
is an analogous situation. I'm not sure that I'm re^plying directly to Anne 
Underbill's point, but I feel that the source term in the source function 
equation is the essential one in interpreting the observations Linsky has 
shown us. 

Bomiet — I don't understand if you really assume that the differences in 
observations between the plages and the quiet regions are mainly due to a 
density effect? Is that correct? 

Pecker — More or less. Yes. 



54 

Bonnet — How then do you explain a similar difference in the continuum 
at 2000 A, where the difference is a temperature effect and not a density 
effect? 

Pecker — I don't want to say it's a temperature effect or a density effect. 
1 just want to point out that the effect of the smaller term on the source 
function is great, even though it's a small fraction of the source function. 
It's still sufficient to produce a tremendous difference in the flux in the 
central part of the line. In the photosphere we might have a different 
situation, wherein the temperature effect dominates. The density effect 
there inay be absolutely negUgible. What counts is source term. That's my 
main point. 

Skumanich — 1 don't agree that the density effect is great. The source 
function is*A(B) at the surface. Now X is proportional to the density N, 
and B a T^ or s (for Cak),'sfX ocA^while B a T'* °' ^ xhus small 
changes in T are more important than small changes in N in influencing 
the central intensities. 

Peytremann — Let me go back to backwarming effects from the 
chromosphere down to the photosphere. The backwarming effect cannot 
be very important because it should be considered as integrated over the 
entire spectrum, and the chromosphere flux is very small compared to the 
total photospheric flux. 

Underbill — Are your remarks based solely on considering the backwarm- 
ing from the H and K lines'? You must consider all the other lines. 

Peytremann — The lines formed in the chromosphere consist of the cores 
of strong Unes, so they don't cover a wide spectral range. What is 
important to backwarming is the total energy integrated over frequency. 

Linsky — I would like to comment on the question of whether the source 
function increases with density or temperature. One should consider the 
ratio of the residual intensities of K to H which increases with K emission 
in the Sun and, as Olin Wilson's work has shown, in other stars as well. In 
the absence of collisions K would be brighter than H where the 
temperature gradient is positive since the thermaUzation length for K is 
one -half that for H on a common optical depth scale. Fine structure 
collisions tend to establish equilibrium in the population ratio of the 
upper states of H and K. Thus the line ratio data on plages could be 
accounted for by either (1) lower densities or, (2) steeper temperature 
gradients, or both, in plages relative to quiet regions*. The same argument 
applies to stars with active chromospheres relative to those with quiet 
chromospheres. 



55 

Cayrel ^ T do not understand how one can exchange density against 
temperature. How can you change the density without changing the scale 
hei^t? ■ • ' - 

Skumanich — I would like to call attention to Dpmenico's work in which 
he asks what kind of parameter changes you must have in scale height 
and in temperature gradient. He found , that the major effect which 
constrains the data (the observed K to H ratio, the observed amplitudes, 
and the. observed half widths of the stellar Ca emission core) is the 
temperature gradient rather, than the scale height. For example, a 33% 
increase in the temperature excess in the chromosphere of solar type stars 
will cover the whole range of Olin Wilson's observation?, 

Thomas — The parameters you have for the Call H and K lines are the 
absolute intensity of the peaks, the ratio of K2 te K3, the half -width and 
the position of the peak. If you give the t§n»perature distribution as a 
function of depth, as we have, shown a long tUno ago, the ratio Kj/Ka.is 
extremely sensitive to the place \yheTe the temperature rises in the 
chromosphere. The absolute intensity is extremely sensitive to the temper- 
ature, in various regions. Elske Smitih showed long ago that over sunspots, 
over plages, and over faculae tiie eniission intensity rises up to various 
fractions of the continuun\. What; Qounts is. the distribution of tempera- 
ture as a function of Qptieal depth, tQ which these things are extremely 
sensitive functions.. And. fof that very probably the density comes in in a 
much different way than we are talking about here. Again in the same 
way, the rtiagnetic field comes in, not because the magnetic field enters 
directly, but because the magnetic field changes in one way or the other 
the rate of deposition of mechanical energy that must be balanced against 
all the rest of things in the energy equation. So, is it sufficient to assume 
a distribution of temperature and density and ask what will come out of 
it? Do we not have to ask how the distributions of temperature and 
density are obtained? If the assumption of a frequency independent 
source function is wrong, the behavior ef the K2 emitting region relative 
to the low photosphere could be in serious, error. And the introduction of 
the microturbulance parameter to match the width of K2 may be 
suspicious. 

Beckers — I would like to make a comment 011 the data presented by 
Linsky on the infrared plage profile. In linsky's plage profiles the 8498 
lines show self -reversal in the center, while the 8542 lines show a shoulder 
but no self -reversal in the center except where the plages are very strong: 
Those two lines have an absorption coefficient, ratio of 1 to 9. This is a 
very large difference compared to the H and K lines. I assume here that 
the source functioris are eqwal and that the levels are strongly coupled. 
The source functions for the three infrared lines are therefore equal. 



56 

I claim that the 8498 profile, because of its ^ape, must be formed near 
to the peak of the source function. The 8542 line has a much higher 
absorption coefficient and the line center therefore originates much higher 
in the atmosphere. The reversal therefore occurs in the wing of the line. 
If the source functions are equal and the absorption coefficients occur in 
the 1 to 9 ratio, then the intensities at the wavelengths where the lines 
have equal absorption coefficient should exactly correspond; the X8498 
profile should be completely reflected in the X8542 profile so that the 
central reversal in 8498 should occur in the wings of the 8542 Une. Why 
don't we always see that? Perhaps the spectral resolution does hot allow 
one to see such a sharp peak in the steep line wing. Or perhaps, since one 
is working in the wing of the line, variations in microturbulence with 
height smooth the contribution function more than in the line center. 

Athay - I have two comments. First, all of those questions are very 
easily answered on a computer in a few minutes. Secondly, I don't 
understand all of the concern about ten percent differences between H 
and K. We've been talking as though there were infinite coupling between 
the source functions. You don't get complete source function equality 
imless the coupling is very strong. It is probably very easy to get, ten 
percent differences in source functions. 

Underhjll — I wonder if it would be helpful to broaden the discussion to 
another spectrum with a similar energy level distribution as Call, namely 
that of Ball. Call has an ionization potential of 11.87 volts and the 
lowest levels are 4^S, 3^D, 4^P, etc. Ball has an ionization potential of 
10.01 volts and there are equivalent 6*S, 5^D (metastable) and 6*P 
levels. Have the solar people looked at the Ball lines? They are much 
weaker because Ba is much less abundant than Ca. 

Aller — The abundance of Ba is about four powers of ten down from that 
ofCa. 

UnderhiU — That would certainly make the two cases.different. 

Jefferies — Has anyone observed the Call infrared triplet lines in stars 
other than the Sun? 

Wilson — Paul Merrill and I did a little of that many years ago but I have 
no good data on it. I don't remember seeing any reversals in these lines i 

Jefferies — Weyman and I made a very few observations of the infrared 
triplet but we certainly didn't see any reversals. 

Cayrel — Of course, the stellar observations would not have sufficient 
spectral resolution to allow one to see such reversals even if they are 
there. 



57 

UnderhJll — Why not observe late type giants with a Fabry-Perot 
interferometer? That would work nicely at 8500 A. 

Lin^ — 1 have some profiles of Procyon and Aldebaran which I will 
show tomorrow in the session on observations. 

Steinitz — I would like to make another comment about the infrared 
triplet. I don't want to suggest an explanation for the differences between 
the behavior of 8498 A on the one hand and 8542 and 8662 on the 
other hand. But just to compUcate matters I would Uke to introduce the 
problem of the effect of Zeeman spUtting on the source function. The 
8498 connecting the 3/2 to 3/2 levels has a different Zeeman pattern 
than the other -two lines. 8542 and 8662 have essentially the same 
Zeeman pattern with only a slight difference in the amount of splitting. 
The patterns are shown as follows: 

J J 

13 11 (1)11 13 X8662 

2"2 II II 15 



3 5 (1)(3)15 171921 X8542 
2 "2 MM MM —5 



3 3 I I I I (4)8(12)16 24 X8498 

2'2 II ''II 15 

Diagram showing approximate Zeeman patterns for Ca II IR lines. 

Now we know that plages have a connection with magnetic fields, 
although I'm not suggesting that this is the ultimate explanation. But it 
may be necessary in transfer problems of this type to take into account 
these magnetic effects, especially since we see the nice differences. There 
is a ratio of about 1:5:9 in the intensities of the lines and these 
observations may be related to a difference in the slope of the source 
function as a function of optical depth. Another complication is that it 
has been generally assumed that the source function over the Une is 
independent of frequency, the frequency dependence coming through the 
optical depth effect. That has been assumed because in the core of the 
Une it is only fair to assume that there is equality of the emission and 
absorption profile, but when you take induced emission into account that 
may not necessarily be true. 

Thomas - Steinitz is much too modest. His thinking is what has made me 
worry about the frequency independence of the source functions. I think 
he is giving us only a suggestion of the mechanism he is thinking about. 



58 

Peytremann — How strong must your magnetic field be so that the width 
of the Zeeman pattern competes with the. velocity broadening? 

Steinitz - I would guess about 1000 - 2000 gauss. 

Sheeley — Assume the Zeeman splitting is 3 x KT^ A/gauss, then 1000 
gauss yields 0.03 A. I suspect that those peaks are located well beyond 
that. 

Steinitz — But that is not the relevant point. It is not a question "of 
whether the Zeeman broadening is larger than the velocity broadening. 
The question is what happens to the source function and how does the 
line core build up. 

Thomas — The point Steinitz is trying to , make is the following. 
Remember, in the source function I have a big radiative term plus a much 
smaller source term, the eB or the t/B*, and in the denominator, unity 
plus again a sink term. A complete theory gives still another term in the 
denominator which results from a difference between the emission profile 
and an absorption profile. How big does the profile term have to be 
before it becomes important? It doesn't have to be big at all, because for 
Call the largest comparable term is e, the collision ratio, which is about 
10''' or lO"*. So the disparity in the profile term must only be bigger 
than 10"* or 10"^ to have an integrated effect big enough to affect the 
profile of the Call line. If the emission profile and the absorption profile 
differ by one part in lO** or 10^ the difference will be important. 

Jefferies — I'd like to translate this discussion in case some are getting a 
bit lost. The problem concerns the preservation of' frequency in the 
scattering process. Consider the absorption of a photon at a certain 
frequency and its subsequent re-emission. Is there any correlation between 
the frequency of absorption and the frequency of re -emission? The 
computed line profile depends very much on this question. The assump- 
tion generally made is that the frequencies of these two photons are 
entirely uncorrected. Under those circumstances the line source function 
is not a function of frequency within the line. What concerns me about 
the arguments given here is the following. One of the infrared triplet lines 
(8498) is observed to have peculiar properties. When a photon in that line 
is observed the atom is raised to the ^^,2 level. What choices are then 
open to the atom? It can come down in the same transition, in another 
infrared line (8542), or in the K line. If it re-emits the same 8498 line 
photon there may possibly be some coherence in frequency between the 
absorbed and emitted photons. If the atom emits a photon in another line 
transition, then knowledge of the frequency of the absorbed photon will 
be lost even if radiative interlocking processes lead to a subsequent 



59 

re-emission of an 8498 photon (a process which could legitimately be 
called scattering). I agree that the profile of the 8498 Une is pecuUar and 
demands some sort of an explanation. I think that this is perhaps the 
most significant thing that came out of Linsky's observations. But I don't 
think we can explain this in terms of a partial coherence in frequency 
because the 8498 line couples so strongly with the other infrared lines 
and with the H and K lines. 

There is one line I know of which may be an important candidate for a 
departure from the assumption of complete redistribution in scattering: 
namely, Lyman alpha. In this line most of the scatterings that take place 
are just direct absorptions and subsequent re-emissions going back and 
forth between the upper and lower states. It is, thus, not at all like 8498 
where you get many sets of possible re-emission paths for an absorbed 
photon. It is interesting that Lyman alpha is characterized in the solar 
spectrum as having extremely extended wings which are in fact character- 
istic of a departure from complete redistribution. 

Thomas — You're talking about the J scattering term. What I'm talking 
about is not the large number of scatterings but the differential effect 
which comes from a source-sink term. That's very small. 

Jefferies - Yes. But you've got the intensities of a lot of different lines 
mixed in together in the source-sink terms. I don't think you can really 
argue on the basis of a two level source function for effects that are as 
sophisticated as this, or even an equivalent two level atom. 

Skumanich - I want to make a plea. We have been talking about 
temperature and inferring from the temperature and the temperature , 
gradient what the mechanical heating requirements are. I think one of the 
very important elements in this whole thing is caUbration. As an example, 
Lemaire and I have compared the magnesium doublet emission with the O 
I lines at 1300 and we find that they don't compare well at all. (I mean 
compare by relating the data to some comparable quantity like the 
temperature distribution which gives you the observed shape as well as 
the ampUtude.) They don't agree to such an extent that the calibration 
can be different between the two lines by as much as a factor of two, 
which I think is terrible. If we are after mechanical energy heating, one of 
the underlying questions we must all have in mind is that we need not 
only shape information on lines and continua, which is the classical thing 
astronomers have been doing, but in the new spectroscopy (to quote a 
colleague of mine) we also need absolute magnitudes, i.e., the absolute 
flux. So, I want to make a plea for not only careful and sophisticated 
theory but careful and sophisticated calibrations. 



60 

Ulrich — I'd like to ask Jeff Linsky just how firmly he beUeves in the 
wing difference of a few percent. I have to agree with Anne Underhill on 
this. I think that's one of the most significant things in these observations 
because that indicates a basic change in the thermal equilibrium of the 
photospheric layers. I feel this is of vital importance. Related to this I 
wonder if there isn't a similar enhancement of the continuum. If the 
continuum far from the core of the lines is also affected under a plage I 
think this would be extremely interesting. As Skumanich has emphasized , 
the results depend critically on the accuracy of the calibration. 

Linsky — I trust ~the data on the enhancement of the calcium line wings 
in plages because spectrohehograms taken in the wings of these lines show 
bright plages and network out to about 10 A from, line center. Whether 
the continuum is enhanced or not in plages is a more difficult question 
that Neil Sheeley could better answer. I would not be surprised if there 
were a 1% enhancement at 4000 A. 

Athay — Isn't it true and well known that the continuum is brighter in a 
plage at least in faculae, that the faculae occur high in the photosphere 
and that they're more prominent in the active regions than they are 
elsewhere? 

Bonnet — This is obvious in the UV spectrum. When you look at the Mg 
II lines you have the same mechanism and if you observe the continuum 
in wavelengths ranging from 2800 angstroms to 2000 angstroms you 
observe a strong enhancement of the continuum emission. 

Sheeley — I'd like to make some comments about plages and continuum 
at the center of the disc at various wavelengths. We've made simultaneous 
spectroheliograms in the 3884 Angstrom continuum, which is the only 
continuum I can find in that range, and the nearby CN bandhead which 
shows faculae very pronounced. In the 3884 continuum a static photo- 
graph does not show brightenings in the continuum. But a time average or 
a movie of this does. It must be therefore a small effect but it's present. 
Ed Frazier has made some observations at Kitt Peak using a photoelectric 
magnetograph looking at the green continuum and finds an effect of about 
one half of one percent with the plages in the continuum being slightly 
brighter than average. Then there are some other confusing details such as 
if you take a spectrogram and look at magnetic field regions sometimes 
the continuum is brighter than average, but then sometimes the con- 
tinuimi is darker than average in the green. So while there are some 
details to be ironed out, time averages and high sensitivities do show a 
small possible effect. 



61 

Cayrel — We should now conclude this part of our discussion on line 
formation. We had a specific question in the program, namely, what lines 
depend on the local physical parameters in a highly sensitive way. We 
should try to Ust those lines that fit the criterion, and then identify those 
Unes that are not too difficult to compute. It seems obvious that the list 
includes the calcium H and K lines, at least for stars later than GO. 

Thomas — The answer, categorically, is collision dominated lines. Which 
lines are collision dominated depends on the star. You can't give specific 
lines for all stars. 

Pecker — This morning John Jefferies started to make a list of lines that 
are coUisionally dominated and those that are photoelectrically dominated 
but which are classified in this way only for solar type stars. Are we able 
to make the same list for other stars at the present time? 

Athay — I want to raise an objection at this point. As far as I know no 
one has ever found a solar line that is really photoelectrically dominated. 
The sodium D lines are collision dominated. Even H alpha shows a strong 
measure of colUsional effects. If you compute Une profiles it's very easy 
to get emission cores in H alpha. In the case of every line we've ever 
computed it's easy to get an emission core' if you simply increase the 
opacity of the chromosphere a bit or raise the temperature a bit. I just 
don't know of any line that is really photoelectrically dominated in the 
case of Sun. H alpha is supposed to be the prime example and is found to 
be a marginal case at best. 

Thomas - I can't say anything except that I completely disagree. 

Athay — A half a dozen people have published results that support the 
contrary opinion. If you disagree, please publish it. 

Thomas — It was published, as you well know, a long time ago. 

Athay - And it's been shot down and you haven't repUed. 

Thomas — No. There isn't a single case of an H alpha profile except in a 
place like a flare which shows some indication of a temperature gradient. 

Athay - The central intensity itself shows it. The only reason that the 
temperature gradient shows up in the H and K lines is that they are the 
only lines that have enough opacity to show it. 

Cayrel - Yes. That was the second point I was going to raise. It's not 
enough of course to have a line with a sufficiently large collision rate but 
you must also have a thermalization length as large as the region where 
the temperature increases. This double restriction is perhaps why we have 
so few lines to work with. It is regrettable that we cannot discuss at the 
same time hot stars and G stars because the conditions are so different. 



62 



Thomas — It seems to me this is the big point. This is a symposium on 
stellar chromospheres. What we are trying to do is to see physical 
principles on the basis of which we can proceed. 

Cayrel — Yes. Now we should select particular lines for different classes 
of stars. The Call infrared triplet is somewhat sensitive to a chromosphere 
but to a lesser extent than the H and K lines. On the contrary the 
resonance Unes of Mg II at 2800 Angstroms are on the whole much more 
sensitive to a chromosphere. I don't know the order, of magnitude but 
Boimet can certainly comment on the comparison between Ca and Mg H 
and K emission. 

Bonnet — The measurements made by Lemaire of the Mg II doublet 
emission show that the contrast between the maximum emission in the 
lines and the adjacent continuum varies from 25% td 40% at the center of 
the solar disk. 

Cayrel — We must also be very careful to indicate what spectral resolution 
is needed in order to see the central emission in sufficient detail. Could I 
ask first, what resolution is necessary to distinguish the separate emission 
peaks with acceptable accuracy and second, what resolution is necessary 
just to show that there is some central emission — both for Ca and Mg H 
and K? 

Bonnet — For the sun this resolution can be estimated to range between 
0.1 A and 0.2 A. 

Athay — I would like to make a suggestion that we ought to look at the 
Fe II resonance lines. We're now talking about an iron abundance that is 
just as high as that of Mg and just as high as Si. The published f values 
for the lines are also just as high as for Mg and so, just on that basis, you 
would predict that the Fe II resonance lines ought to be just as strong as 
the resonance lines of Mg II. However, it is clear from looking at the 
rough spectra we have that this is not true at all. The Fe II are very much 
weaker than the H and K lines of Ca, but if there is as much Fe II as 
some people say, (and as I believe there is) then there's just no reason 
why these lines should not also show self -reversals. 

Thomas — What about the Boltzman factors for these ionized lines? 

Cayrel — And is not the partition function of ionized iron rather large? 

Athay — You put all the Boltzman factors in and you still predict lines as 
strong as those of Mg, even with only a fourth of the ionized atoms in 
the ground state? 



63 

Thomas — I would like to comment on a related matter. Noyes and 
Kalkofen have produced a model atmosphere of the sun coming from the 
Lyman continuum analysis. If you remember, this model is strikingly 
similar to the one we had in that book of ours a long time ago. There we 
made the same kind of a model on the basis of an analysis of the 
free-bound and the H-emission in the solar atmosphere. All that depended 
very carefully on being able to determine b, and b2 of hydrogen. The 
basis of that determination was that the nj and the n^ levels were fully 
ionization controlled; so that there is a large population of the n2 state 
throughout the atmosphere, and also that H alpha was photoionization 
controlled, so that one could make a correction to the ionization 
equilibrium coming through the presence of H alpha. The Noyes and 
Kalkofen model essentially agrees with ours. So now if you beheve this 
current model of the solar atmosphere you have to beheve that H alpha is 
photoelectrically dominated. 

Athay — All that says is that we were approximately right. 

Thomas — Kalkofen, in your ionization equilibrium calculations, don't 
you find that the ionization terms are the dominant ones? 

Kalkofen — It is true that the most important transition upwards from 
the second level is by photoionization. 

Thomas — OK. That's the thing that controls the population. 

Cayrel — I presume that this discussion is still related to iron, in which 
the interlocking terms may be more important than in hydrogen or 
calcium because of the greater complexity of the atom, hence, many 
more possibilities beyond the l-*2-*l process. 

Underhill — There are some interesting peculiarities because some of the 
Fe II lines go into emission before you cross the Umb. Somebody 
mentioned these lines earlier in the day. There are quite a few such Unes 
in the solar spectrum, for example, Ce II and other rare earths. However, 
the Fe I lines apparently do not have this behavior. 

Cayrel — I would add to this list the lines of the type suggested by 
George WaUerstein, forbidden lines in which C21 is much larger than A21 . 
The point was raised that the .C2 1 should then be also larger than other 
competitive transition probabilities, so that we are sure that the source 
function is really the Planck function. One point is that these lines are 
never as strong as the permitted lines, and that they do not allow you to 
reach very high in the chromosphere. 

Pasachoff — I have some Sacramento Peak spectra that show the 
resonance line of Sr II going into emission slightly inside the limb. Nearby 



64 

aie various rare earth lines including mostly Ce II. They are also in 
emission inside the limb, which is well known since Menzel's work and 
they are in emission further inside the limb than the Sr II seems to be. 

Cayrel — The problem of Zeeman splitting has been raised which may 
make the whole theory described this morning by Jefferies more compli- 
cated, if one wants to take into account redistribution due to changes 
between Zeeman components. It should be pointed out that the Zeeman 
spUtting is much less of a problem for H and K than for the infrared 
triplet lines; This should be true for Mg as well as Ca. 

Johnson — May I add Na D to this Ust? Since its source function is 
coUisJonally dominated (an exception to the rule mentioned), it may be 
sensitive to a temperature reversal. Also, whereas these other lines may be 
weak in cooler stars, Na lines are extremely strong, and are sometimes 
used as luminosity indicators. Does anyone know of observations showing 
emission reversals in the cores of these lines in cool stars or the Sun? 

Underhill — They appear in emission in a few pecuUar hot stars. 

Sheeley — I think that this may be a matter of height of formation more 
than what the particular energy level scheme is. SpectroheUograms in 
many lines such as the core of the Na D lines, Sr II, Ba II, Sc II, Fe 
II . . . (all strong lies) the core of Mg I b lines, the Ti II resonance lines at 
3349 and so forth all look similar. They fall into a special class of their 
own. This business of classifying isn't too umeasonable since you can get 
the same sort of classes that Jefferies got this morning ... for example, 
from the same approach. So, I think it's a matter of where the Unes are 
formed. The classes that Jefferies indicated are formed high in the 
atmosphere. All these other lines (Fe II, Sc II, Ti II, etc.) are formed in 
the intermediate chromosphere. And in the lower chroniosphere or the 
upper photosphere, whatever you want to call it, there is another class of 
lines and itiolecules — neutral iron lines, neutral metals in general, and so 
forth — which also show very bright plages as for example CN shows. The 
CN bandhead at 3883A shows faculae that are brighter at that height in 
the atmosphere than even the K line. The K line has a contrast of say 
50% in the lower chromospheric faculae (AX««3A) whereas the CN 
bandhead has a contrast of 100%. So perhaps CN is worth looking at in 
stars. 

Pecker — By all means we should look very carefully at molecular lines, 
but primarily for very cold stars. 

Underhill — No, the molecular lines, in particular CN, are very important 
in moderately hot atmospheres. Consider the flash spectrum of the Sun. 
You can look back to the 1930 list of lines in the flash spectrum by 



65 

Menzel and some of the most prominent are due to CN. They're low 
chromosphere lines even thou^ they are molecules and they are formed 
where the temperature may be 8000 degrees. When you say cool stars and 
molecules, you may be thinking 3000 degrees or less. CN arises at twice 
such a temperature and I think CN is a very important intermediate 
temperature indicator. The reason I say that is because of the well- 
documented presence of CN in the flash spectrum, which is defmitely 
chromospheric. 

Pecker — I completely agree with you. I just wanted to stress the fact 
that so far this is the first time a molecular line has been mentioned 
today. And that we shouldn't forbid the molecular lines to enter into our 
analysis. 

Boesgaard — I want to add to the list of lines the Fe II lines discovered 
by Herzberg in M stars and found in an MS star and in Carbon stars. 
There are 17 lines in the region 3150-3300 A from multiplets 1,6, and 7. 

Cayrel — Can you observe these from Mauna Kea? 

Boesgaard — Mauna Kea is one of the best observing sites because of the 
high UV transparency at 14,000 feet. However, these cool stars are not 
emitting very much in the continuous background in that wavelength 
range so the exposure times are long. 

Cayrel — I am surprised that nobody has mentioned the He 10830 line. 

Beckers — The helium lines are very strongly radiation dominated. If 
there is any line that is not collisionally dominated, it is this line. 

Sheeley — At Kitt Peak, Giovanelli, Harvey and Hall have taken some 
very nice spectroheliograms in 10830 with high spatial resolution. They 
look very similar to, although not exactly the same as, H alpha. 10830 
would fall in the same category as H alpha, H beta, gamma and so forth. 

Cayrel — But it is an absorption: 

Sheeley - Yes. 

Cayrel — We don't worry too much about what kind of source function 
we get in this line as long as we detect it is absorption. The attractive 
thing is that you can observe it in hotter stars if it exists, without having 
a bright continuum masking a weak emission line. 

Linsky — Another helium line that appears prominently in absorption in 
strong plages is the D3 Une at 5876 A. This line certainly indicates a 
chromosphere and should be looked for in solar-and later-type stars. I 
would like to point out that the CN bandhead at 3883 A is a very 
interesting spectral feature to study. A detailed non-LTE analysis of the 



66 

violet system of CN will not be easy, but the bandhead should be 
sensitive to temperature at the temperature minimum and above for stars 
hke the sun and somewhat later. Since the CN bandhead consists of about 
five overlapping lines, it is essentially a piece of continuum and thus 
insensitive to broadening, velocity fields, and magnetic fields. Spectro- 
heliograms taken by Neil Sheeley in the CN bandhead show great contrast 
between bright and dark regions and appear to show fine structure in the 
chromospheric network quite well. George Mount, a graduate student, and 
I are presently studying CN spectroheliograms and center-to-Umb photo- 
electric data in an effort to understand what the spectroheliograms are 
telling us." 

Pasachoff — I should say that I am now working on a continuing program 
of- observing D3 lines in late type stars to look for stellar chromospheres. 
I think that a report is better fitted for the discussion tomorrow morning. 
It is a tricky line to detect and there are some atmospheric Unes in the 
region so it is not just a matter of looking for it and finding it. The 
original work done on the D3 line was by Wilson and Aly, published in 
the PASP in 1956 (68, 149) in which they reported finding a line near 
the D3 wavelength in several stars. The M star spectra are too complicated 
to tell whether a line that falls at that wavelength is the D3 line or not. 
Since that time Vaughan and Zirin (Ap. J., 152, 123, 1968) have 
published results of their extensive observing program and Zirin is 
continuing a program on 10830 with the 200-inch telescope. They 
published many equivalent widths of 10830 lines both in emission and in 
absorption in late type stars, finding some that even seem to vary in 
intensity. In my search I had the benefit of knowing which stars, such as 
X Andromeda, have a lot of 10830 in them. One way we can tell the 
origin of lines that we see at the D3 wavelength is whether the intensities 
correlate with 10830. I should point out to people here who are 
calculating models that it would be of great interest to have more detailed 
models for the He lines, in particular the expected intensities and ratios 
of equivalent widths of 10830 and D3 for various' kinds of stars of type 
F, G, and K. 

Fosbury- M.W. Feast (M.N.R.A.S. 1970, 148, No. 4, 489) reported, in a 
paper on Lithium Isotope Abundances in F and G dwarfs, seeing X5876 
in absorption in an F8 dwarf. The star is Zeta Doradus and is slightly 
pecular in several respects. It lies slightly above the main sequence 
(AM=0.6) and Feast measured a higher Li* /Li' ratio than in any of the 
other stars in his program. It also shows unusually strong H and K 
emission for its spectral type. Wesson and I have looked for the X5876 
line in some later type giants; we have also had^ discussions with Griffin 
and looked at some of his very fine high dispersion tracings. We could not 



67 



be certain of an identification in any of our samples. Figure 1-24 shows 
the Hel X5876 line in three spectra of Zeta Doradus. (Original inverse 
dispersion 13.7 A/inin. M.W. Feast) 




Cayrel — Can we now give the narhe of a line in a hot star (a B star) 
which is the best case for detecting a chromosphere if B stars have 
chromospheres. Is anyone ready to answer this question? 

Pecker — I'm not ready to answer this question, but this goes back to the 
discussion that Jefferies made about the geometrical eiriission properties 
and the real, true emission properties of a line. 

Cayrel — If you are in a geometrically thin layer in which you have a 
temperature that is significantly higher than the boundary temperature 
that you predicted from a rnodel in LTE, how will you detect that? I 
think that the distinction into two classes by Thomas is not the real 
point, because the coUisional rate is certainly large for most Unes, because 
the electron density is high when hydrogen is ioriized. I refer here to hot 
stars. 

Thomas — I disagree. I really think what you want to do is look at the 
very recent calculations Mihalas has been doing on this distinction 
between the photoioriizatioii doniinated lines andcoUision dominated 
lines. He's imposed the conditions oif radiative equilibrium but it's easily 



68 

generalized to the case where you have a chromosphere and lots of Mg 
lines, lots of Ca lines, although not Paschen alpha. He has very specific 
results on this. 

Cayrel — I don't doubt that you can find lines that are collisionally 
dominated in hot stars, but I doubt whether there are lines strong enough 
in the visible spectrum, so that you could detect a chromosphere if it is iiot 
geometrically thicker than in the Sun. That's the problem. 

Jennings — I would like to comment on the shell properties. I think if 
you make a distinction between stars with shells and stars with chromo- 
spheres, you're going to run into trouble among the late type stars. I 
would cite as an example alpha Orionis, which is certainly a late-type star 
with a chromosphere, since it has Call H and K, as well as Fe II, in emission. 
On the other hand, from the work of Deutsch and Weymann, there is 
certainly evidence for a very extended atmosphere involving mass loss. So 
here we obviously have a chromosphere co-existing with a very massive 
shell; and so I would argue that one would have to be careful in dividing 
stars into those having only a shell or only a chromosphere. 

Underhfl] — They're not mutually exclusive; the shell is never accurately 
defined for B stars. To add to the list of lines, I would guess that for the 
middle B stars the Si II lines are important. It is well known observa- 
tionally that 4128, 4130 change their intensity relative to the red Si II 
lines 6347, 6371 which are from simple levels, are well behaved and are 
associated with the other multiplet at 3856A. Now this has never been 
explained, though it has been observed. You never know whether the 
4128 and 4130 lines are going to be strong or weak. The f values have 
been calculated by detailed configuration-interaction calculations. They've 
been observed and we know pretty well what they are with respect to 
other Unes. Anyway you can't count changing one multiplet very much in 
one star and blaming it on f values. So the only thing that is left is the 
effect of chromospheric conditions. You have to compare the 4128 and 
4130 lines with the red multiplet and the violet one. 

Cayrel — But they are very weak. 

Underbill — No. They're quite strong. The other lines will vary in 
intensity as 4138 and 4130 vary. They come from a 3^D level and 3^D 
levels always cause you trouble. 

Thomas — There's one more thing. We've been concentrating here as 
though what you need to do is take a line such as H or K whose profile 
somehow tells you the existence of a chromosphere. But just as the 
10830 line in the Sun indicates for you that there's a chromosphere 
simply because you see it, so does any line in a hot star which should not 



69 

be produced tinder conditions of radiative equilibnum; for example, lines 
of VI in the Wolf Rayet stars, tell you that there is either a 
chromosphere or a corona. Since listening to Kuhi this summer I am 
convinced that Wolf Rayet stars have coronas rather than chromospheres, 
but I think the thing one should put here as an indicator of the presence 
of chromospheres and coronas are ionization levels. Simply the presence 
of any lines, no matter how they are formed, which you would not 
observe under radiative equilibrium in that star indicates a chromosphere . 
For that reason it is absolutely essential that we have good ideas of upper 
level limits of temperature such as Auer and Mihalas have been calcu- 
lating. We need to know the highest temperature levels you would have 
under radiative equilibrium. 

Cayrel - I think it is time to end the discussion on lines. At least we 
know how to raise interesting problems for theoreticians. For example. 
Someone should determine what happens with Si II in hot stars and see if 
these lines are really collisionally dominated and if the optical thickness is 
large enough to indicate a chromospheric temperature rise! I would now 
like to turn the discussion to continua and ask what are the good 
continua that indicate a temperature rise in the surface layers of stars. 

UnderhiU — I would like to stress the importance of continua as 
chromospheric indicators. If you think about the long wavelength region 
around 8000 A where H" comes to a maximum you have one sort of 
opacity pattern. If you heat the atmosphere up to a temperature of 
12000° or so instead of 7000° the opacity pattern in this spectral range 
changes its shape considerably, and free-free becomes one of the more 
important sources of opacity. 

It has a different shape than H". That means your lines are going to fight 
against a different opacity, and it will change your relative intensities in 
that region. Therefore, there is the possibility of the continuous source 
changing, whether the star has an extended atmosphere with a tempera- 
ture that goes down or goes up. Continuous opacity is an important 
indicator in regions where there can be differently shaped continua 
corresponding to a change in temperature. 

Pecker — I agree with Anne Underbill; the Paschen discontinuity is 
important in hot stars, and there is a strong relation between it and the 
H~ opacity. 

Jefferies — Perhaps the source function is not always the Planck function. 
If the absorption coefficient is decreasing toward longer wavelengths and 
if the radiation temperature is decreasing toward longer wavelengths, then 
you probably have a case for saying that the temperature is increasing 
upwards — this is the sort of thing Mme Gros will talk about in the 



70 

session tomorrow. However, when you get into regions where the 
hydrogen continua dominate you might have good reason to question 
whether LTE is the correct description for the source functions. 

Underhiir — When you get into the hot stars you may have a hot 
chromosphere starting at 50000K, then a high radiation field from 300 to 
500A. If you have radiation from such continua, this is going to affect 
the rest of the atmosphere. What sort of criteria could we suggest to look 
for? Lines in these spectra might serve as criteria for the presence of a 
chromosphere. 

Pecker — Jacqueline Bergeron has computed several early type star models 
with a corona to explain the IR spectra, and the heating of the HI region 
which is outside the HII region surrounding the star. 

Cayrel — Can anyone propose continua or Unes in the visible as a 
diagnostic for hot stars? 

Peterson — Hot stars have strong metal continua, particularly carbon 
continua primarily in the UV. 

Peytremann - I would object to the continua since they are hidden by 
lines. UV spectra show that you never see a nice absorption edge. They 
are washed out by the high density of lines. 

Underbill — Continua with no lines are the only ones that can be used. 
There are too many lines from 9 12 A to 6OO0A from average stellar 
spectra to do much with the continua. 

Sheeley — Where no energy is put into the spectra, it doesn't really 
matter, I would think the lines would have a negUgible effect. 

Underbill — Look between 3000 and 4000 A. There are so many lines no 
one knows what to do. In a paper by Houtgast and Namba a couple of 
years ago, In BAN they found between 40 and 50% line blocking, which 
is quite a bit. Line blocking can alter the spectra in these regions 
considerably. 

Cayrel — From the viewpoint of models, is the continuum brightness 
temperature sensitive to the chromospheric temperature? 

Cuny — Yes, it is sensitive. 

Kaikofen — You couldn't use the Lyman continuum as a chromosphere 
indicator for stars earlier than B. 

Thomas — From the HII region I can observe whether or not I have a 
chromosphere<orona. The HII region is a big part of the stellar atmos- 
phere. 



71 

Underhill — Don't forget that we use the planetary nebula to tell us what 
the nuclei are producing in the way of flux. One of the best photon 
counters is a planetary. 

Aller — Are you sure it is strictly a photon counter and that the emitted 
radiation cannot sometimes be enhanced by energy imparted by a stellar 
wind? 

Underhill — The gas is moving, and there is mass motion, but it's still a 
photon counter, a gas flow counter. Now, for cooler stars, is there 
anything else we can use for a photon counter? 

Pecker - I just want to object to what Anne Underhill just said. Is a 
planetary nebula a real good photon counter, or is it a counter of only 
detected photons? The Zanstra mechanism shows that Te in a PN is 
sensitive to the quality of the radiation, not to its quantity. The state of 
ionization, to the contrary, in an HIl region, is a function of quantity of 
UV photons. So the sentence of Anne's is ambiguous, and should be used 
with a great deal of caution! 

Linsky — One potential indicator of chromospheres in very late type 
stars, which has not been mentioned, is the pure rotation band of water 
vapor in the region of 20|i and longer wavelengths. Many very late type 
stars exhibit infrared excesses at 20/i, which have been interpreted as 
circumstellar emission. An alternative explanation is that the pure rotation 
band is sufficiently opaque that the region of formation of the band is in 
the lower chromospheres of these stars. 

Jeimings — I would like to comment on the H2O. Even though water 
may have bands at 20fi, it is difficult to explain the strong features at 
10/1, and it should be pointed out that various people have suggested 
silicates which have 10 and 20/i peaks. A number of investigators have 
discussed the shape of these peaks, and find that molecules cannot 
reproduce it while grains like Mg and Fe silicates can. 

Johnson — Besides the spectral feature aheady discussed, there is another 
class of observations that might indicate stellar chromospheres. Spectral 
lines in late type stars often appear to be broadened by very large 
turbulent velocities (sometimes supersonic), and there are displaced lines 
in other stars that show outflowing material. In these stars we thus see 
evidence of energy dissipation or matter flowing from the photosphere, 
both of which phenomena we might call chromospheres. 

Vemazza — We determined an empirical solar chromosphere model by 
assuming a temperature as a function of height and solving the hydro- 
static equilibrium, statistical equiUbrium and the radiative transfer 
equations for a 44evel H atom, an 84evel Si I atom, an 8-leveI C atoni, a 



72 

5 -level Ca II atom and H-, to obtain the continuum emergent intensity at 
any wavelength. T^ vs. height is adjusted until agreement with the 
observations is reached. As a result we are able to match the observed 
solar continuous spectrum from 500A to centimeter wavelengths, as well 
as several lines such as Lya Ly)3 and He. From the model, which also 
includes a microtUrbulence structure, we can determine approximately the 
radiative energy losses at every height and every continuum frequeiicy^ as 
well as the losses in some of the hydrogen lines. I wfll give a brief 
summary of how the temperature model shown in Figure 1-25 is adjusted. 
Essentially, the T^ Vs. height iiiodel begins iii the upper photosphere, 
extends through the temperature minimurn at 500 km above t 5000 = 1 , 
through a quasi plateau in the chromosphere and finally through a high 
temperature plateau between 2000 km and 2200 km in the transition 
region. The temperature minimum is put at 4100 K. The first qiiasi- 
plateau is around 6000 K and the second at roughly 20000 K. In the 
photospheric region between the temperature minimum and 5000 K the 
temperature structure coincides with the H.S.R.A. Below 5000 K our 
model has a lower temperature because we solve the non-L.T.E. problem 
for H. The departure coefficients from L.T.E. for H are less than one, 
which gives a higher electron density than in L.T.E. As a result we have a 



TCK) 



LYMAN LINES 



1 LYMAN 
CONTINUUM 
(740-50OJS) 



H/3 



' K, 






I 

Co 2 


INFRARED 


1 
TRIPLET 


Co 1 H a K 


I 


1 


I 



CKIIOOA ) 

' "*CI(I2 39A1 

1CI|I444A) 




1200 
h (km) 



Figure 1-25 



73 

lower Tg, but we nevertheless compute the emergent infrared intensities 
as they are observed. In the region of the temperature minimum the Si I 
^P, 'D and IS continua are formed. These continua serve to give us a 
good hold on the temperature structure at the temperature minimum. 
Until recently all realistic solar models have obtained the Si I continuum 
intensity in L.TE., (except for some preliminary work by Y. Cuny) and 
required a higher Tg to explain the U.V. observations. Since we have a 
non-L.T.E. Si I solution the temperature can be lower because the Si I 
ground state source function is larger than the Planck function. This is 
due in part to the interaction between the Si I 'P continuum and the 
Lya line. Since the Lya line has a higher source function than in L.T£., 
it controls the Si I continuum source function. The C I^P, 'D and'S 
continua, are formed above the temperature minimum. These continua 
provide information about the temperature distribution at around 6000 
K. The observed continuum intensities between 1440A to 912 A are 
reproduced by the present temperature model. In addition Ha H/? and Pa 
which are formed over an extended chromospheric region are also 
reproduced. At around 8400K the Lyman continuum is formed. Above, 
in the 20000K plateau the Lyman lines are formed. There are several 
reasons for the existence of this small plateau at 20000K. One of the best 
observations we have is the ratio of the Lya, Ly^, Ly7, Ly6, and 
Ly7 to Ly5 integrated intensities. 

In order to satisfy these observations we need to have the 20000K 
temperature plateau. We know the Lyman continuum is formed at 
approximately 8400K. So above the Lyman continuum formation region, 
we are forced to have a very sharp temperature rise. Otherwise the optical 
depth in the Lyman continuum will be too large, and will be formed at a 
much higher temperature. Then somewhere at 20000K the temperature 
gradiant must flatten to the point of producing a plateau to reproduce 
the Lyman line integrated intensity ratios and their absolute intensities. 
At the same time the plateau is necessary to obtain the central reversal in 
Ly/J that, otherwise is impossible to obtain. Unfortunately there is only 
one observation of Ly/3. The only way we have to reproduce the Ly^ 
profile is by having a Ly/3 source function which decreases toward the 
surface. And the only way to obtain this decreasing source function is by 
means of a plateau. In addition we have center-to-limb observations of the 
integrated intensity of Lya, Ly^, Ly7, Ly5 , and at six wavelengths in the 
Lyman continuum. 

The limb darkening observations are not good because inhomogeneities, 
namely spicules or dark mottles could introduce additional darkening, and 
by how much we do not know. That is the reason we do not rely too 
much on limb brightening or darkening observations. Lyman a has strong 



74 



limb darkening, about 75% of the Sun's center. Most of this XUV data 
comes from the Harvard OSO IV and VI experiments as well as from 
some unpublished rocket data from H.C.O. With this temperature struc- 
ture we can compute the energy losses in the chromosphere. We have to 
keep in mind that these are still provisional results. In Figure 1-26 the 
solid line represents the radiative energy loss as a function of depth for 
the present temperature distribution. The Lyman a contribution is shown 
by a short dashed line, Ly^ by a long dashed line, Ha by a dotted line, 
and the Lyman continuum by a dashed -dot line. In the upper chromo- 
sphere Lya is the main cooling agent, while in the low chromosphere Ha 
is responsible for most of the cooling. There is a diffusion of Lya photons 
from the upper chromosphere into the low chromosphere. This produces 
some heating in the low chromosphere. The continuum losses are 
negligible except by some CI continuum cooling around 5500K. 

Delache - I would like to ask if this 20000° Lyman plateau exists 
because of mechanical energy deposition in this region, or because the 
radiative losses have to occur in Lyman a . 

Vemazza - We have calculated these loss curves from a temperature 
model which has been chosen empirically in such a way that the 
predicted spectrum agrees with the observed one. Then we have deduced 
the radiative gains and losses in order to determine the mechanical energy 
input necessary to maintain the temperature model. 



10 



10 



UJ ^ 

uj 10 



10 




-2500 



-200O -1500 

HEIGHT (Km) 



J I I 1 • L. 



-1000 



-500 



Figiue 1-26 



75 

Jennings — The loss rates should be proportional to the area under the 
curves you have drawn for Lyman alpha and H alpha. Do your results 
imply that Lyman alpha is giving up the largest part of the chromospheric 
energy loss? 

Vemazza — Yes. 

Skumanich — In addition to these results based on the divergence of the 
radiative flux you might find it interesting to compute the contribution 
of the divergence of conductive flux. 

Vemazza — I understand that for a temperature of 10000°, Ulmschneider 
has computed the conductive flux coefficients in L.T.E. Given the 
extreme departures from L.T.E. I would be reluctant to base the 
conductive flux contribution on such results. 

Ulmschneider — Using the temperature distribution determined from the 
Lyman continuum observation (Noyes and Kalkofen 1970, Solar Physics, 
IS, 120) one can compute the conductive flux. One finds that this flux is 
about 2 X 10^ erg/cm^ sec compared with the observed radiation flux of 
about 6.4x10^ erg/cm^sec, (Friedman 1963, Ann. Rev. Astr. Astrophys., 1 
59), the difference being due to mechanical and radiation heating. The 
amount of radiation heating through the absorption of Lya and 
Ly)3 photons in this region between the Ly continuum and Lya emitting 
regions appears now to be crucial for the existence of a temperature 
plateau. This may be seen as follows. 

The radiative loss in the Ly continuum, Lya, Ly/3 regions is balanced by 3 
competing heating mechanisms, thermal conduction, mechanical heating 
by shock waves and radiation heating. Of these mechanical heating 
becomes unimportant at greater height because, first, the increasing sound 
speed increases the wavelength, decreasing the strength of the shock wave 
and thus its dissipation, second, the dissipation of shock waves is a slow 
process and can not rapidly balance strongly increasing radiation losses. If 
radiation heating were also unimportant then thermal conduction would 
be the only significant heating mechanism. In the Ly continuum region the 
coefficient of thermal conductivity K, due to the increasing degree of 
ionization, is a decreasing function of temperature or height. 

d7rF„ . d dT 
Ml= K 



dh dh dh 

Thus through this equation any radiation loss and even zero radiation loss 
would lead to an increase of the temperature. This argument is especially 
vahd in the main Lya emission region. In this region we expect a strongly 
rising temperature due to thermal conduction. 



76 

On the other hand if radiation heating is appreciable then it could 
decrease the conductive flux leading to a temperature plateau between the 
Ly continuum and Lya emitting regions. For example if a radiative flux of 
Lya photons going toward the sun of about 2 x 10^ erg/cm^ sec were 
absorbed in the region between Ly continuum and Lya emission then 
assuming, for example, no emission in this region one could get 



dT 
=0 

dh 



as seen from the integrated version of the previous equation. 

(note added in proof.) A numerical check of the importance of this 
Lya back heating was done after the conference by W. Kalkofen. He 
found that it invariably occurred in various different models so that the 
existence of a temperature plateau seems to be fairly certain although for 
reasons different than originally proposed (Thomas and Athay 1961, 
Physics of the solar chromosphere. Interscience, New York. p. 156). 

Vemazza — (Note added in proof:) I referred to the conductive flux 
coefficient published by Ulmschneider (Astro & Astrophys. 4, 144, 1970 
which is calculated assuming L.T.E. Later, however, Ulmschneider kindly 
provided me with a more general conductive flux coefficient subroutine. 
The divergence of the conductive flux was calculated and was found to be 
insignificant. 



PARTn 

OBSERVATIONAL EVIDENCE FOR 

STELLAR CHROMOSPHERES 

Chairman: Leonard Kuhi 

INTRODUCTORY REMARKS BY SESSION CHAIRMAN KUHI 

Today we would like to discuss the basic observational facts relating to 
the detection of chromospheres in the Sun and in other stars. Francoise 
Praderie will be talking to us about the solar and stellar data obtained 
from ground-based observations in the visible and infrared. Afterward, 
Lowell Doherty will discuss the ultraviolet data. 



77 



Page Intentionally Left Blank 



EVIDENCE FOR STELLAR CHROMOSPHERES PRESENTED BY 
GROUND-BASED SPECTRA OF THE SUN AND STARS 

Francoise Praderie 

Institut D'Astrophysique, Paris 



INTRODUCTION 

NEED FOR A DEFINITION OF A CHROMOSPHERE 

Before starting to survey recent observations related to stellar chromo- 
spheres, an operational definition of a chromosphere is needed; such 
definition must satisfy two requirements: (1) it must be bound to a set of 
observables which we agree indicate the presence of a chromosphere; (2) 
it must be reasonable in terms of the physical effects which we say 
characterize a chromosphere. Indeed one does not want to be a priori 
confined to call chromospheric indicators only those spectral features 
which, in the Sun, have been attributed to the chromospheric regions of 
formation of the spectrum, and which, by analogy, can be said to be a 
sign of a chromosphere in stars similar enough to the Sun. 

The superiority of the Sun lies in the fact that a correspondence has been 
established between chromospheric observables and the chromosphere as a 
physically defined layer of the atmosphere; a combination of both very 
detailed observations and a refined theory of spectrum line formation 
have made this correspondence meaningful. Consequently, a safe way to 
proceed, at the moment, would be to study stellar chromospheres as 
examples of solar type stars. This approach, although good if the aim is 
to give a quantitative description of solar-like stellar chromospheres, 
excludes many stars with "anomalous" spectral features; those features do 
not necessarily have a counterpart in the Sun's chromospheric spectrurri, 
but nevertheless suggest that the stars showing them have an energy 
supply due not exclusively to radiation in their outermost layers. For the 
latter stars, our diagnostic tools are still poor, and this will prevent us 
from giving any but qualitative descriptions of their chromospheres. While 
we must here look at the Sun as a typical example, about which we know 
more because of better observations, and which will therefore serve as a 
guide, we will try to classify (but not to interpret in fuU generality) 
observed features pertaining to stellar chromospheres in the definition of 
a chromosphere based on energetic considerations. 



79 



80 

LIMITS OF AN EMPIRICAL DEFINITION 

The preceding section implies that we already have in mind a representa- 
tion of what the solar chromosphere is, both in terms of observables and 
in terms of physical effects. Concerning the observables, we know 
empirically what is the chromospheric spectrum of the Sun as observed at 
eclipses, and what are classically called the solar chromospheric layers, i.e. 
those extending from T^^^g (5000 A) = 1 to t^^^^ (Ha) = 1. Further out, 
in the Sun, lies the corona. But clearly we have said nothing regarding the 
physical effects which define a chromosphere by locating it in terms of 
tangential optical depths. Moreover this last variable is not accessible in 
the majority of stars (except in eclipsing systems, eg., f Aur). As a 
matter of fact, when starting to interpret empirical features in the solar 
chromospheric spectrum like emission gradients, or intensity reversals in H 
and K lines, one recognizes primarily that not optical depth but electronic 
temperature T^ is the basic physical quantity which contrasts a chromo- 
sphere relative to a radiative equilibrium (RE) atmosphere; T^ describes 
the energy balance and its departures from the pure RE case. 

What we ideally want then is to give a unified definition of a stellar 
(including solar) chromosphere, thereby avoiding a purely empirical one, 
and relating it to the physical effects controlling T^. From this stand- 
point, the atmospheric regions above the photosphere are combined, and 
in the following discussion there will be no need to separate chromo- 
sphere from corona. Only the problem of the base of the chromosphere 
will be treated, not that of its top. 

TENTATIVE DEFB^ITION OF A CHROMOSPHERE 

We suggest that the chromosphere is the region of the star giving rise to 
observables depending upon the existence of a) a mass flux, b) a 
non-radiative energy dissipation. Two questions immediately arise: first, 
why link the existence of a chromosphere to both phenomena a) and b) 
and not simply to b) and, second, what kind of observables are indeed 
chromospheric indicators? We now turn to consider the necessary and 
sufficient conditions for a chromosphere. 

In a star, considered as a non-equilibrium system, motions are produced 
in the subphotospheric or in the photospheric regions from the electro- 
magnetic energy flux, thrbugh various instabilities. In the contracting 
envelope of a protostar, mass falls toward the center of the cloud. In both 
cases, any motion of a mass m, directed or non-isotropically turbulent, 
generates a mass flux which, per unit surface at time t and location z 
along the radius, is 



81 



j,t) = mj 



F„ (z.t) = m Iv f (v,z,t)d'v 



where f(v;z, t ) is the distribution function of velocities v . The existence 
of such a mass flux does not mean that the star is, at each z, in 
hydrodynamical flow: This may be the case (expansion, mass inflow, mass 
loss) but other situations exist where the mean value of F^ is zero over t 
(e^. acoustic waves), or over some characteristic length (e^. convective 
motions). The mass flux is accompanied by a mechanical energy flux 



i 



Pme (Z,t) = mf V^ Vf(v,Z,t)d3v 



Hence a mass flux over a certain depth range |z[ in the atmosphere is a 
necessary condition to have a non-radiative ener^ transport (We will not 
consider magnetic energy here.). 

But a mass flux is by no means a sufficient condition of existence for a 
chromosphere. Mass flux can indeed be present in the photosphere, and, 
stricfly speaking, it impHes departures from radiative equihbrium and 
from hydrostatic equilibrium there. But in the photosphere, there is, by 
definition, no dissipation of mechanical energy. By contrast, in the 
chromosphere, as soon as characteristic particle velocities become some 
fraction of the sound velocity, the energy contained in macroscopic 
motions is converted into microscopic, thermal ones and heating starts. 
Then, physically, the base of the chromosphere (or of the chromosphere - 
corona) is the lowest place where this dissipation starts to be effective. 

The observables which point out a chromosphere are either direct 
indicators or indirect ones. Direct indicators are spectral features whose 
origin is in the chromosphere itself; they directly imply a chromosphere, 
provided a theoretical analysis allows one to attribute them to such a 
region. As an example, a line core presenting an emission may imply a 
source function that does not decrease monotonically outwards. It can be 
a sign of T^ increasing outwards in the atmosphere (cf. Jefferies's talk). In 
such a case, a correspondence is estabUshed between the observable and 
the location where T^ rises, identified with the chromosphere, if more- 
over, this rise in Tg is not produced under RE. 

Not all direct indicators of chromospheres have been analyzed in full 
detail; some of those which have not been analyzed are nonetheless said to 
be heating indicators, although only on analogical grounds at the moment. 



82 

Indirect indicators are phenomena observed in the photosphere or in the 
chromosphere, from which one can predict the presence of a chromo- 
sphere, without those indirect indicators necessarily being found jointly 
with direct observed effects. They include all signs of the presence of 
non-radiative energy sources. Interpretation of these signs leads not to a 
local Tg, but to the recognition of the presence of mechanical energy, 
which might dissipate higher up in the atmosphere, or at the location 
where the sign is formed. 

In the case which we will exclusively consider in the following, namely, 
production of chromspheres from dissipation of mechanical energy, such 
indirect indicators directly reveal the existence of a mass flux in the star. 
Examples are oscillatory motions in the solar low chromosphere, astro- 
nomical turbulence, solar granulation, etc. . . . 

THE BOTTOM OF THE CHROMOSPHERE 

The organizers of this conference asked for a discussion on the most valid 
criterium to decide where the chromosphere indeed begins. Are we in the 
chromosphere as soon as the temperature gradient dT^/dh, derived from 
observations, is positive? Have we enough tools of analysis to non- 
equivocally attribute a positive dT^/dh to a pure RE effect or to a 
dissipation of mechanical energy, or to both? Let us consider different 
possible situations and their meanings. A first case is that in which 
dTg/dh < 0, or T^ is decreasing outwards monotonically. This case is met 
when there is either pure radiative or radiative plus convective energy 
transport, and when inelastic collisions maintain populations of energy 
levels. 

When, in a continuum j, photoionizations take over from collisions, the 
effect first shown by Cayrel (1963) to act in the solar H~ continuum 
produces an increase of T^ under RE. If we ignore the lines, T^ may 
increase up to some colour temperature T^., characteristic of the most 
transparent <;ontinuum. Each continuum successively contributes to the 
increase in T^ (see Feautrier, 1968; Auer and Mihalas, 1969, 1970; 
Mihalas and Auer, 1970; Gebbie and Thomas, 1971). The location of the 
layer where T^ starts to rise is both frequency dependent, because the 
rate of photoionization in each continuum (Rj^ is, frequency dependent 
and density dependent through the rate of collisional ionization V j^ . This 
dependence evolves from star to star along the spectral sequence with the 
nature of the main absorber in the transparent layers of the star (H' in 
the Sun and F, G, and K stars; HI in hotter stars; Hel?) and with the 
gravity, which, combined with Tg governs the electron density in the star. 



83 

But, as radiation is not carried exclusively in the continuum, lines enter 
to modify the preceding conclusions. To be brief, let us mention the 
work by Frisch (1966), and Athay (1970), who conclude that the lines 
they have considered (lines not coupled to the continuum) act as cooling 
agents in the Sun. 

In consequence, even if dT^/dh is inferred to be negative from observa- 
tions, in a region where one can show that the density is low enough that 
Fjc '^ <Rjg but where the effect of lines is mainly to cool, we are in a 
practical situation in which we are not able to recognize the starting layer 
of the Cayrel effect. Suppose now that observations lead to dTg/dh =0. 
It may mean that the Cayrel effect is present but exactiy balanced by 
cooling due to lines; or that we have the same, plus a strong cooling due 
to lines, but with a contribution of heating by mechanical dissipation. If 
properly analyzed observations lead to dT^/dh > 0, either one has one of 
the former situations, with continuum influence, plus some lines coupling 
to the continuum to produce a heating effect stronger than the cooUng 
due to other lines; or the same plus mechanical heating; or mechanical 
heating alone, if, for instance, T^ is higher than the colour temperature 
Tj, of the most transparent continuum. 

My conclusion is that it is impossible, at present, to decide unam- 
biguously what is the proper interpretation of a dT /dh inferred from 
observations in the low. density layers of a stellar atmosphere, without 
having carefully studied which are the opacity sources and how lines 
interact with them in governing the temperature run, as well as the 
inechanical energy sources and where their energy is dissipated. Despite 
valuable efforts on this purely theoretical problem, a considerable amount 
of work is still needed to unravel the non-LTE photosphere from the 
chromospheric regions. 

But the Cayrel effect in no case can increase Tg over T^. If, then, through 
appropriate observables, one diagnoses a temperature hi^er than Tg,one 
can claim, without the detailed analysis of all the above mentioned 
physical processes, that mechanical heating operates and that one sees the 
chromosphere. However, at present, direct indicators of a chromosphere 
cannot by themselves lead to the location of the base of the 
chromosphere, not even in the Sun. 

Considering that in the Sun the question of the bottom of the chromo- 
sphere is not settled, and that the best semiempirical models have been 
obtained from eclipse data and from high resolution disk spectra in the 
core of strong lines and in UV and IR con tin ua, we will not be able, in 
stars, both from lack of theoretical analysis and from the lesser quality of 
observations, to fulfill the program announced to be ideal in this 



84 

introduction. Only a survey of observables and an attempt to classify 
them are possible, and we will make such a survey in the following 
paragraphs. 

SURVEY OF RECENT OBSERVATIONS 

Two review papers on observations of stellar chromospheres were present- 
ed in 1969 (Feast, Praderie). We will attempt here to gather the recent 
observations and some of those which were omitted in the previous 
reviews and will examine successively indicators of mechanical energy 
dissipation, some selected indicators of mass flux, and after the Sun's 
example, indicators of horizontal inhomogeneities and of temporal varia- 
tions in chromospheres. The present survey is restricted to observations in 
the visible and in the infrared. 

INDICATORS OF HEATING 

These indicators are mainly lirie profiles showing excitation-ionization 
anomahes; UV and IR continua have aheady been mentioned (Praderie, 
1970). The identification of lines as chromospheric indicators proceeds 
from the theoretical understanding of their formation. The most famous 
example is that of the solar H and K central reversals (Jefferies and 
Thomas, 1959). As recalled by Jefferies during this conference, all the 
so-called coUision dominated lines are, in the same way, model dependent 
and may reflect chromospheric values of Tg and N^. Emission in some 
other lines is not as well understood, as the following examples will show. 

Excitation anomalies include, first, the extreme case of all lines in 
emission (examples: Wolf-Rayet stars spectrum, or the solar spectrum 
below 1800 A); second, the case where some Unes are in emission 
(examples: He II X4686 in Of stars, Mgll and Call resonance doublets in 
the Sun and many late type stars); third, the case where absorption lines 
appear Which correspond to an excitation much higher than that existing 
in the photosphere (examples: He I X587^or X10830 lines in cool stars). 

ionization anomalies include the presence of Unes of highly ionized atoms 
(coronal Unes) and (or) of a continuum emission in the radio wavelengths, 
emission whose origin is probably in a hot corona. 

EXCITATION ANOMALIES 
H AND K LINES OF CA U 



Observations of the central emission in the resonance doublet of Ca II, 
which were extensively made by Wilson and Wilson et al (1954, 1957, 



85 

1962, 1963, 1964, 1966, 1968) and others, have been pursued actively, 
not so much to study individual atmospheres, as to take advantage of the 
pre§encg of this feature to derive other stellar properties to which the 
emission js correlated. These correlations may lead to a better understand- 
ing of thg sources of heating of the chromospheres as functions of 
spectral typ§ (Skumanich, 1972). We first consider here time-independent 
observations ; 

• Dependenge of I^ and K eniission with bolometric luminosity 
(Wilson, 1970 ^ For 65 stars of the same age (F 4 to K 5, main 
sequence Hyades stars) the mean flux ratio for the emission com- 
ponents of H and K increases from B — V = 0.45 to B — V = 1.25, 
and the emission intensity to bolometric luminosity ratio increases 
by 8 factor of 2 in the same spectral type range. It is not known if 
this trend is universal, or if it is age dependent. 

t Dependence of H and K emission with age of the star - From 
Wilson's work (1963), it is known that field main sequence F and G 
Stars, studied at 10 A/mm dispersion, show no more emission for 
Stars hotter than F 5, and that 10^ of the stars of type later than F 
5 have an emission in H and K. For F and G main sequence stars in 
galactie clusters, all stars of type later than F 5 have an emission in 
H and K, Wilson and Woolley (1970) have studied the Ca II emission 
at 38 A/mm in 325 main sequence stars. The emission is found to be 
intense for star? whose orbit eccentricity is close to one and whose 
orbit inclination relative to the galactic plane is weak, hence which 
are the youngest in the saniple. It is concluded that Ca II emission is 
one of the best age indicators available, being the weakest when the 
Star is advancing in age. As a result of this age dependence H and K 
emission has been used as a tool to detect faint members in young 
clusters (Kraft and Greenstein, 1969). Because the majority of the 
members of the Pleiades (according to proper motion) have Kj 
ernission twice as strong as Hyades stars of the same type, the 
assumption was made that such an emission identifies members of 
the cluster even for stars fainter than V = 13. Observations have 
been successfully conducted at 200 A/mm for stars later than K 5 in 
the Pleiades. Prolongation of the main sequence toward faint mem- 
bers allows a determination of the contraction time of the stars in the 
cluster, 

• Ca II emission and polarization. Dyck and Johnson (1969) have 
shown that the deviation of the mean degree of intrinsic polarization 
per night relative to the mean degree is anti-correlated to the 
intensity in Kj for ten cool giants and supergiants. These observa- 
tions have been extended to long period irregular variables by 



86 

Jennings and Dyck (1971). In those stars, H and K emission occurs 
only if the polarization degree is weak (0.1%), and it is exclusive 
with IR emission around 10/Lt. It is suggested that polarization and 
IR emission are due to a dust shell, the formation of which prevents 
a strong heating of the chromospheric gas. 

• Ca II emission in binary systems. Popper (1970) mentions that 25 
echpsing systems are known with emission in H and K in the 
primary or in the secondary component; their types are F to K 0. 
The emission may undergo the eclipse. It is observed in dwarfs as 
well as in supergiant systems. Carlos and Popper (1971) have found 
the same effect in a spectroscopic binary, H D 21242, the emission 
being localized in the spectrum of the secondary (K O IV; the 
primary being G 5 V)- Inversely, the presence of a strong K2 
emission in giants can be used to detect binary systems. Abt, Dukes 
and Weaver (1969) have studied 12 Cam (KO III) and checked that 
assumption with success. 

• Wilson-Bappu effect. The well-known empirical relationship estab- 
Ushed by Wilson and Bappu (1957) for G, K and M stars is 

M^ = 14.94 log w„ + 27.59 

where M^ is the visual absolute magnitude, and Wq is the width of 
the emission, corrected from the instrumental profile. I will not 
discuss this relationship and its evolutive implications here, except to 
mention that it has been recently extended to 200 more southern 
stars (Warner, 1969). The question of caUbration in terms of 
absolute magnitudes has been critically reviewed by Wilson (1970). A 
possible influence of metal abundance which could perturb the 
general use of the relationship and was suggested by Pagel and 
Tomkin (1969) receives objections from Wilson in that article. 

Let us recall that not all stars showing H.and K emission obey the WB 
relationship; T Tauri do not (Kuhi, 1965); nor do Cepheids (Kraft, 
1960). But the Sun does verify the WB relationship. This is why attempts 
to explain the luminosity effect on the Kj emission width have turned 
first to the physical parameters of the solar chromosphere, where it is 
formed. Turbulence has not proved to be the key, although it was shown, 
originally by Jefferies and Thomas (1959), and more recently by Athay 
and Skumanich (1968) that the emission width, defined by Wilson, is 
indeed a function of the Doppler width. Recently, studies of high 
resolution spectrograms of the Sun have been performed, with the aim of 
recognizing the contribution of discrete chromospheric elements in the 
formation and position of the Kj peaks of Ca II, by Pasachoff (1970, 
1971) and by Bappu and Sivarawan (1971). By a careful study of a series 



87 

of K profiles and of K232 spectroheliograms in the quiet Sun, Bappu and 
Sivaraman have derived the distribution of the K2 peak to peak distance 
on the solar surface. This width can of course be measured on spectra 
only when both K2R and K^y exist as bright features (about 95% of the 
situations). In that case, the WB relationship is satisfied. From a study of 
intensity fluctuations in K2Y and K2R along the sHt, the authors identify 
the emitting regions for which the WB relationship is valid with the. bright 
fine mottles. On the other hand, it is known that the Kj width decreases 
over plages (Smith, 1960), and at the super-granulation boundaries, where 
magnetic fields of the order of 100 gauss are present. Those two results 
suggest: (1) that in stars where the K2 width obeys the WB relationship, 
an inhomogeneous structure like the solar mottles exists, and (2) that a 
deviation from WB relationship will occur in particular in stars with a 
magnetic activity, and will also tend to be associated with a light 
variation. According to Bappu and Sivaraman, ^e rotation of the star is a 
decisive parameter in modulating the rate of plages on the visible disk. At 
the present stage, and iri spite of its interest, it is clear that this 
interpretation of the WB effect is somehow incomplete, in the sense that 
it does not offer a reason for the variation of the properties of the fine 
mottles with luminosity in such a way that w„ is kept proportional to 
visual luminosity L,,'/*. 

An example of the above picture seems to exist; 7 Boo (A 7 III) is a star 
with a high rotational velocity (v sin(i)=135 km/s); it shows short time 
scale variations in the K Une core. That is, it exhibits variable asymmetry, 
and despite the high v sin(i), the temporary occurrence of an emission (Le 
Contel et al., 1970). The K emission width is smaller than that expected 
from the WB relation, which fits Bappu and Sivaraman 's suggestion if 
emission comes only from plages; the star is also variable in light; one of 
the proposed interpretations for these phenomena is that the star's surface 
is perturbed by plages. An extension of this scheme of interpretation to 
deviations from the WB relationship for Cepheids or T Tauri seems 
hazardous at the moment. 

IR TRIPLET OF Ca II - The infrared lines of Ca II near to 8498 A show 
no central emission in the quiet Sun. An emission core is seen over plages, 
the most intense being in the otherwise weakest line of the triplet, as was 
beautifully described by linsky during this conference. In long period 
variables, like R Leo (M 8 e), Ca II triplet occurs in emission (Kraft 
1957); in T Tau stars it occurs also. 

BALMER LINES OF HYDROGEN - Because their source functions have 
source and sink terms dominated by photoionizations in solar type stars, 
these lines are comparatively insensitive to the local physical characteris- 
tics of the atmosphere, and depend mainly on the radiation field in the 



88 

various continua (Thomas, 1957). The influence of a decrease of gravity is 
to enhance the photoelectric character of the source function. As 
suggested by Mihalas, the character of the Bahner Unes source function 
changes in hot stars. Therefore, the observed emission of Ha in hot 
supergiants, if not due to a geometrical effect, could be a sign, not of a 
chromosphere, as previously defined, but of a non-LTE photosphere. But 
Ha in emission is not found only in hot stars. It appears in d M e stars, 
often simultaneously with K emission; in symbiotic stars where emission 
lines are superimposed on an M type spectrum; in flare stars; in T Tau 
stars, etc. (Bidelman, 1954; Herbig, I960). 

Wilson (1956) reported emission in He, observed on 10 A/mm spectra of 
K and M type stars. Emission is first observed in K stars, and is well 
developed in M giants, but not in the supergiants. Excitation of the 7th 
level of Hydrogen by the Ca II H line does not seem hkely, as Hg lies too 
far in the wing of the H line (A\= 1.58 A). Lyrj could do the same, but 
until now it has not been observed in those stars. One wonders why only 
this single Balmer line (H), would be in emission through such an 
excitation process. 

Other Balmer lines can be in emission in special groups of late type stars 
(symbiotic stars, Mira variables). A recent observation reports H7 and 
H 5 in emission in o Ceti at phases close to the maximum of light (Odell 
et al., 1970). 

PASCHEN LINES OF HYDROGEN - Pa has been predicted to be in 
emission in stars under radiative equilibrium (Mihalas and Auer, 1970), 
but. observational difficulties at that wavelength (1.8751ju) have until now 
prevented a check of this prediction, or finding other stars where this 
emission could occur. But PjS (1.2818ai) and P7 (1.0938/i) have been 
observed in emission: PjS in o Ceti (Kovar et al., 1971), and PT in 7 Cas 
(BO IV e), which is not a shell star ^eisel, 1971). 

No equivalence of emission cores in Paschen or Balmer lines exists when 
observed over the disk in the Sun. 

HELIUM I LINE - The triplet series lines X10830 and X5876, in 
absorption or in emission, correspond to a high excitation, and are not of 
photospheric origin in late type stars. X10830 (^S - ^P°) has been 
discovered in emission in. P Cyg and in carbon Wolf-Rayet stars (Miller, 
1954), then in emission in all Wolf-Rayet stars (Kuhi, 1966). Vaughan 
and Zirin (1968) have searched for this line in 86 stars at 8.4 A/mm and 
found it in absorption in normal G and K stars, and in emission in five 
stars, where the profile is of the P Cyg type. Meisel (1971) observed it in 
emission in 7 Cas. The presence of X5876 ('P° - ^D) is attributed to hot 
chromospheric layers in late-type stars. Wilson and Aly (1956) detected it 



89 

in G and K stars, the warmer being of type G 5 V (k Ceti). Feast (1970Z») 
found this same Hne in V Dor (F 7 V), a star which otherwise has also an 
inteiKe emission in H and K. Fosbury and Pasachoff reported more 
observations during this conference. 

In the Sun, besides the flash spectrum, X5876 (also called D3) is observed 
in absorption only above active regions; X10830 is seen in absorption 
over selected regions of the disk (network cells, plages and filaments)(e.g. 
Zirin and Howard, 1966). Both lines can be observed in emission only in 
bright flares. They are assumed to be formed in the strongly non- 
homogeneous chromosphere, namely in the hot regions, above 2000 km 
from the limb. 

Coming now to a quite different class of objects, it has been argued by sev- 
eral authors (Nariai, 1969; Wickramasinghe and Strittmatter, 1970; Bohm 
and Cassinelli, 1971), that helium stars and white dwarfs could have a 
chromosphere-corona, because, according to the mixing length theory, 
their convection zone is predicted to be important (effect of increased 
He abundance or of density). Nariai gave v Sgr as a good candidate. 
Observations performed on the helium star G 61-29 show broad He I 
emission lines, among which X3889 has a central reversal (Burbidge 
and Strittmatter, 1971). No detailed interpretation of any of these He I 
lines in helium stars has yet been worked out, but the He I and He II 
spectrum in stars is the object of an important study by Auer and 
Mihalas (1972). For many other lines, which might be related to chromo- 
spheres, no detailed analysis is yet available. We will only briefly mention 
them now. 

OTHER EMISSION LINES 

• The K I resonance doublet seems to appear definitively in emission 
in a small number of very peculiar stars such as the long period 
variable x^yg, the pecuUar supergiant VY C Ma. A single reversal is 
also seen in the core of this line when observed in sunspots (Maltby 
and Engvold, 1970). 

• The O I infrared line at X8446, observed by Wallerstein (1971) in 
stars showing an IR excess occurs in emission when Ca II X3933 is 
broad, while it shows no emission when Ca II is sharp and in 
emission. 

Fe II also builds an emission spectrum in many late type stars as 
well as in some early types and in symbiotic stars (see e.g., Bidelman, 
1954; Herbig, 1960). Can one say that their origin is chromospheric, 
or do they show an increase in excitation in a rather cool (relative to 
a chromosphere) circumstellar shell? Weymann (1962) attributes 
those Fe II lines observed in a Ori around 3100 A to a chromo- 



• 



90 

sphere, although in that star the Fe I excitation temperature is very 
low, and Fe I lines are formed in a shell. Those lines are often 
simultaneously present with an excess of IR in the 2-1 0;u range. 
Geisel (1970) gives a list of 35 stars, mainly hot (Be - P Cyg, Ae, Fe, 
Ge, and some others) where the IR excess has been predicted, and 
found, from the physical relationship between Fe II and [Fe III] , 
emission and the IR excess. Such a correlation, if extended, and the 
already quoted exclusivity effect between Ca II K emission and 
polarization plus infrared excess put in full Ught the problem of the 
mutual relationship of chromospheres and dust shells around Be stars 
as well as around cool stars. 

All the excitation anomaly indications reviewed here are lines. Moreover, 
all the corresponding observations concern/the integrated disk of the star. 
In the perspective of having the Sun as a running example, we must stress 
that the first modern models of the solar chromosphere have been derived 
from the analysis of ecUpse data (emission gradients in Paschen and 
Balmer continuum, lines of metals, Balmer lines .... see Thomas and 
Athay, 1961). A limited number of ecUpsing systems consist of a main 
sequence B star and a K or M supergiant whose chromosphere is 
illuminated by the B star Ught during the eclipse. Those stars contain 
more inforrnation on chromospheric layers of the K or M component 
than any other observed only in the disk. Their prototype is f Aur. A 
review of observations and interpretations was given by Groth (1970); 
they will not be mentioned further here, in spite of their major interest 
in attacking the chromosphere problem in stars. 

Besides the ecUpsing systems of the f Aur type, several groups of stars 
deserve special attention relative to the observations of chromospheres. 
Some were incidentally mentioned: Mira variables. Wolf Rayet stars, T 
Tauri, heUum stars, symbiotic stars. We shaU add flare stars but it is not 
possible here to give a meaningful account of them. A recent paper on 
chromospheres in flare stars is that of Gershberg (1970), and a review has 
been given by Lovell (1971). 

IONIZATION ANOMAUES 

Observations of the radio continuum have been performed, without 
success, on a Ori M 2 I ab) at X = 1.9 cm by Kellermann and 
Pauliny-Toth (1966), and with success on a Ori and uAur (M 3 II) at X = 
2.85 cm by Seaquist (1967) and on a Sco at X=ll.l cm by Wade and 
Hjellming (1971) and Hjellming and Wade (1971). In this last case, the 
radioflux at 3.7 cm happens to be higher or smaUer than the 11.1 cm 
flux, showing that the sowce is variable both in intensity and spectral 
index; the source seems to be associated with An tares B (B 3 V) rather 
than with Antares A (M 2 I b). 



91 

Coronal type lines have been observed in the spectrum of novae. The 
identified lines, allowed or forbidden, belong to highly ionized atoms. A 
bibliography can be found in the C.N.R.S. International Colloquium on 
novae, supernovae, novoides (1965). Recent work due to Andrillat and 
Houziaux (1970a, 1970b) identifies coronal Unes in the near infrared 
region of Nova Del 1967: lines of [Fe X] , [Fe XI] , [A XI] , [Ni XV] . 

Solar chromospheric temperatures have been derived from the observa- 
tions of mm and cm radiation jointly with eclipse data to infer densities 
(e.g. Dubov, 1971). As to the coronal lines, their ionization and excita- 
tion mechanisms are fairly well understood in the Sun. But very few 
attempts have been made to extend the solar corona type of analysis to 
novae. 

One of the lines having been used to characterize the properties of the tran- 
sition region between the solar chromosphere and corona is the O VI doublet 
at 1031.9 - 1037.6 A. I don't know of any observation of this line in stars, 
but other VI lines are well known in Wolf Rayet stars, and have been re- 
ported in planetary nebulae central stars and in stars which are not central 
(Sanduleak, 1971). 

INDICATORS OF MASS FLUX 

To review all indicators of mass flux in photospheres is beyond the scope 
of this talk, although it would be most valuable to do so, and to examine 
simultaneously why some velocity fields become turbulent and others do 
not, and why some of them evolve until their energy is converted back to 
the thermal pool of the atmosphere by heating. 

Let us focus our attention here only on those mass flux indicators which 
pertain to the chromospheric layers themselves, because these indicators 
are Unes formed in the chromosphere. The whole question of mass loss, 
namely of net systematic escape of matter from the star, will be set aside. 

ANOMALOUS LINE-WIDTHS 

A good example is that of Ha in the solar chromosphere. This line alone 
cannot lead to an inference of T^ in chromospheric layers. But suppose 
we know T^ (h). To interpret the halfwidth of tiiis line, as well as of 
others, a statistical broadening of the Doppler type must be added to the 
thermal one. This additional broadening is attributed to microturbulence. 

In stars, assuming that the core of Ha is formed in the same layers as 
the emission peaks of the H and K lines, Kraft et ai. (1964) studied the 
width of Ha called H^ . They found a correlation between H^ and the 
absolute magnitude in the U band pass. This work has been repeated by 
Lo Presto (1971) with improved observational facilities. He observed 



92 

about ten stars with the solar tower at Kitt Peak, and obtained a better 
relation than Kraft's between Hq and My. This result extends in fact to Hq 
the Wilson-Bappu relationship, without, nevertheless, reinforcing an inter- 
pretation of this relationship in terms of solely a turbulence effect. 
Further work is in progress on late-type stars of all luminosity classes 
(Fosbury, 1971). 

No exceptions have been reported (to my knowledge) to the empirical 
relationship between Hq and M^ and so there is no counterpart on H^ to 
T Tau or Cepheids disobeying the WB relationship. 

According to Vaughan and Zirin (1968), the He I M0830 Une seems also 
to show a broader profile than photospheric hues in stars where it has 
been observed. 

The same is true (enhanced line-width, from which astronomical turbulence 
is invoked) for Wolf-Rayet stars emission lines, certain of which show a 
P Cyg profile, and hence reflect that the emitting region experiences mass 
ejection. 

ASYMMETRICAL LINES 

Both Ca II and Mg II resonance doublets are strongly asymmetric in the 
quiet Sun (e.g. Pasachoff, 1970; Bappu and Sivaraman, 1971; Lemaire, 
1971). For Ca II, a statistical analysis has been performed by Bappu and 
Sivaraman on the occurrence of different patterns for the relative K^y 
and KjR intensities: Ikjv '^ bigger than Ikor ^ ^^% °f the profiles; 
they are equal in 4.7%; Ik^v *^ smaller than Ik2r i" 25%; Ikjr = in 
22.3%; Ik2v = in 0.7% of the cases. 

In stars, the profiles of Ca II K line obtained by Liller (1968) or by 
Vaughan and Skumanich (1970), even if they show only one central 
emission core, are very far from being symmetric. The core of Ha is also 
often asymmetric in late type stars (see Kraft et al., 1964; Weymann, 
1962). Some of the Hel \10830 profiles observed by Vaughaii and Zirin 
in hot stars exhibit a P Cyg type profile. The chromospheric layers are 
then associated with directed velocity fields indicating mass transport 
towards the interstellar medium. 

INDICATORS OF HORIZONTAL INHOMOGENEITIES 
AND OF ACTIVITY 

In the Sun, Doppler shifts and intensity fluctuations along the sUt in Unes 
allow study of both the propagation of waves and the solar fine structure 
in the upper photosphere and low chromosphere. On the other hand, on 
spectroheUograms and filtergrams, one sees the coarse network, coarse 
mottles and fine mottles, as well as spots, -filaments and other features, 
and inhomogeneities prove to extend high up in the chromosphere. In 
stars, no such observations can be performed, except possibly in eclipsing 



93 

systems of the f Aur type. We will then restrict ourselves here to 
indicators of temporal variations in stellar chromospheric spectra, ignoring 
spacial inhomogeneities. 

Variations have been observed in H and K lines and for stars where these 
lines happen to show central emission. Several other chromospheric Unes 
undergo variations also. 

In H and K, these variations affect the intensity of the emission peaks 
and the shape of the profile. Let us consider first late-type stars. Griffin 
(1963) and Deutsch (1967) first reported such variations in a Boo and 
other cool giants. Variations in the K emission can be occasional (e.g. 
Kandel, 1966, in the dwarf HD 119850; Boesgaard, 1969, variations in 
the MS star 4 Ori). Although they have been searched for, to the best of 
my knowledge, no cyclic variations in the K line flux have yet been 
reported (Wilson, 1968; Liller, 1968). This might only reflect the lack of 
long enough time sequences of observations. 

If these variations are associated with changes in the physical properties 
of the emitting atmosphere (occurrence of plages, for instance), one 
wonders if this activity is correlated with a general brightness variation of 
the star. Such photometric variations have been searched in the UBV 
filters by Blanco and Catalano (1970), on HD 119850 ( d M 2.5 e), a 
Boo (K 1 III) and a Tau (K 5 III). No clear variations can be detected. 
Similar observations were made by Krzeminski (1969) on a sample of d 
Me and d M stars. Light variations exist in some d M e stars, showing that 
activity is a continuous process; but none are present in d M. The 
extreme example of stars showing activity in light as well as in chromo- 
spheric lines (Ha core, Ca II) is that of flare stars, also classified as UV 
Ceti variables. 

Among variables with chromospheric characteristics, Mira stars also prove 
to be variable in their emission Unes; e.g., variation in H 7, H 5 reported 
by Odell et al., (1970), variation in PjS reported by Kovar et al., (1971). 

Toward hotter stars, the already mentioned A 7 III star, 7 Boo, shows a 
quasi-periodic velocity field from radial velocity measurements at mid- 
intensity in the K line, and a variable K line reversal within time intervals 
of 2 hours (Le Contel et al., 1970). Due to lack of observations, no 
period has been recognized for the K line core variation; hence, it has not 
been related to the Ught variation which the star experiences with a 
period of 0.29 d. The light amplitude is variable, and phases of calm with 
no variations at all do exist. 

In Of stars, which have not been considered in detail in this paper, 
variations in streiigths of the emission lines N III X4034, 4640, 4641 and 
He II 4686 have been observed by Brucato (1971) with a time scale of 
the order of ten minutes. A typical Of stars, f Pup, is also one of the 
stars which ejects mass at the highest known velocity (Carruthers, 1968). 



94 

The Hel line XI 0830 experiences variation, as in the Sun (Vaughan and 
Zirin, 1968), in several late type stars. 

A puzzling case appears to be that of the star R Cr B, whose 
chromospheric properties have been pointed out by Feast (1970), after 
Payne-Gaposhkin (1963) and others. The H and K cores, D lines of Na I 
and sharp Sc II, Ti II, Sr II, and Fe II lines appear in emission when the 
star (F 7 carbon supergiant and irregular variable) goes through the 
minimum of light. That phase has been suggested to coincide with the 
ejection of condensed graphite which obscures the star. If this is the case, 
it seems difficult to reconcile the presence of this carbon black cloud 
with that of a chroinosphere, namely a heated layer, because to have 
carbon change phase, one most likely requires heat absorption instead of 
dissipation. On the other hand, during phases of maximum light, and over 
one year, R Cr B has been variable in the infrared continuum (Forrest et 
al., 1971) at 3.5/i, while at ll.l/x it was quasi-stable. The variation 
amounts to 1.5 mag, which means that the circumstellar carbon grains 
have been heated, whatever the form of energy input. We may assent to a 
possible alternation between absorption of heat to produce grains, and 
heating of those grains. 

CONCLUSION 

Obviously, an enormous gap exists between observations as they stand, on 
the one hand, and their interpretation in terms of the general structure of 
a stellar atmosphere, on the other hand. 

There is no such thing as an available grid of stellar chromospheric models 
(although stellar coronas have been quantitatively predicted). One has to 
realize, case by case, for each interesting star, that the observational 
information is scarce enough so that one has difficulties applying a solar 
analogical method, such as .described by Avrett, to analyze them. Attempts 
were made by Kandel (1967) and by Simon (1970) to produce chromo- 
spheric models for d M stars, in one case, and for Arcturus (aBoo), in the 
other. 

At the moment, we have not fulfilled the scheme for analysis which the 
introduction claimed to be legitimate in looking at stellar chromospheric 
indicators. This may mean that we have not giveri the useful definition of 
a chromosphere required at the beginning of the conference. We have 
been able to classify many of these indicators by referring them to 
heating or to mass flux. But we have met at least three important 
problems on which we have had to be vague. One is diagnostical, and has 
been outlined by Jeff cries. Are all emission Unes a signature for a 
chromosphere? The second is structural. How could we specify the base 
of the chromosphere at all, and how do we do this when a circumstellar 
shell is related to it, especially in stars where the shell seems to be very 
close to the photospheric layers? The third question relates to the physics 



95 

of velocity fields. Do all motions detected in photospheres become 
turbulent and are they a result of atmospheric heating? If not, what are 
they Uke and what causes them? 

A way to progress is surely to call for more observations, but for more 
systematic ones, in the sense that we want them to be led as closely as 
possible by a physical question to answer. The most immediate step to 
take would be to collect, from a Umited number of objects, information 
from all spectral regions, lines and continua, to be able to construct 
reliable spherically symmetrical models of Tj(h), those models being 
obtained using the static energy balance equation, taking into account line 
effects, and treating the mechanical energy input as a free parameter, if 
no better treatment is possible. A simultaneous effort should be pursued 
to answer the precedingjy quoted questions, whose answers will influence 
the construction of a model. 

This paper was prepared partly when I was in JILA, as a Visiting Fellow 
(1970-1971); I have benefitted from numerous clarifying discussions 
there, as well as in France, and I acknowledge especially the continuous 
interest of Ph. Delache, J. - C. Pecker, R Steinitz, and R.N. Thomas. I 
am also indebted to all colleagues who sent me preprints of their current 
work before the Goddard Conference. 



REFERENCES 

Abt, H.A., Dukes, R.J., Weaver, W.B., 1969, Ap. J. 157, 717 
Andrillat, Y., Houziaux, L., 1970, Astrophys. Space Sc. 6, 36 
Andrillat, Y., Houziaux, L., 1970, Astrophys. Space Sc. 9, 410 
Athay, R.G., Skumanich, A., 1968, Ap. J. 152, 141 
Athay, R.G., 1970, Ap. J. 161, 713 
Auer, L.H., Mihalas, D., 1969, Ap. J. 156, 157, 681 

1970, Ap. J. 160, 233 

1972, Ap. J. Suppl. 24, 193- 

Bappu, M.K.V., Sivaraman, K.R., 1971, Sol. Phys. 17, 316 

Bidelman, W.P., 1954, Ap. J. Suppl. 1, 175 

Blanco, C, Catalano, S., 1970, PASP 82, 2293 

Boesgaard, A.M., 1969, PASP 81, 283 

Bohm, K.H., CassineUi, J., 1971, Astr. Astrophys., 12, 21 

Brucato, R.J. 1971, MNRAS 153, 435 

Burbidge, E.M., Strittmatter, P.A., 1971, Ap. J. 170, 139 

Carlos, R.C., Popper, D.M., 1971, PASP 83, 504 

Canuthers, G.R., I 1968, Ap. J. 151, 269 

Cayrel, R., 1963, C.R. Ac. Sci. 257, 3309 

Coll. Int. C.N.R.S., 1965 Novae, Novoides et Supemovae, Ed. C.N.R.S., 

Paris 
Deutsch, A.J., 1967, PASP 79, 431 
Dubov, E.E., 1971, Solar Phys. 18, 43 
Dyck, H.M., Johnson, H.R., 1969, Ap. J. 156, 389 



96 

Feast, M.W., b 1970, MNRAS 148, 489 

a 1970, in Ultraviolet Stellar Spectra and Ground Based 
Observations, Ed. L. Houziaux, H.E. Butler, p. 187 
Feautrier, P., 1968, Ann. Astr., 31, 257 
Forrest, W.J., Gillett, F.C., 1971, Ap. J. 170, L 29 
Fosbury, R.A.E., 1971, private communication 
Frisch, H., 1966, JQSRt 6, 629 
Gebbie, K.B. Thomas, R.N., 1971, Ap. J. 168, 461 
Geisel, S.L., 1970, Ap. J. 161, L 105 
Gershberg, R.E., 1970, Astrofizika 6, 191 
Griffin, R.F., 1963, Observatory 83, 255 
Groth, H.G., 1970, in Spectrum Formation in Stars with Steady-State 

Extended Atmospheres, Ed. H.G. Groth, P. Wellmann, NBS Spec. Publ. 

332, p. 283 
Herbig, G.H., 1960, Ap. J. Suppl. 4, 337 
Hjellming, R.M., Wade, CM., 1971, Ap. J. 168, L 115 
Jefferies, J.T., Thomas, R.N., 1959, Ap. J. 129, 401 
Jennings, M.C., Dyck, H.M., 1971, K.P.N.O. Contr., 554, 203 
Kandel, R.S., 1966, in Coll. on Late Type Stars, Trieste, Ed. M. Hack, p. 

146 
Kandel, R.S. 1967, Ann. Astr. 30, 999 
Kellermann, K.I., Pauliny-Toth, I.I.K., 1966, Ap. J. 145, 953 
Kovar, RJ»., Potter, A.E., Kovar, N.S., 1971, BAAS 3, 351 
Kraft, RJP., 1960, in Stellar Atmospheres, Ed. J.L. Greenstein, Chicago 

Univ. Press, p. 401 
Kraft, R.P., Preston, G.W. Wolff, S.C, 1964, Ap. J. 140, 235 
Kraft, R.P., Greenstein, J.L., 1969, in Low Luminosity Stars, Ed. S.S. 
Kumar, p. 65 

Kraft, R.P., 1957, Ap. J. 125, 326 

Krzeminski, W., 1969, in Low Luminosity Stars, Ed. S.S. Kumar, p. 57 
Kuhi, L.V., 1965, PASP 77, 253 

1966, Ap. J. 145, 715 

Lecontel, J.M., Praderie, F., Bijaoui, A., Dantel, M., Sareyan, J.P., 1970, 

Astron. Astrophys. 8, 159 
Lemaire, P. 1971, Thesis, University of Paris 
LUler, W., 1968, Ap. J. 151, 589 
Lo Presto, J.C, 1971, PASP 83, 674 
LoveU, B., 1971, QJRAS 12, 98 
Maltby P., Engvold, 0., 1970, Solar Phys. 14, 129 
Meisel, D.D., 1971, PASP 83, 49 
Mihalas, D., Auer, L.H., 1970, Ap. J. 160, 1161 
Miller, F.D., 1954, A.J. 58, 222 
Nariai, K., 1969, Astrophys. Space Sc. 3, 160 
GdeU, A.P., Vrba, F.J., Fix, J.D., Neff, J.S. 1970, PASP 82, 883 
Pagel, B.E.J., Tomkin, J. 1969, QJRAS 10, 194 
Payne-Gaposhkin, C, 1963, Ap. J. 118, 320 
Pasachoff, J.M., 1970, Solar Phys 12, 202 



97 

Pasachoff, J.M., 1971, Ap. J. 164, 385 

Popper, D.M., 1970, in Mass Lxjss and Evolution in Close Binaries, Ed. K. 

Glydenkerne and R.M. West (Copenhagen: Univ. Publ. Fund) p. 13 
Praderie, F., 1970, in Spectrum Formation in Stars with Steady-State 

Extended Atmospheres, Ed. H.G. Groth, P. Wellman, NBS Special Publ. 

332, p. 241 
Sanduleak, N., 1971, Ap. J. 164, L 71 
Seaquist, E.R., 1967, Ap. J. 148, 123 
Simon, T., 1970, Thesis, Harvard. 
Skumanich, A., 1972, Ap. J. 171, 565 
Smith, E. van P., 1960, Ap. j. 132, 202 
Thocias, R.N. 1957, Ap. J. 125, 260 
Thomas, R.N., Athay, R.G., 1961, Physics of the Solar Chromosphere, 

Inter-Science Publ. 
Vaughan, A.H., Zirin, H., 1968, Ap. J. 152, 123 
Vaughan, A.H., Skumanich, A., 1970, in Spectrum Formation in Stars 

with Steady-State Extended Atmosphere, Ed. H.G. Groth, P. Wellman, 

NBS Spec. Publ. 332 p. 295 
Wade, CM. HjeUming, R.M., 1971, Ap. J. 163, L 105 
Wallerstein, G., 1971, PASP 83, 77 
Warner, B., 1969, MNRAS 144, 333 

Wesson, P.S., Fosbury, R.A.E., 1972, Observatory (in press) 
Weymann, R., 1962, Ap. J. 136, 844 

Wickramasinghe, D.T., Strittmatter, P.A., 1970, MNRAS 150, 435 
Wilson, O.C, 1954, Conference on Stellar Atmospheres, Indiana Univ., 

Proc. Nat. Sc. Foundation, Ed. M.H. Wrubel, p. 147 
WUson, O.C, 1956, Ap. J. 126, 46 
Wilson, O.C, Aly, M.K., 1956, PASP 68, 149 
WUson, O.C, Bappu, M.K.V., 1957, Ap. J. 125, 661 
Wilson, O.C, Skumanich, A., 1964, Ap. J. 140, 1401 
Wilson, O.C, 1962, Ap. J. 136, 793 
Wilson, O.C, 1963, Ap. J. 138, 832 
Wilson, O.C, 1966, Ap. J. 144, 695 
Wilson, O.C, 1968, Ap. J. 153, 221 
Wilson, O.C, 1970, Ap. J. 160, 225 
Wilson, O.C, 1970, PASP 82, 865 
Wilson, O.C, R. WooUey, 1970, MNRAS 148, 463 
Zirin, H., Howard, R., 1966, Ap. J. 146, 367 



Page Intentionally Left Blank 



EVIDENCE FOR STELLAR CHROMOSPHERES PRESENTED BY 
ULTRAVIOLET OBSERVATIONS OF THE SUN AND STARS 

Lowell Doherty 

Space Astronomy Laboratory, Washburn Observatory 
University of Wisconsin 

I would like to describe observations of emission lines in stellar sources, 
in the ultraviolet region of the spectrum not accessible to ground 
observation. As we have heard, the interpretation of emission lines may 
involve both geometrical and temperature effects, so that the occurrence 
of emission Unes does not constitute prima facie evidence for chromo- 
spheres. On the other hand, we have not yet, at this conference, 
formulated a definition of a chromosphere that excludes any particular 
category of stellar emission-line objects. 

In principle, information on chromospheric structure is also contained in 
the continuum. However, the measurement of accurate spectral energy 
distributions depends on the very difficult process of ultraviolet photo- 
metric calibration. This work is continuing both at Goddard and the 
University of Wisconsin. I will not discuss continuum observations here. 
Wilson and Boksenberg (1969) have extensively reviewed instrumentation 
and results in ultraviolet astronomy up to 1969. The most recent results 
will be discussed in a forthcoming review article by Bless and Code 
(1972). 

Observations of ultraviolet emission lines are as yet confined to a few 
stars, and I will try to describe most of these observations briefly, with 
emphasis on work done since Wilson and Boksenberg (1969). Let us begin 
with the stars of earliest spectral type. The spectra of Wolf-Rayet stars 
are sprinkled with the resonance Unes of C, N, and Si, excited lines of 
these elements and of He II. Figure II- 1 shows OAO photoelectric scans 
of two Wolf-Rayet stars. The short-wavelength -segments of these scans 
(X< 1800A) have a resolution of about 12 A, while the long-wavelength 
segments, made with a different spectrometer, have a resolution of about 
25 A. Even at the low resolution of these scans, P Cyg profiles are 
evident in a number of lines, especially the resonance doublets N . V 
XI 240 and C IV XI 550. In HD 50896 (WN5), XI 496 and XI 7 19 of N V 
and XI 640 of He II are strong, as are other longer-wavelength lines of N 
and He. In 7 Vel (WC7) the C spectrum is well developed. 7 Vel has also 
been observed at 10 A resolution (Stecher 1970) and photographically at 
higher resolution (Wilson and Boksenberg 1969). L. Smith (1972) has 
interpreted the strengths of ultraviolet C, N, and O lines in HD 50896 to 



99 



100 




a BOO — 0- 



1200 



1600 



2000 



2400 



2800 



3200 



3600 



X[A]- 



Figure II-l OAO scans of selected stars. Short-wavelength segments have a resolution 
of approximately 12 A , and the long-wavelength segments 25 A. 

mean that selective excitation processes are unimportant, with the 
implication that differences between WN and WC spectra reflect real 
abundance differences. 

Among and B stars, emission has been observed in 6 Orion stars of 
spectral type 09 to B2 and luminosity class I to III, and in f Pup (05f) 
and f Per (07). Analysis of 2A resolution photographic spectra of 5 of 
the Orion stars (Morton, Jenkins and Bohlin 1968) established that 



101 



expansion velocities of some 1 500 km/sec exist in the envelopes of these 
stars, and that there is a velocity gradient for the ultraviolet lines. The 
highest velocities were obtained from the absorption components of the P 
Cyg profiles of resonance lines of Si III, Si IV, C IV, and N V. For XI 175 
of C III, velocities were between 500 and 1000 km/sec, substantially 
lower than for the resonance lines. Since XI 175 arises from a 6 ev excited 
level of the resonance triplet and is presumably formed closer to the 
stellar surface, the velocity of expansion must increase outward. Later A. 
Smith (1970) and Carruthers (1971), with resolution close to 1 N, 
obtained XI 175 velocities near 1600 km/sec in the two very hot stars f 
Pup and I Per. However, as Carruthers points out, there is the possibility 
of blending of the C III lines with N IV XI 169. 

A. Smith (1970) recorded the spectrum of f Pup nearly to the Lyman limit 
and found the resonance lines of O VI and S VI, which had previously 
been observed only in the solar spectrum. S VI X933 has a velocity of 
1380 km/sec, while VI XI 030 and the X990 resonance line of N III 
have velocities close to 1800 km/sec, which is typical of the resonance 
lines at longer wavelengths in f Pup. The more recent observations also 
suggest a greater range of velocities. Carruthers (1971) found 2650 km/sec 
for N V X1240 in | Per, while A. Smith (1970) determined the very low 
value of 150 km/sec for the excited XI 340 line of IV. 

A number of emission lines in f Pup, e.g. N V X1240, Si IV X1400 and C 
rV XI 550, are sufficiently strong to be detected in OAO scans. The Si IV 
and C IV lines have also been seen in f Ori (09.5 lb) and k Ori (B0.5 la), 
and Si IV X1400 in the 4th magnitude 09.5 supergiant a Cam. 

Emission lines have not been found in B dwarfs. For the bright Be star y 
Cas, Bohlin (1970) identified the C IV X1550 line as P Cyg type, but 
absorption features of other resonance lines such as Si III XI 206 and Si 
IV X1400 have their expected wavelengths and are labelled photospheric. 
Between the excited N IV X1718 line and 2100 A the spectrum of 7 Cas 
at 2. A resolution is rather featureless. |3Lyrae (B9 pe) shows an emission 
spectrum which probably arises in a large cloud surrounding the com- 
ponent stars (Houck 1 972). A sample OAO scan is shown in Figure 1 . In 
addition to some of the far ultraviolet resonance lines we have mentioned, 
Mg II X2800 emission is also apparent in y Lyrae. 

Although of less interest, perhaps, for the problem of stellar chromo- 
spheres, ultraviolet observations exist for Nova Serpentis 1970 (Code 
1972). OAO scans of the X > 2000 A region indicate a changing complex 
spectrum whose features cannot be easily identified at low resolution. 

Among normal stars of later type, the sun, if located a few parsecs away, 
and viewed with spectral resolution comparable to that used in present 



102 

stellar rocket experiments, could be recognized as a star with a chromo- 
sphere. Low flux levels would make such obse^yations difficult, however. 
Shortward of Mg II X2800, the ultraviolet emission spectrum of the Sun 
does not appear until Si II X1810, and C IV XI 550 is the first indication 
of fairly high temperatures. Observation of the corona would be limited 
to O VI A1030, since interstellar hydrogen would obliterate the spectrum 
below the Lyman limit. The solar Lyman lines would also be strongly 
absorbed. 

OAO scans are available for a number of bright stars of spectral type G 
and later. For such cool stars, data can be obtained only with the long 
wavelength spectrometer, and in most cases the scans are useful only for 
X > 2500 A approximately. Figure 1 includes scans of a Boo {K2 III) and 
a Ori (M2 lab), which show how rapidly the flux decreases toward 
shorter wavelengths. Mg II X2800 is clearly in emission in these stars. No 
features, either in absorption or emission, have been identified for X < 
2800 A in OAO scans of these or other K and M stars. Even where 
counting rates are relatively large, only gross features of the spectrum are 
apparent at 25 A resolution. Figure II-2 shows part of an OAO scan of a 
Cen (G2 V). One OAO (reduced) count equals 64 photomultiplier events. 
For comparison, the solar spectrum has been smeared to a resolution of 
20 A and normalized to the stellar scan at 2900 A. The major features of 
this spectrum are Mg I X2852, Mg II X2800, and the group of Fe II lines 
near X2740. There is no indication of solar Mg II emission at this 
resolution. The OAO spectrometer is stepped at intervals of 20 A, and, as 
Figure II-2 shows, it would be difficult to interpolate accurately between 
the discrete data points without the aid of the known solar spectrum. 
Moreover, scanner wavelengths are normally known only to about ± 10 A. 
Thus OAO scans of late-type stars must be interpreted with caution. 

Figure II-3 shows the changing character of the spectrum with later 
spectral type for the region X > 2800 A. Ordinate scales are different for 
each of the four stars. The location of prominent features of the solar 
spectrum are marked here for comparison. The scans at least appear to 
form a fairly smooth sequence with differences attributable to differences 
in excitation. One noteworthy feature of a Ori is the bump near 3180 A 
which is due, presumably, to Fe II emission which Weymann discussed a 
number of years ago (1962). It is not known where these Unes are 
formed. Profiles of one group of lines are similar to solar Ca II K, but 
complex velocity fields make the interpretation of these Unes difficult. I 
beUeve Aim Boesgaard will report on some recent' observations of these 
lines later today. I would Uke to point out that OAO scans of a Ori set 
upper Umits to the flux in several Fe II multiplets whose upper levels are 
common to the multiplets that produce the near ultraviolet emission 
(Doherty 1972). 



103 



800 



600 



I- 
z 

3 
O 

o 



o 

< 
o 



400 



200 




X (MICRONS) 

Figure II-2 GAG scan of a Cen compared with the solar spectrum smeared 
to a resolution of 20 A and normalized to the scan at 2900 A 

For all very cool, bright stars Mg II emission is clearly seen in OAO scans. 
Figure II-4 illustrates the 2800 A region in several class III giants.' Dots 
indicate OAO (reduced) counts measured at discrete intervals of 20 A. 
Approximate sky background has been subtracted. Exact wavelength 
registration caimot be determined, but, 2800 A does fall between the 5th 
and 6th channels, as counted from the left. Figure II-5 shows the Mg II 
region for supergiants. Only the class I stars definitely show emission 
here. Although Mg II emission fluxes can be determined only approxi- 
mately from the OAO scans, there is evidence from stars with the 
strongest emission that the ratio of Mg II to Ca II K emission flux does 
not differ greatly from star to star. Figure II-6 compares estimated Mg II 



104 




.32 
X (MICRONS) 



Figure II-3 Changes in unltiaviolet spectral features with different spectral type at 
approximately 25 A resolution. Ordinate scales are arbitrary. Principal 
features of the solar spectrum are indicated. /3 Her, G8 III; o Boo, K2 
III; a Tau, K5 UI; a Ori, M2 lab. 



105 



20 r 



10 - 



Her (4) 
n Dra (2) 



15 r 




10 



5 - 



e Cen (2) 



12 




4 - 



a Ari (1) 




Z) 

o 

" 30 



20 - 



10 - 



a B'oo (3) 



30 




20 - 



10 - 



12 r 



a Tau (2) 



And (2) 



.^i. 



/v^ 



k 2800 REGION IN GIANTS 

Figure II-4 Spectra of selected G-M giant stars in the 2800 A region. These averaged 
OAO scan segments cover 220 A, with the position of X2800 falling be- 
tween the 5th and 6th channel as counted from the left 



emission, counts for 8 stars with IW, a measure of the Ca II K emission 
flux observed at the earth (Doherty 1972). 

Vertical bars indicate the Umiting values for the Mg II counts that must 
be assigned as a result of the uncertainty in the strength of the underlying 
absorption feature. These stars are giants and supergiants of spectral type 
K2-M2. Within the eriors of measurement it is possible that the ratio Mg 
Il/Ca II K is the same for all of these stars. The solar symbol shows the 
position the Sun would occupy if its visual magnitude were zero. The 
method of calculating IW does not attempt to subtract the underlying 
absorption profile of the K line. This does not affect the stellar values 
appreciably, but the solar value of IW in Figure II-6 represents the total 
flux emitted in the wavelength band that includes the K emission core 
and not the net emission. Thus the significance of the approximate 
agreement between the ratio for the Sun and stars with strong K emission 
is not immediately apparent. 



106 



15 



Dra (2) 



10 - 



15 



10 



a Cas (2) 



15 



10 



y Aql (2) 



5 - 



i- 

O 
■^ 6 



4 - 



2 - 







< Cep (2) 




15 



10 - 



5 - 







a SCO (1) 




15 



10 



5 - 







a Ori (6) 




X 2800 REGION IN SUPERGIANTS 
Figure II-5 Spectra of selected G-M supergiant stars in the 2800 A region. 



Recently, Kondo, Modisette and Giuli (1971) have obtained high- 
resolution (1/2 A) photoelectric scans of the 2800 A region in 5 stars 
covering a wide range of spectral type. The observations were made from 
a balloon. They find that a Ori has doubly-reversed Mg 11 cores, 
quaUtatively siniilar to the profdes of the solar lines. The only other cool 
star for which Mg II has been observed with better than OAO resolution 
is Arcturus. At a resolution of 7 A Mg II appears as a single emission line 
in this star (Kondo 1972). Arcturus has also been observed in the far 
ultraviolet by Moos and Rottman (1971) who report the measurement of 
emission in Lyman a and a Une which is probably XI 304 of 01. 

It is exciting to consider the prospect of having further, more detailed 
observations of the ultraviolet spectra of stars that we expect to have 
chromospheres similar to the Sun's. Such observations will, however, be 
relatively difficult and costly, due to the very low fluxes that must be 
measured. If we look at the characteristics of the rocket spectrographs 
(both photographic and electronographic) that have been used to obtain 1 



107 



14 



12 



10 - 



I- 

z 

o 
o 

C3> 



8 - 



6 - 



4 - 



1 

1 




®- 

1 1 1 1 1 1 



IW(CanK) 



Figure II-6 Mg II X2800 emission (OAO reduced counts) vs. IW, a measure of Call K 
emission flux at the Earth. The Sun is shown as it would appear if it were 
a V=0 star measured in the same way. 



A resolution spectra of and B stars, these instruments have, on the 
average, a product of collecting area times exposure equal to roughly 
1500 cm^ sec. To obtain the same kind of data for cooler stars of the 
same visual magnitude, the aperture or the observing time must be larger. 
In the far ultraviolet, the increase can be enormous. Figure II-7 is a 
color-color diagram obtained from OAO wide-band filter observations at 
1700 A. Relative to the visual, the 1700 A flux of stars varies by a factor 
of almost 10"* from type O to the coolest stars shown, which have 
slightly earher spectral types than the Sun. Increases in collecting area and 
exposure of this magnitude cannot be accommodated in rocket exper- 
irnents. Thus different techniques must be considered. For example, 
completely photoelectronic recording can increase the instrumental sensi- 
tivity. At present, however, the gain is fuUy reaUzed only by observation 
of one spectral band in one object (with one photometei). Continuing 
development of electronic image intensification and recording systems 
promises eventually to help this problem by making possible essentially 



108 




Figure II-7 SteUar Xl700 - V color vs. B-V with 1700 A wide-band . 
photometry from OAO. 

simultaneous observation of many image elements. Nevertheless, different, 
generally more restrictive kinds of observations will be necessary for cool 
stars. 

It is possible that the already large factor of 10** decrease in flux we have 
seen in Figure 6 will not become greater for certain observations made at 
wavelengths shorter than 1700 A or for cooler stars. In the Sun the 
strongest chromospheric lines between 1700 A and the Lyman limit 
produce about the same photon flux as 1 A of the continuum near 1700 
A. If stars of later type than the Sun have chromospheric temperatures 
more nearly like the solar chromosphere, then the detection of their 
strongest emission Unes might be possible with the same effort required to 
observe solar-type stars, for which the factor 10^ applies roughly to all 
strong lines. 



109 

Given the much greater difficulty of obtaining ultraviolet data for cool 
stars, perhaps some theoretical work might be directed toward the 
question of which specific ultraviolet measurements would be most 
helpful in understanding the nature of stellar chromospheres. GuideUnes 
of this sort could prove very useful for the efficient selection and design 
of future ultraviolet experiments. 

Preparation of this paper was supported-, in part, by NASA NAS 5-1348 
contract. 

REFERENCES 

Bless, R.C. and Code, A.D. 1912, Ann. Rev. Astron. Astrophys., in press. 

Bohlin, R.C. 1910, Astrophys. J., 162 571. 

Carruthers, G.R. 191 1 , Astrophys. J., 166, 349. 

Code, A.D. 1972, in Sci. Results of OAO-2, ed. A.D. Code (Washington: 

U.S. Government Printing Office), in press. 
Doherty, L.R. 1972,/6af. 
Houck,T.B. 1972, ibid. 
Kondo, Y. 1912, Astrophys. J., 171, 605. 
Kondo, Y., Modisette, J.L., and Giuli, R.T. 1971, paper presented at 

136th meeting of A.A.S. 
Moos, H.W., and Rottman, G.J. 1971, ibid. 
Morton, D.C., Jenkins, E.B., and Bohlin, R.C. 1968, Astrophys. J., 154, 

661. 
Smith, A.M. 1910, Astrophys. J., 160, 595. 
Smith, L.F. 1972, in Sci. Results of OAO-2, ed A.D. Code (Washington: 

U.S. Government Printing Office), in press. 
Stecher, T.P. 1910, Astrophys. J., 159, 543. 
Weyman, R. 1962, Astrophys. J., 136, 844. 
\Wlson, R. and Boksenberg, A. 1969, Ann. Rev. Astron. Astrophys., 7, 

421. 

DISCUSSION FOLLOWING TALKS 
BY PRADERIE AND DOHERTY 

Kuhi — Now I'd like to call on Rottman to give you a sununary of his uv 
spectral work on Arcturus. 

Rottman — J would like to discuss an ultraviolet spectrum of Arcturus 
obtained from a sounding rocket flight. This experiment was a sequel to 
one which identified the Ly a emission as reported in Ap. J. 165, 661, 
1971. In the present experiment, definite emission lines were observed 
in the spectral region 1200 A to 1900 A. It is expected that such 



110 

emission lines will give unambiguous evidence of the existence of and 
detailed information on chromospheric type layers. This work will be 
published by Warren Moos and myself. 

Kuhi — I'd like for Kondo to present his work on high resolution scans of 
the Mg II resonance doublet in late type stars. 

Kondo — This work was done in association with Tom GiuU and A.E. 
Rydgren of the NASA Manned Spacecraft Center and Jerry Modisette of 
Houston Baptist College. We report the initial results of a balloon-borne 
experiment designed to investigate emission of the Mg II resonance 
doublet in stars. The Mg II resonance doublet at 2795.5 A and 2802.7 A 
(3s ^S - 3p ^P°) is the ultraviolet magnesium counterpart of the Ca II 
resonance doublet at 3933.7 A and 3968.5 A (4s ^S - 4p ^P°). For 
certain spectral type stars the Ca II doublet has been observed in 
emission, which is believed to indicate chromospheric activity in these 
stars. 

The Earth's atmosphere is opaque to radiation at 2800 A, and untU 
recently the Mg II doublet emission had been observed only in the solar 
spectrum, by means of rocket-borne and satellite payloads. Comparison of 
the Ca II and Mg II emission in the solar spectrum indicates that the 
latter is by far the more distinct and prominent of the two. 

There are several theoretical reasons why the Mg II emission should be 
more prominent than the Ca II emission, at least for certain spectral 
types. First, the cosmic abundance of magnesium is about 17 times 
greater than that of calcium (Allen 1963). Second, the ionization and 
excitation potentials of magnesium and calcium are such that in A and F 
stars, the Mg II resonance lines are nearer to their maximum strength than 
are the Ca II resonance Unes. Thus, for these stars one expects deeper and 
wider absorption lines for Mg II than for Ca II, which makes weak 
emission in the line bottom easier to detect. Third, for stars of spectral 
type later than A, the continuum level of 2800 A is lower than at 3950 
A, facilitating detection of any weak emission. The Ca II doublet emission 
becomes difficult to observe in stars earlier than mid-F, and one of the 
objectives of this experiment is to determine whether the difficulty is due 
to observational hmitation or to the disappearance of the mechanism 
re^onsible for the chromospheric emission. The other objective of this 
experiment is to survey the behavior of the Mg II resonance doublet in 
stars of various spectral types. 

Recent low resolution UV spectrophotometry from OAO-2 (Doherty, 
1971) and from a rocket (Kondo 1972) show Mg II doublet in unresolved 
emission for stars later than K2. 



Ill 

The current experiment was conceived to scan the Mg II doublet with 
spectral resolution of at least 0.5 A for emissions anticipated for F-type 
dwarfs brighter than m^ <*< 5. It was felt that the 0.5 A resolution would 
be required to unequivocally detect weak emission and also to study the 
detailed structure of stronger emission lines. The 0.5 A resolution is a 
compromise between high resolution and available observing time. Current 
operational balloons can carry a sizeable telescope to altitudes approxi- 
mating 40 1cm and can maintain those altitudes for an entire night. At 
these altitudes the atmospheric extinction for X 2800 radiation is 
approximately 50% (Goldberg 1954), so one can expect balloon payloads 
to have decided advantages over rocket payloads for observations in this 
wavelength range. 

Our payload consists of a 40 cm Cassegrain telescope with an Ebert-Fastie 
spectrometer, a three-stage star acquisition and tracking system, command 
and telemetry electronics, and structural components. Figure II-8 is a 
drawing of the assembled payload. A sketch of the instrument portion of 
the payload is shown in Figure II-9. 

For acquisition of a target star, the telescope is pointed to within 1°.5 of 
the star in azimuth by referencing a two-element magnetometer to the 
horizontal component of the Earth's magnetic field. The telescope is 
pointed to within 0°.5 of the star in elevation by means of a position- 
sensing potentiometer referenced to local vertical. The platform star 
tracker acquires and centers the target star, which need not be the 
brightest star in the 1° by 3° field of view of this star tracker. This star is 
then tracked by the platform star tracker with an accuracy of — 1 arc 
minute. 

A dichroic filter located behind the primary telescope mirror reflects into 
the spectrometer the Ught from the star which is in a narrow band of 
wavelengths centered at 2800 A. The visible light from the star is 
transmitted through the dichroic filter to an image position sensor. 
Position signals from this sensor are used to control the movable 
secondary mirror to maintain a fine-pointing accuracy of ± 1 arc seconds. 
The spectrometer grating has 2160 lines per mm and gives a second-order 
spectrum with a dispersion of 3.3 A mm^ . The detector for the 
spectrometer is an ITT F4012 image dissector tube with a i4 A "slit". 
The spectrum is scanned repetitively in % A steps with scan lengths of 4 
A, 24 A or 50 A. The appropriate scan length is chosen in real time and 
placed anywhere in the spectraT range 2775 to 2825 A by command from 
the ground. For further details regarding the payload and instrument, see 
Kondo et al. (1972), Gibson et al. (1972) and WeUs, Bottema and Ray 
(1972). 



112 




Figure II-8 Balloon-borne ultiaviolet stellar telescope-spectrometer payload. 

The payload is carried to an altitude of 40 km by a 430,000 m^ 
polyethylene single cell balloon. Observations are begun after payload 
sunset and continue until payload sunrise or until the payload drifts out 
of telemetry range (600 - 650 km from the ground station). The zenith 
obscuration at float altitude due to the baUoon has a radius of 27°. The 
ground station at the launch site maintains continuous telemetry and 
command communication with the payload. 

For target acquisition, it is necessary to provide the elevation and azimuth 
angles of the star relative to the payload's local vertical and magnetic 
north respectively. The latitude and longitude of the payload are 
monitored by means of the DOD Omega navigation system. The necessary 
calculations for target acquisition are performed in the ground station 
using a desk-top digital computer while observing another star. Normally, 
less than ten minutes are required to perform the calculations, transmit 
the commands and acquire the target star. 



113 



PLATFORM STAR 
TRACKER 



E BERT- FAST IE 
SPECTROMETER 




40CM.APERTURE F/7. 5 
TILTED APLANATIC TELESCOPE 



DICHROIC FILTER 
r- IMAGE POSITION SENSOR 



IMAGE DISSECTOR TUBE 



Figure II-9 Schematic telescope and spectrometer layout. 



Once a target star is acquired, the scanning of the spectrum is begun and 
the data are telemetered to the ground station. The accumulated spectrum 
is displayed on a large oscilloscope so that the investigators can watch the 
counts build up, and the data are simultaneously recorded on magnetic 
tape for subsequent analysis. The oscilloscope data display allows the 
investigators to make real-time decisions regarding scan mode and length 
of observing time for each star. 

Our raw data were in the form of counts per 50 milliseconds per Va A 
channel. The magnetic tapes containing the data were analyzed to 
separate and accumulate the data for each star and to give the wavelength 
calibration and background count information. Using in-fUght scans of an 
on-board wavelength reference lamp, we have calibrated our wavelength 
scales to an accuracy of ± i^ A. Corrections for the Earth's orbital motion 
have been applied to reduce the observed wavelength scales to the Sun. 
No corrections for sky background and dark count have been made, since 
with the possible exception of the continuum of a Ori, they were 
negUgible compared with the stellar flux. 

From laboratory measurements and the analysis of in-flight wavelength 
reference line profiles, we have determined our resolution to be between 
0.25 and 0.5 A. Except as noted for y Lyr, our data are presented in the 
form of observed counts per \i A channel. The statistical uncertainty of 
each data point is the square root of the plotted value. 



114 



For the c Lyr data, an alternate approach was made to the error analysis, 
by generating Monte Carlo simulations of the spectrum taking into 
account both counting statistics and smearing in wavelength. The results 
with regard to identification of features were not significantly different 
from the conclusions indicated by the error bars in Figure 11-10. 



80 - 



60 



40 



20 - 




2780 



2790 



2800 



WAVELENGTH 



Figure 11-10 Observation of the Mg 11 lines in /3 Lyr on 1971 June 6/7. The arrows 
indicate the Mg II line centers at the radial velocity of the B-star com- 
poment at the time of observation. 

We have thus far observed Lyr, 7 Lyr, ^ Cas, a CMi and a Ori. The 
first two were observed on the night of 1971 June 6/7, and the latter 
three were observed on the night of 1971 October 7/8. 

^ Lyr (Bpe, rriy = 3.7v) - The well-known ecUpsing binary /3 Lyr was 
observed near S** UT on 1971 June 7. The presence of numerous emission 
features in the visible spectrum of ^ Lyr su^ested that it would be a 
likely candidate for interesting spectral features involving the Mg II 
resonance doublet. This was borne out by our observations. One represen- 
tative scan of j3 Lyr is shown in Figure 3. This shows broad overlapping 
emission features with deep absorption on the short-wavelength sides of 
the emission peaks. The line profiles are similar to the profiles of the 
emission lines in the visible spectrum of this star. 

Using the ephemeris of Wood and Forbes (1963), we compute the phase 
of our observation to be OP .89. The radial velocity curve of Abt (1962) 



115 



gives a radial velocity of + 1 20 km sec^ for the B-star component at the 
phase of our observation. The line centers of the Mg II doublet in the 
B-star are near the tops of the emission peaks. The two absorption 
features are about 2 A or 200 km sec ^ in width. Abt determined the 
7-velocity of the system to be -19.5 km sec"*. The line centers at 
the 7-velocity of the system are located in the deep absorption features. 

We note that the emission spikes longward of the two emission peaks are 
statistically significant and are displaced equal amounts from the B star 
line centers. We obtained three other 50 A scans of j3 Lyr along with 
several partial scans. Intercomparison of this data suggests that there were 
significant changes in the emission portions of the features on a time scale 
of tens of minutes. 

7 Lyr (B9III, m^ = 3.3) - We observed 7 Lyr briefly during the first 
flight to confirm the accuracy of the pointing system of the payload. In 
the scan mode used to observe 7 Lyr, the time required to obtain 8 
counts per V4 A channel was measured. Because of the low accuracy of 
this data, we have averaged this data over Vi A intervals. These data points 
have been converted for display purposes to the number of counts which 
would have been observed in 3.2 seconds per ^ A channel. The resulting 
scan of 7 Lyr is shown in Figure II-l 1. The statistical uncertainty of each 
plotted point is 25% of the plotted value. 



16 - 



3 
O 
U 




27eo 



2790 2800 

WAVELENGTH 

Figure II-H Observation of the Mg 11 Unes in 7 Lyr on 1971 June 6/7 



2810 



116 

The Mg II resonance doublet in 7 Lyr appears as two deep, separated 
absorption lines. Correction for the stellar radial velocity of -22 km sec"* 
(Hoffleit 1964) places the line centers at the observed absorption minima. 
The 2795 A line is deeper and wider than the line at 2802 A, as expected 
from the statistical weights. Although the exact continuum level is 
somewhat uncertain, the residual intensity in the bottom of the 2795 A 
line appears to be about 0.1. There is no evidence for any emission 
associated with the Mg II lines in this star. 

One objective of this project is to look for Mg II emission in early and 
mid F stars along the main sequence. Wilson (1966) studied rotational 
velocities and Ca II H and K emission along the main sequence between 
b-y = 0.240 and b-y = 0.440. He determined the regions of fast and slow 
rotation in the Ci -(b-y) diagram as shown in Figure 11-12. Wilson found 
that the "fast rotation" region contained some slow rotators, while the 
"slow rotation" region contained no fast rotators. The boundary between 
the regions intersects the zero-age main sequence (ZAMS) near b-y = 
0.285. Using 10 A mm ^ Coude spectra, Wilson detected Ca II emission 
only as early as b-y = 0.304, although he suspected that higher-dispersion 
spectra might show Ca II emission as early as b-y = 0.275. We observed 
the Mg II resonance lines in the main-sequence F-stars |3 Cas and a CMi 
during the second flight. Both stars are plotted in Figure 11-12 on the 
basis of the uv by photometry in the Stromgren-Perry Catalog (Stromgren 
and Perry 1965). 

/3 Cas (F21V, m^ = 2.2) - Using the absolute magnitude caUbration of 
Stromgren (1963), we find that jS Cas is about 1'".4 above ZAMS. The 
Mg II resonance lines in ^ Cas (Figure 11-13) appear as broad overlapping 
absorption lines with distinct minima. The 2795 A line is deeper than the 
2802 A line. There is no prominent Mg II emission in this star. In order 
to investigate the existence of weak emission in the 2795 A component we 
have smoothed the data over successively more channels in Figure 11-14. 
The curves demonstrate that, even when the data are smoothed over 1 A, 
the possible emission is still apparent. The stellar radial velocity is + 12 
km sec^ (Hoffleit 1964). (Although |3 Cas is Usted by Hoffleit (1964) as a 
spectroscopic binary, Abt (1970) finds no convincing evidence for this.) It 
is interesting to note that the low data points at 2795.5 A are at the 
expected Une center and might be a "K3 " component. The flat residual 
intensity which occurs in the bottom of the 2802 A line may constitute 
weak emission at this wavelength. 

a CMi (Procyon F51V, m^ = 0.3) — According to the Stromgren-Perry 
catalog photometry and Stromgren's (1963) caUbration, Procyon is about 
o'".4 above ZAMS. Procyon's b-y value of 0.272 places it just outside 
Wilson's sjow rotation region, but he classified it as a slow rotator. Kraft 



117 



.80 


_ 


1 

• 


1 


1 1 




~ N 


/3 Gas 




- 


.60 


- 


"^ 


O. CMi 


- 


1 

.40 


- 


/ 
ZAMS 

1 


1 


1 1 



.20 



.25 



.30 



.35 



b-y 



Figure 11-12 Ci-(b-y) diagiam for F stars. The solid line is Stromgren's (1963) Zero 
Age Main Sequence. The broken line is the boundary between Wilson's 
(1966) fast and slow rotation regions. 

and Edmonds (1959) found "feeble but definitely present" Ca II emission 
in Procyon, using 3.2 and 4.8 A mm"' spectra. They noted that the 
short -wavelength side of the emission appeared stronger than the long- 
wavelength side. Our microdensitometer tracing of the Coude plate of 
Procyon provided by O.C. Wilson (Figure 11-15) also shows a similar weak 
Ca II K emission feature. Recently, Linsky (1972) observed similar K 
emission. Our Mg II observations of Procyon appear in Figure 11-16. 
Procyon has a faint companion (Bco A 10) with an orbital period of 
about 40 years. Ihe y velocity of the system is 4 km/sec and the 
semi-amplitude of the spectroscopic orbit is only 1.3 km/sec (Jones 
1928). Thus the true Mg II Une centers should be at 2795^1 and 2802 3/4 
A. The most noticeable difference between the Procyon and /3 Cas Mg II 
lines is the distinct emission which appears in the Procyon lines. The 
emission feature at 2795 A is asymmetrical, with the stronger emission on 
the short -wavelength side, analogous to the Ca II observation in Procyon. 

a Ori (Betelgeuse M2Iab, m^ = 0.8v) — Our Mg II observations of the 
supergiant a Ori are presented in Figure 11-17. This shows both of the Mg 



118 



3 
O 
O 



200 


- 


1 

Beta 

A 


1 
Cos 


1 ■— 1 ■ 


> - 


100 


V 


\ 


1 • 


1 1 


1 1 1 



2790 



2810 



2800 
WAVELENGTH 
Figure 11-13 Observation of the Mg 11 lines in /3Cas on 197 1 Oct. 7/8. 



II resonance lines dramatically in emission, with each Une showing 
prominent self-reversal. Figure 11-18 shows a microdensitometer tracing of 
the vicinity of the Ca II K line in a Ori from a Cbude plate loaned by 
O.C. Wilson. The Mg II emission is far more pronounced than the Ca II 
emission in this star. 

The Mg li line centers corrected for the stellar radial velocity of + 21 km 
sec^ (Hoffleit 1964) should be located at 2795 3/4 and 2803 .0 A. The 
observed self-reversal minima are located at 2796.0 and 2803.5 A. 
Considering our wavelength caUbration uncertainty of ± ^ A and our 
resolution of between 0.25 and 0.5 A, it is not clear that the observed 
separation of the "K3" and "H3" minima is significant. We note that the 
"K3" minimum in a Ori is deeper than the "H3" minimum. 

One of the striking features of the Mg II emission in o Ori is that the 
2802 A line is almcut perfectly symmetric, while the 2795 A line is 
definitely asymmetric . The height of the shorter-wavelength "Kj " peak is 
significantly lower than the height of the longer-wavelength "Kj" peak, 
although the "K3" minimum is centered on the emission feature. Our 
planimetering of the two lines shows that the area under the 2802 A line 
is about 12% greater than the area under the 2795 A line. This difference 
in line shape between the 2795 and 2802 A components is most puzzling. 
We are not sure how much of the count level outside the emission is true 
stellar continuum and how much is background count. 



119 



300 



200 



3 
o 



100 




2790 



2800 
WAVELENGTH (A) 



2810 



Figure 11-14 The observation of the Mg II lines in 0Cas smoothed 
successively over 1, 2, 3, 4, 6 and 8 channels. 



We have measured the widths of both Mg II emission features in a Ori, 
the width of the 2795 A emission in a CMi and the width of the possible 
2795 A emission in |3 Cas. We have also estimated the width of the 2795 
A emission in the solar spectrum from the published data of Purcell et al. 
(1961) and Lemaire (1970). Our estimates of the Mg II emission widths 
and their uncertainty are given in Table II-l . 





TABLE 11-1 




Mg II Emission Widths 


Star 


Width (A) 


Uncertainty (A) 


a Ori 
jSCas 
a CMi 
Sun 


3 3/4 
2 1/2 
1 1/2 
0.7 


■%. +y2 

±0.1 



120 




Figure 11-15 Microdensitometer tracing of the Ca II K line in aCMi 
The arrows indicate the Kj peaks. 



Figure 11-19 is a plot of absolute visual magnitude versus Log W, where W 
is the full width of an emission hne at its base in km sec"" . This figure 
shows the Wilson-Bappu (1957) relationship between My and Log W for 
Ca II K emission. On this figure we have superimposed our Mg II emission 
widths with error bars. Excluding ^ Cas, for which we are not certain that 
there is emission, we find that the Mg II emission widths are wider than 
the corresponding Ca II widths by A log W » 0.4. The present data are 
too limited to indicate definitely whether or not there is a unique 
relationship in this diagram from Mg II emission which is essentially 
independent of spectral type and emission strength, as is the case for Ca 
II. 

The difference in width between the Ca II K and Mg II 2795 A emission 
lines probably depends in part on the greater abundance of magnesium 
over calcium. However, it may also depend on the heights at which these 
"collision -controlled" lines are formed. The higher excitation and ioniza- 
tion potentials of magnesium provides an argument for Mg II lines being 
predominately formed at higher temperature and hence higher altitudes in 
the steDar chromosphere . An additional argument for Mg II line formation 
at higher altitudes is the increased optical thickness of the Une due to the 
greater magnesium abundance. If the lines are formed at higher altitudes, 
then either increased turbulence, Doppler spreading due to a progressive 
increase in the radial flow velocity (if there is a stellar wind), or diffusion 



121 





- 


' 


1 1 


1 1 


- 


800 


_ 






A 


_ 




_ 


Alpha 


CMi 


/ 


_ 


600 


- 






/ 


- 


400 


: \ 


K 


aA 


/ 


- 


200 


- 


1 


1 1 


r 

I 1 


- 



2790 



2800 
WAVELENGTH 



2810 



Figure 11-16 Observation of the Mg II lines in aCMi on 1971 Oct. 7&8. 

of the photons in wavelength for an optically thick line center could 
work to increase the line width. 

We wish to thank the many people who supported us in the design, 
fabrication, testing, and flight support of the instrument. Finally, we 
would like to thank Dr. O. C. Wilson for making available his ground 
based Coude plates for comparison with our balloon observations. 

REFERENCES 

Abt, HA. 1962, Ap. J. 135, 424. 

. l970,Ap.J.Suppl. 19,387. 

Doherty, L.R. 1971, Phil. Trans. Roy, Soc. Lon. A270, 189. 

Gibson, W.C, Guthals, DJL., Jensen, J.W. and Eccher, J A. 1972, sub- 
mitted to Rev. Sci. Instr. 

Goldberg, L. 1954, The Solar System, II, GP. Kuiper, ed. (Chicago: 
University of Chicago Press), p. 434. 

Hoffleil, D. 1964, Catalogue of Bri^t Stars (New Haven: Yale University 
Observatory). 



122 



120 - 



S 80 



40 - 




2790 



2600 
WAVELENGTH 
Figure 11-17 Observeration of the Mg II lines ina Ori on 1971 Oct. 7/8. 



2810 




Figure II-l 8 Microdensitometer tracing of the Ca II K line in a Ori. 
The arrows indicate the K2 peaks. 



123 




1.4 1.6 1.8 2.0 2.2 2.4 2.6 



LOG W 

Figure 11-19 Plot of My versus Log (W), where W is the width of an emission line in km 
sec"*. The filled circles are Ca II widths from Wilson and Bappu (1957) 
The dotted circle is the Ca II width in the Sun (Wilson and Bappu 1957) 
The squares are Mg II widths in a Ori, j3 Cas and a CMi respectively, in 
order of decreasing luminosity. The triangle is the solar Mg II width. 



Jones, H.S. 1928, M.N.RA.S. 88,403. 

Kondo, Y. 1972, Ap.J. 171, 605. 

Kondo, Y., Giuli, R.T., Modisette. JL. and Rydgren, A.E. 1972, sub- 
mitted to ApJ. 

Kraft, RP. and Edmonds, F.N. Jr. 1959, Ap. J. 129, 522. 

Lemaire, P. 1970, in Ultraviolet Stellar Spectra and Related Ground-based 
Observations; L. Houziaux and HE. Butler, ed. (Dordrecht: D. Reidel 
Pub. Co.), p. 250. 

Linsky, J.L. 1912,IAU ColloguiumNo. 19, in press. 

Purcell, J.D., Boggess, A. Ill' and Tousey, R. \96\, Ann. Intern. Geophys. 
Year 12, Part II, 627. 

Stromgren, B. 1963, Basic Astronomical Data,. K. Aa Strand, ed. 
(Chicago: University of Chicago Press), p. 123. 



124 

Stromgren, G. and Perry, Ci. 1965, Photoelectric uvby Photometry for 

1217 Stars Brighter than 6m.S, unpublished. 
Wells, C.W., Bottema, M. and Ray, AJ. 1972, submitted to Applied 

Optics. 
Wilson, O.C. and Bappu, M.K.V. 1957, ^pj. 125, 661. 
Wilson, O.C. 1966, ApJ. 144, 69^5. 
Wood, D.B. and Forbes, J.E. 1963, AJ. 68, 257. 

CONTINUATION OF DISCUSSIONS FOLLOWING 
TALKS BY PRADERIE AND DOHERTY 

Kuhi — Now let's have a general discussion of Francoise Praderie's paper. 
Let's first discuss the question of what we do mean by a chromosphere 
from an observational point of view. One thing that bothers me a great 
deal is the distinction between a stellar chromosphere as we've come to 
think of it in the Sun and the changes that seem to take place as one 
goes from cool stars Uke the Sun to hotter and hotter stars in which the 
distinction between the defining characteristics becomes ever more vague, 
in separating out a chromosphere, an extended atmosphere, an extended 
envelope, and so on. 

Aller — I think it is very- important to make, as you say, a distinction 
between a chromosphere on the one hand, and what have loosely been 
called extended envelopes and shells on the other. There are a number of 
objects in which the gradation from one to the other is certainly not clear 
cut. A good example is RR Telescopii. In that star you see a spectrum of 
ionized titanium and iron that looks quaUtatively somewhat like the flash 
spectrum of the Sun. Superimposed on it, however, are increasingly higher 
levels of excitation; both forbidden and permitted iron lines, ranging on 
up from [Fe II] to [Fe VII]. In fact, [Fe VII] suppUes the strongest 
features in the emission spectrum of this object. In looking at the 
spectrum carefully there seems to be no place where you can say 
everything of one or two levels of ionization should be assigned to an 
ordinary chromosphere and everything else is to be attributed to some- 
thing else. There seems to be a steady gradation in excitation. It's almost 
as though we were looking at the solar spectrum, in the near UV region. 

Steinitz — I would like more clarification of the definition of a 
chromosphere. One of the necessary conditions was defined to be mass 
flux, and it wasn't clear whether the idea was mass loss, or accretion, or 
just mass motion. Also could you clarify what exactly is meant by 
non-radiative energy transfer? Should this include or exclude specifically 
convection? 

Praderie — I did not want to include mass loss as such as a necessary 
condition for a chromosphere, because I have no clear evidence that the 



125 

mass loss is unequivocally bound to the existence of a specific region in 
the atmosphere. One can find mass loss as shown fi-pm the shape of 
profiles in lines of photospheric origin in some stars, whereas, in other 
stars, the mass loss is expected to occur only in the corona. So the mass 
loss itself I did not include in my discussion. Mass flux was meant as any 
net transport of natter in a certain re^on, of v^ich maybe the mean 
value over time or over some distance can be zero. Now, concerning the 
non4^adiative energy transport, it is not restricted to the chromospheric 
layers. In the photosphere you can have it too (turbulent, progressive 
waves, convection, etc.), but there is no dissipation to heat the thermal 
pool at that very place. So then I call chromospheric the region where the 
dissipation starts to act. 

Steinitz - It is not clear how the observables which you discussed are 
directly connected, even though they were classified as direct and indirect 
observables with those criteria just now mentioned. 

Praderie - I am aware that I have not clearly made a bridge between 
what one would wish to do, according to the scheme which was given in 
the introduction, and all the detailed observations which are available 
now. This is a diagnostic task which is far from being completed. 

Athay - I think the question of the definition of chromosphere is very 
critical. We ought to use a definition that will allow us to talk about 
chromospheres with the least amount of confusion. I think that the way 
we defined it yesterday and today would lead to a maximum amount of 
confusion. The proposed definition requires a very careful interpretation 
of data and is not one which you can very easily go to from observations. 
We should define chromosphere for use in the literature as requiring the 
minimum amount of interpretation of data. I think it ought to be defined 
in terms of temperature reversal which you can at least hope to get to in 
a simple way. I don't see how an observer could ever get to an observable 
of mechanical energy flux. So, if we use that as the definirig characteristic 
we'd have to restrict the observers from ever using the term 
chromosphere, leaving it oiJy for the use of theoreticians. 

Kuhi - By mechanical energy flux do you exclude mass loss then? 

Praderie - I exclude it, maybe for convenience. In reply to Athay, I 
admit that we have apparentiy confused things by giving a definition 
which is bound to theoretical considerations; but it is my feeling that only 
from properly analyzed observations can you presume the presence of a 
chromosphere. I tried to show that if you have a positive outward 
temperature gradient it doesn't tell you enough. Even if you have none, 
you may miss the start of the chromosphere. 1 think one has to look for 
general definitions, not only for operational ones. 



126 

llioinas — Here I also disagree with Athay. Let me give you two 
examples. It seems to me that we should be defining things which the 
observers can use unambiguously when they look at data. My two 
examples are the atmosphere of the Sun and the atmosphere of a 15,000° 
star. The basic question for the interpretation of stellar atmospheres is, is 
it sufficient just to drop the assumption of LTE? Or must I also drop the 
assumption that there are only radiative energy sources? To me, a 
chromosphere is that atmospheric region for which I must drop the 
assumption of radiative equilibrium. This is very clear conceptually. From 
a purely observational standpoint what then is the situation? In the Sun, 
at T = 1,1 have a temperature of about 6000°. I have a temperature 
minirhum of about 4200°, judging from the observations. At a height of 
about 500 km in the chromosphere, the temperature is again about 
6000°. Now the maximum temperature one would get from radiative 
processes alone is about 5300°, based on the work of Cayrel, Frisch and 
others. Hence, for the Sun, we can infer the input of non -radiative 
energy. Now for the 15,000° star, pure continuum models give a 
maximum boundary temperature of about 9500°, based upon the work of 
Auer and MihaUs and the simple calculations of Gebbie and Thomas. The 
introduction of the effect of Unes on populations may raise this value as 
high as 13,800°. The clear cut observational question to be answered, 
then, is do the temperatures prevailing outward from the temperature 
minimum of the 15,000° star exceed the value predicted from radiative 
equihbrium models? If so, we can infer the dissipation of non-radiative 
energy and hence the existence of a chromosphere. 

Conti — I would like to take a heretical view of the chromosphere by 
defining it in a simple way. Suppose we say that any time you see 
emission lines you have evidence for the existence of a chromosphere. 

Kuhi — How would that allow one to distinguish between chromospheres 
and large scaleextended atmospheres? 

Conti — Maybe there is no essential difference, except in the scale. If a 
theoretician tells me that a chromosphere is present, I know that I'll see 
emission lines. The only question that remains is, if you see emission Hnes 
in Wolf-Rayet stars. Of stars, or early A or B stars, does it necessarily 
imply the existence of a temperature rise, mechanical heating or mass 
loss? I don't wish to go into a detailed theoretical discussion on this, but, 
as far as I know, where emission lines are seen, at least one of these three 
phenomena is always present. So we could have, as a working definition, 
that a chromosphere is a region in a stellar atmosphere which gives rise to 
emission lines. 

Kuhi - Are there contrary views? I beUeve the problems for both the 
observer and the theoretician are much worse than Dick indicated. 



127 

Underhill — I agree with Conti. However, I believe the problems for both 
the observer and the theoretician are much worse than Dick indicated. 

Kondo — With regard to Conti 's definition, I wonder if you would 
include close binaries in this category. They do have different problems 
than other stars such as those involving mass transfer and mass loss. Our 
balloon observations and OAO-2 observations show that j3 Lyrae has 
magnesium doublet emission, for example. 

Conti — One could make exceptions but one could also use these to 
ilustrate the point. There are close binaries which have greatly enhanced 
H and K emission. X Andromedae is a fine example. Its emission Unes are 
certainly chromospheric. And so we see that the chromospheric pheno- 
menon has been accentuated by heating in a close binary. 

Underiiill .— My definition of a chromosphere is that region of a stellar 
atmosphere that deviates from a simple model. Figure 11-20 shows the 
predicted flux envelope for an ordinary 13,000°, log g = 4.0 model 



I I I I I I I I I I I I I 




2B00 3200 3600 4000 MOO 4800 5200 S600 



Figure 11-20 



128 

atmosphere, calculated in hydrostatic equilibrium, in LIE, with the plane 
paraDel assumption, etc. 13,000° is a fair choice of effective temperature 
for a B7 or B6 star like a Leo. The ground-based observed absolute fluxes 
are in units of 10^° ergs/ cm^ /sec/ A. As shown the model calculations fit 
the ground-based data like a glove. Also shown are the UV observations 
from OAO and froni rockets. The OAO scanner 1 observations 
(3700-1800 A) are calibrated with the relative sensitivity function given 
to me by Savage. The rocket observations in the same wavelength range 
are tied into quite a decent absolute calibration and lie considerably 
below the OAO observations. I have concluded that the Savage sensitivity 
function must be in error and I have derived a new sensitivity function by 
forcing the scanner 1 data to fit the rocket observations. The short 
wavelength OAO scanner 2 observations have also been calibrated against 
absolute rocket fluxes. What I want to point out is that up to now we've 
been talking about the visual part of the spectrum which can be fit well 
with models, as long as you don't look at the results too closely. But as 
soon as you get into the ultraviolet below about 2800 A, the observed 
flux drops away from the model very rapidly. These results for a B7 star 
are similar to those I've also found for a BO and a B3 star. 

Something even worse is illustrated in Figure 11-21 which shows the 
observed flux for a rapidly rotating AOV star, 7UMa. The continuous 
line gives the flux envelope for a hydrogen line blanketed model, effective 
temperature 9750°, which fits the observations in the visible region. The 
observed flux shortward of 1800 A lies very much below the model, 
indicating line blanketing of a factor of about two. In Figure 11-22 is 
shown the observed flux distribution for Vega, which is also matched to 
theoretical fluxes in the visible. Now, you see a difference between those 
two AOV stars, one rapidly rotating and one not. For Vega, we have an 
excess of flux below 1600 A, with respect to the reference distribution 
(that of the model atmosphere), while for yUMa we have a deficiency 
of flux with respect to the reference model. 

Figure 11-23 shows rocket and ground-based observations of aCMa, fitted 
to the same reference model. Teff - 9750°. Again there is a lot more flux 
below 1600 A than you have in the rapidly rotating AOV star, 7UMa, but 
not as much flux as there is in Vega. 

What I really want to say is summarized in Figure 11-24. Here are the 
three AO stars, or Al in the case of aCMa, plotted with respect to the 
same model. You get considerable UV line blanketing in yUMa; aLyr has 
a large brightness,' or flux excess. It is 50% brighter than yUMa at 1800 A 
or so; and aCMa lies in between. One would never have known that these 
three stars differ so much, from studying the ordinary ground-based 
spectral region, to which we have been fitting models. In Vega's far UV 



129 



1200 1400 ISOO 1800 2000 2200 2<00 2500 2900 3000 3200 3100 3eD0 3800 4000 4200 4400 4SaO 4800 SOOO S200 MOO 5600 S800 6000 



I ' I ' I ' I ' I ' I ' I ' I ' I ' I ' I ' I ' I ' I ' I ' I ' I ' I ' I ' I ' I ' I 



-n=T 



I 




I'. I . I . I 



I . I , I I I I I I I , I I I , I , I , I , I I I , I . I , 



1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3200 3400 3600 3600 4000 4200 4400 4600 4800 SOOO 6200 5400 5600 5800 6000 



Figure n-21 

flux excess are we seeing a hot chromosphere or a companion? I reaDy 
don't know. qLyr is a very funny star; it has been previously postulated 
to be double. The point is that around T^jj = 10,000°, the predicted 
ultraviolet spectrum is terribly sensitive to the details of the model 
shortward of 3000 A. Nothing that we've been able to observe from the 
ground is nearly as sensitive. So the ground-based observer is up against a 
real problem in trying to determine if a chromosphere is present or not. 
Simple classical models predict continuously dropping temperatures and 
pressures as you go outward in the atmosphere. I defined, half jokingly, a 
chromosphere as being that region which reflects a departure from such 
simple models. Unfortunately, most ground-based observabies are not very 
sensitive to these departures. 

Hack - I would like to make a comment about the Conti definition of a 
chromosphere, having in mind the extended atmospheres of A-type 
supergiants. If we look at spectra of la supergiants we see Ha in emission, 
and according to the Conti definition we should say that these stars have 
a chromosphere. If we look at the spectra of lb A-type supergiants we 
generally don't see Ha emission. But in both types we observe the same 



130 



3E00 




75 




70 


- 


ES 




GO 


- 


55 


- 


50 


liki 


^ 45 


" 


40 


- ,/ 


35 


- / 


30 


- 


25 


- 


20 




15 


- 


10 


- 



kind of radial velocity fields, and Balmer velocity progression, which 
indicate an expanding atmosphere. Hence, in my opinion, we must use 
the same definition (chromosphere, or extended atmosphere?) for both la 
and lb atmospheres. The line contours are rather different in spectra of 
normal B-type stars and in spectra of /3 Canis Majoris stars, which 
sometimes show one, two or three components, variable with time and 
having different radial velocities. So I don't agree that they are equal to 
those of the normal main sequence stars. As a matter of fact there are 
some evidences that they are surface rather than atmospheric effects. 
Huang has shown that the sum of the equivalent widths of the com- 
ponents (measured at phases when the line is divided in two components) 
is equal to the equivalent width of the line (measured at phase when the 
line is single). He interpreted this fact as a proof that the components are 
not formed at different heights in the atmosphere, but rather in different 
parts of the stellar surface. 

Kuhi — I think that is the problem with a definition that says anytime we 
see lines in emission we have a chromosphere. 



131 



T^ 


1 1 1 1 1 


1 1 —I 1 1 r I 


— 1 — 111 — 1 — 1 — 1 — 1 — 


1 1 1 


- 








- 


- 






r\ 


-- 


- 








■ 


- 


/ » \ 


:^, 1 


\ 


- 


■ 


/ ' 


^^^^^^^^ 


N 


\: 


- 




• 


o CANIS MAJOniS 




. 








- 


- 








- 


-J 


1 1 1 1 1 


J 1 1 1 1 — 1 — 1 — 1 


1 1 1 1 1 1 1 1 


1 1 1 



1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3200 3400 3600 3800 4000 4200 4400 4600 4800 5000 5200 5400 5600 5800 6000 

A 

Figure 11-23 

Cayrel - I am going to propose a very simple definition of a chromo- 
sphere, because I think it is too dangerous to have a definition based on 
assumptions you are making in your work. Very clearly, when people first 
defined the chromosphere of the Sun, they had the idea that when you 
look tangentially (at the solar Hmb) you get an optically thin situation in 
the continuum. So 1 would propose that the base of the chromosphere is 
where you have tangential optical thickness equal to one. There is then 
the problem of what kind of optical thickness we are using in the 
continuum. I would propose to define a wavelength Xo by Xo T^fj = 
0.288, and select a wavelength in the continuum which follows the 
spectral type or effective temperature. The other problem is what is the 
upper boundary of the chromosphere. In the word chromosphere you 
have "chromos" which means color, the idea being that when you look 
tangentiaUy above this layer you are looking into Unes. If there is a 
dominant line you get the color of this line. I would propose to take as 
an upper boundary t tangential = 1 in the strongest line of the spectrum 
which may be quite different in a cool star and in a hot star. In the sun I 
think that would be Ha. I don't know what the strongest line would be 
in hot stars. I think this would eliminate the problem of extended 
envelopes, because even in Unes you are optically thin in envelopes. 



132 



1400 2200 3000 3800 4600 5400 




't AO 7 a LYR/MODEL 




Al Y a C MA/MODEL 
J L I 1 1 1 L 



1400 2200 3000 ^ 3800 4600 5400 
A 
Figure 11-24 

Kuhi - I'm not so sure that's true. There are stars with large envelopes 
that have optical depth much greater than one in emission lines. 

Cayrel — In that case perhaps the chromosphere merges into the envelope. 

Auer — I will be heretical about the definition of a chromosphere. Some 
objects are interesting because they have a chromosphere. If you ask the 
average graduate student what the solar chromosphere is he will say it is 
that region where there is an outward temperature rise. Would someone 
please tell me what is wrong with that definition. There are lots of 
reasons for having emission lines. One of them is a temperature rise, and 
that is one phenomenon that I would call a chromosphere. It is the 
simplest definition. There are problems with definitions that require 
mechanical heating. After all there are granules in the solar photosphere 
which are evidence of the presence of a mass flux. Are you therefore 
going to make the photosphere a part of the solar chromosphere by the 
mechanical motion definition? 

Kuhi - We are dealing with observations here today and I think the 
question is simply how do we define chromospheres in stars from an 
observational point of view. 



133 

Auer — I think the answer is clearly from phenomena related to a 
temperature rise. There are different ways to get emission lines, one of 
which is by means of a temperature rise. Certain lines will show emission 
because of this temperature rise. 

Kuhi — So how do we go backward from observing emission lines to 
inferring the presence of a temperature rise? That is a little hard to do 
without good models. 

Auer — It is hard to do, but that is not the problem of a clean definition 
of a chromosphere. 

Steinitz — From an observational point of view, couldn't one say that a 
sufficient condition, not a necessary one, would be that you find emission 
lines with excitation temperatures higher than the color temperature of 
the star? 

Kuhi — But one can think of stars that don't fit that. ^ 

Praderie — We have called a chromosphere a region where we find a 
temperature higher than that which you would expect in a radiative 
equilibrium. If we take all emission lines as characterizing a chromo- 
sphere, we can get into trouble because some of them, those formed by 
very specific excitation processes like fluorescence, will say something 
only about the radiation field and not about the gas kinetic temperature. 
Secondly, I also suggest that with Auer's definition of the chromosphere 
as being a region with a temperature rise outward, you have hidden the 
confusion within the definition, because you do not know what is the 
cause of the temperature rise at that place. I admit that I have not 
proved, in any of the indicators I have given, that they say something 
directly about the heating, except in the sense that Steinitz has just 
stated, i.e., whether the temperature derived is higher than some color 
temperature in the spectrum. 

Frisch — I would like to know why we need a definition of a 
chromosphere. We need a word that everyone agrees about. Perhaps when 
we have many observations and people can do statistics, then we will 
need a definition. But now it is premature. 

Kuhi — I don't really want a defmition of a chromosphere. I would like 
to know the answer to the reverse question. If we observe emission lines 
in a star, are we necessarily observing a chromosphere? 

Magnan - The only relevant point is, given a spectrum, can we determine 
the temperature vs. height relation. Also the definition of an emission line 
is not clear. 



134 

Pecker — The main problem is that we have a hint that emission lines 
mean something. They might mean many things. The job of the exper- 
imentaUst is to fish in the pond. The job of the theoretician is to take the 
fish and see if there is a chromosphere in the fish, or what amounts to a 
chromosphere. 

Thomas — Clearly what you call something is not important. What we 
would really like to do is to understand what causes the structure of a 
star. We know the difference between the atmosphere and the interior in 
a vague sort of way. The only reason one introduces atmospheric 
subdivisions is because different physical phenomena characterize these 
different subdivisions. We want really to determine what is the evolution 
of physical phenomena as I go outward in a star. In a very classical way 
the temperature and the density, by themselves, will suffice to describe 
everything, if I can make all of the standard classical assumptions. This 
isn't true if I go far enough out in an atmosphere. For example, in some 
cases there is a complete breakdown in the notion of describing a velocity 
field only in terms of a thermal component and a three dimensional 
macroscopic component. So, we should make some definition of atmos- 
pheric subdivisions which tell you what are the physical phenomena 
happening in those subdivisions. 

UndeihiU — That is the physical approach and it is a lo^cal and correct 
one. The problem for the observer is that he normally has to observe over 
a short wavelength interval. As we extend our wavelength region, we find 
we are observing different parts of the same object. A physical model 
which fits well the observations in one wavelength region may not fit 
observations at all in a different wavelength interval. Trying to extrapolate 
from one region to another on the basis of physical models is where we 
go astray. The observers are right to go after emission lines or extra deep 
absorption lines. In the ultraviolet, however, we have to take care that 
what we are calling emission lines are not really re^ons of residual flux 
between strong absorption lines in heavily blanketed regions. I'm not yet 
fully convinced of Yoji Kondo's arguments for seeing emission lines, but 
he really can't say anything else at this stage. With the kind of line 
blanketing I see at 20 A resolution in that region in OAO-2 scans, I 
wonder how much of the "emission" he sees is residual flux between 
lines. This is precisely the problem — the observations .The more observa- 
tions we can get the more we're going to know. The theoreticians should 
proceed, but don't anchor yourselves to a fixed scaffolding of theory and 
get so fixed that the poor observers think it's there for good. 

Kuhi — I don't think the observers have that problem. 

Athay — So far I haven't heard two people give the same definition of a 
chromosphere. Let me be the first to support the definition Larry Auer 



135 

gave, namely those situations where the temperatures rise outward in the 
atmosphere. That is a case where we can hope to give some simple 
diagnostic to the observer that he can use in saying a certain phenomenon 
indicates a chromosphere. If the theoreticians want to invent another 
word to describe a place where there is mechanical energy dissipation, we 
can leave that up to them. 

0. Wilson - I've come to the conclusion after listening to this httle hassle, 
that one man's chromosphere is another man's extended atmosphere. 
(Laughter and applause.) 

Kuhi — I would suggest that we go on now to look at what the 
observations are trying to tell us. In her survey Francoise Praderie 
discussed many cases which we can cover one-by-one, starting with the 
questiori of excitation anomalies. Were there any questions of clarification 
about the Ca II H and K lines? 

Skumanich — One should be very careful about Usting universal criteria 
for chromospheres, when using the H and K lines. For example, one thing 
that was listed was intensity — age relationships which only apply to 
main-sequence stars. As I've shown in a study that has appeared in 
abstract form only. Call emission in the K ^ants is not an indicator of 
age. There is no kinematic difference, for example, between the emitting 
and the non-emitting K-giants. 

Kuhi — But how about the pre-main-sequence stars? Not the T-Tauris, but 
those that are farther along than T-Tauris and almost on the main- 
sequence. Do you know what they do? 

Skumanich - No, I don't. 

Kuhi — Are there any other questions about the CA II emission in the 
Sun or in the stars? 

Linsky — I would like to show some work by Tom Ayres, Dick Shine and 
myself at JILA. We have observed a few stars which are reasonably similar 
to the Sun in an effort to get absolute fluxes if it is at all possible. I'll 
start by presenting the data on Procyon which is an F5 IV star. Kondo 
mentioned that there is likely to be emission in Mg II H and K in this 
star. What I have here in Figure 11-25 is a low spectral resolution scan of 
the region including Ca II H and K. The imits here are flux in 
ergs/cm^ /sec/hz at the surface of the star. I show this scan for two 
reasons: (1) to show that at low spectral resolution you see no emission 
in H or K and (2) to show how we calibrated our data in absolute units 
at the surface of the star. We took a 10 A interval centered at 3950 A 
and tied this through photometry to Vega at 5000 A for which an 
absolute flux is known. We put in the radius and parallax of the star to 



136 



s 
o 

CO 
o 




Figure 11-25 

get absolute values of the flux at the surface of the star. Figure 11-26 
shows a high resolution 7th order scan of the K line of Procyon. This is 
in the center of the Une over about 1.7 A interval. The data have been 
filtered. This is data taken with the Kitt Peak solar tower and I might 
point out that this represents 5 hours observing. Again the units are flux 
at the surface of the star. On the right hand side of the diagram we have 
turned the flux units into an equivalent brightness temperature. In this 
scan we see a profile very similar to the K line in the Sun. There is 
definitely a reversal on the violet side, although such a reversal is unlikely 
on the red side. Also the brightness temperature corresponding to Ki is 
about 4900°. If the minimum temperature in the Sun is about 4300°, 
which is the same as the brightness temperature in Kl , and if one thinks 
of Kl as a good measure of the minimum temperature in the Sun, then 
we may indeed have a direct measure of the minimum temperature in 
Procyon. What is especially interesting is that the ratio of the brightness 
temperature in Ki to the effective temperature of the star is 0.745 for 
Procyon and the Sun. 

It may well be that there is a scaling law which is applicable, wherein the 
physical processes that determine the minimum temperature in Procyon 
and the Sim are the same. So perhaps one could extrapolate at least over 



137 




nSOOO 
4900 
4800 ^ 

ID 

4700 •" 

4600 

4500 



3933& 



3934& 



Figure 11-26 



a limited range in the H R diagram to determine the minimum tempera- 
tures in related stars. 

Figure 11-27 shows the K line profile of Procyon again, now in residual 
intensity units. Also shown is the K line for the Sun, now viewed as a 
point source. This is to show that the shape of the profiles is the same, 
although die Procyon profile is much broader. In addition the K Une for 
Arcturus is shown; it possesses a much more significant double reversal. 
The data for Arcturus are taken from Griffin's Atlas. 

Figure 11-28 shows additional data we obtained for Procyon near 8542 A 
(the pluses in the diagram). Note the central intensity in X8542 is the 
same for Procyon as for the integrated solar flux, although the Procyon 
profile is of course broader. We also observed Aldebaran (K5 III) where 
the profile is actually quite similar to the solar core. 

Peytremann - How did you put the Sun on a flux scale? 

linsky - We put the Sun on a flux scale by taking the observations at the 
center of the disc and at a few /i points and doing an integration. We also 
took into account continuum limb darkening. It is sort of a fictitious, 
quiet Sun as we've ignored plages, active regions, etc. 

In Figure 11-29, if again we go to Griffin's Atlas for Arcturus and plot the 
five Call lines on the same scale with residual intensity on the ordinate 



138 



o.i6|— — I 1 — — 1 1 r 



0.12 



0.08 



0.04 



T 1 r 



1 1 r 



PROCYON 




3933.78 

I _i I I L 



•0.6 -0.4 



-0.2 

AX(A) 



0.2 



0.4 0.6 



Figure 11-27 



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SUN 


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ALOEBARAN 

1 1 1 


1 , 1 • 1 1 1 





8538 8540 8542 
X(&) 



8544 



Figure 11-28 



139 



1.00 - 



0.50 




Figure 11-29 

and a common AX scale on the abscissa, two things strike me as 
interesting. Youll recall that yesterday I showed observations of a very 
weak solar plage in the same five Call lines. There is quite a lot of 
similarity between that case and Arcturus. In a very weak plage in the 
Sun you get some emission in H and K (of course it is broader in 
Arcturus) and you get pure absorption lines in \8542 and X8662. In the 
weakest of the triplet lines, X8498, there is a hint of a central emission, 
in the plage. There is also a hint of an emission feature in X8498 in 
Arcturus, as taken from Griffin's Atlas. It may well be that X8498 is a 
very interesting line to look at in a range of stars, as an indicator of 
chromospheric emission. 

Athay - Jeff, is it certain that X8498 does not have a blend in there? 

Linsky - There are no known lines at the required wavelengths. It would 
have to be a very complicated blend, being the same in Arcturus as in 
plages, but absent in the quiet Sun. 

In Figure 11-30 we have a low resolution scan of Aldebaran (K5 III), 
taken at Kitt Peak. The point here is that even at low resolution 
(20,000-30,000), you can see emission in the core of H and in the core of 
K. The emission is brighter in K than in H. The low resolution eliminates 
the Ka feature. 

In Figure 11-31 we have a low resolution scan of Sirius which shows that 
Call H and K exist in this star and that H is a small perturbation in the 
wing of He. 



140 




Figure 11-30 

Figure 11-32 shows a high resolution scan of Vega. This is really quite 
interesting. Here we are in the broad wing of Hg with the wing decreasing 
in this direction. This is about 10-15 minutes worth of data taken while 
we were waiting for Procyon to rise. We didn't really expect to see very 
much in Vega, but it may well be ,that this feature seen on the red wing 
of the H line of Call is in fact an emission feature. This may indicate a 
chromosphere on a star as early as an AO dwarf. 

Praderie — What is the wavelength scale? 

Lindcy — It is about 1.4 or 1.7 A for the fuU width. Before anyone takes 
this too seriously, I should mention the last figure, Figure 11-33. This 
illustrates the unfiltered data, for purposes of honesty. This is the 
emission ieature I was talking about. The data are very noisy and the 
observations should be done again. The emission hump does seem to be 
there in the unfiltered data and if you look then at the filtered data, 
perhaps the hump is there or perhaps it is not. I wouldn't stake my life 
on it. However, I wouldn't be surprised if Vega, which has already been 
mentioned as a star potentially with a chromosphere, indeed shows some 
emission in the Call H line. 



141 




Figure 11-31 

Underbill - Might the Call K line for Vega be double? 

Linsky — We had intended to do both the H and K lines on Vega after 
we had seen data of this sort. However, it snows on Kitt Peak. We'll have 
to wait for our next observing program. 

Kuhi — The next major topic covered by Francoise was also related to 
Call emission, namely the Wilson-Bappu effect. I have one question about 
this. It is always stated in the literature that a correlation exists between 
the absolute visual magnitudes and the width of the Call K emission. Has 
anybody looked to see if there is a correlation with absolute bolometric 
magnitude as well since the bolometric corrections are so small for these 
stars. 

0. Wilson — I've never done that. I presume that there is a correlation, but it 
wouldn't be linear. I do not know what the correlation is. I've always 
used the visual because there the correlation is beautifully linear and 
therefore handy. 

Peytremann — I have some comments about the Wilson Bappu effect. 
Yesterday, Gene Avrett told you about some theoretical non-LTE com- 



142 




Figure 11-32 

putations we have done at Harvard on calcium line profiles. He showed 
some profiles wdiich I will not show again now. Once we had these 
profiles, we tried to test them against one very well established observed 
effect, i.e., the Wilson-Bappu effect. The first question that arises is again 
qiie of definition, but this time it is a definition related to the observed 
quantity. The width of the Call K emission as defined by Wilson and 
Bappu (1957) is the difference in wavelength between what they call the 
violet edge and the red edge of the emission. If you have a theoretical 
profile you also need to define "an edge." On the top of Figure 11-34, 1 
show the red pari of a calcium line with a flux scale on the ordinate and 
arbitrary wavelength units on the abscissa. I adopted three possible 
definitions of the width, which I call Wj , W2 , and W3 . Wj is the width at 
the minimum, Ki . Wj is the width at half the flux difference between 
the maximum of the einission, Kj , and the minimum, Kj . W3 is the 
width at one quarter the height in flux units between the maximum and 
the minimum. This is irnportant as will be seen in Figure 11-35. 1 should 
add that if you measure the width on a photographic plate, even if you 
have the densitometry profile on the plate, you still are on a density 
scale. Even if you define the width on a density scale on the photo- 
graphic plate, you still have to convert it back to flux units before 



143 




Figure 11-33 

comparing it to theoretical calculations. Obviously, a densitometry profile 
is not going to look the same as a flux profile. 

In Figure 11-35, 1 plotted absolute magnitudes as a fijnction of the log of 
the half -width as defined by Wilson and Bappu. Before I discuss this 
graph, I have to say how we go from model atmosphere calculations to an 
absolute magnitude scale. The absolute magnitude is 

M^ = -101og,o Tgff + 2.5 1og,o g 
-2.5 logio M + C,,^, + constant 

My = absolute visual magnitude 

Tgff = effective temperature 

g = surface gravity 

M = stellar mass 

C,,j,j = bolometric correction 

In model atmosphere computations I specify T^ff and log g and also 
roughly the abundance — metal poor or metal rich. These three quantities 



144 



- 


1 1 


1 






/\ AF/2 




X 

3 


r 


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• log g = 4.44 




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1 1 


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1 





w, w. 



w, 



Figure 11-34 

do not allow me to uniquely define the absolute magnitude, because I 
need the mass. I don't know anything about the mass in atmospheres that 
are roughly plane parallel. The bolometric corrections can be taken from 
metal line blanketed models and in any event this correction is not too 
big in the range between Tg^f = 4000° and 6000° K. The main problem is 
how do, we get the mass. We can start from evolutionary tracks in terms 
of gravity and Tgjj ; i.e., one looks at that star which at some point in its 
evoluation would have a specified Tg^j and log g. This star has a certain 
mass, which one uses to calculate M^. Here we have to rely on 
evolutionary model calculations and that introduces another uncertainty. 
This solution is not necessarily unique because there can be a region in 
the HR diagram, corresponding to a Tg^^ — log g combination through 
which stars of different masses can evolve. That is an uncertainty that can 
bring trouble. 

We started with a solar model. We then calculated another model in 
which we just changed one parameter - i.e., the surface gravity — and 
left everything else as in the solar model. Avrett described yesterday how 



145 



V^^ (5780, 4.44) OBSERV. 



^r (6500, 4, V=0)- 




(5780, 2) 



0,6 -0.4 -0.2 

log Wo/2(A) 



Figure 11-35 

we re-scaled the temperature. There will be objections to the way we did 
this rescaling in order to have a chromospheric rise. For what we want to 
show, this is not an important problem. We just want a temperature rise 
in order to get an emission peak in calcium. It has been shown that the 
Wilson-Bappu effect is independent of the intensity of the emission peak. 
So whatever temperature gradient we take should give the right answer as 
far as the Mson-Bappu effect is concerned. What we then have to prove 
is that it is also going to work for temperature gradients other than the 
ones we have adopted. 

On this graph I show the Wilson-Bappu relationship as a solid Une. The 
value for the sun given by Wilson and Bappu is indicated by © . The open 
circle (o) conesponds to definition Wj.at half -height between K2 and Kj . 
Wi (A) is at Kl. W3 (•) is in between. The first thing that you can see is 
that the results one obtains depend significantly on which width defini- 
tion one adopts. For the Sun the problem is not too bad, but for the 
giant (log g = 2) case, the definition adopted can change very significantly 
the results you get for the theoretical width. An extreme case is the 



146 

model at T^fj = 6500°K and log g = 4, where the emission peak is very 
narrow; (We have taken zero turbulent velocity in this case.) Then one has 
a very flat Ki minimum. In such a case, one is in trouble because there is 
a tremendous difference depending on whether one adopts the definition 
W3 or Wj , Wi being obviously inappropriate . 

In addition to the solid Une, I have shown a dashed line which joins the 
points conesponding to definition W3. In this case, the slope is roughly 
parallel to the observed effect, although there is a slight shift to the right. 
However, if one takes the giant (Tgjf = 5780°K, log g = 2) case, one sees 
that the calculated points between Wj and W3 bracket the observed 
relation. 

For the model with T^fj = 5780° log g = 2, and from evolutionary tracks 
(Iben, 1967) I derived a mass of 6M., which corresponds to M^ = 3.4. 
In addition to this procedure I took a more direct route to get M^. In a 
recent paper by Bohm-Vitense (1971), a star of luminosity class II has log 
g = 2. With this and the spectral type one can go to tables like the one of 
Schmidt-Kaler (1965), which then gives M^ = -2.1 . This gives two 
independent determinations of My. One sees that the observed width - 
luminosity relationship (solid line) is bracketed by the theoretical joints 
between definitions Wj and W3, and M^ = 3.4 and -1.4 Within the 
uncertainties in the width definition and in the derived values of M^, it 
would seem that we can explain the Wilson-Bappu relationship just in 
terms of an opacity effect. We did not put in any extra velocity fields. I 
do not say* that there are no velocity fields. But such fields may not be 
required to explain the WUson-Bappu effect. These are very preUminary 
results which are presented here only because this meeting is supposed to 
be a working conference. Further calculations with various temperature- 
height relations are needed to confirm these first results, and to improve 
the shape of the emission peak. These investigations are currently under 
way. 

REFERENCES 

Bohm, Vitense, E. 1971, Astron. Astrophys., 14, 390. 

Iben, I. 1967, Ann. Rev. Astron., 5, 571. 

Schmidt-Kaler, Th. 1965, Landoh-Bomstein, Gruppe VI, Bd. 1, p. 298, 

(Springer, Ed. Berlin). 
WUson, O.C. and Bappu, MJC.V. 1957, Ap. J. 125, 661. 



147 

CONTINUATION OF DISCUSSIONS FOLLOWING 
TALKS BY PRADERIE AND DOHERTY 

Kuhi - Peytremann has given us a very interesting explanation of the 
Wilson -Bappu effect which did not require the velocity parameter 
suggested by others and relied entirely on the opacities. I wonder if there 
is any comment or discussion on this point. 

Rosendhal — It should be pointed out that there is some observational 
evidence that velocity fields may have something to do with the 
Wilson-Bappu effect and other related phenomena. Referring to observa- 
tional studies in the literature, in the case of the F stars, Osmer has 
empirically established that there is a conelation between the width of 
the infrared oxygen lines at 7774 and absolute magnitude. There is nearly 
a linear relationship for stars more luminous than absolute magnitude -2 
or -3. He also finds that in this absolute magnitude range a change in the 
behavior of the turbulent velocity in the sense of an increase in the more 
luminous F stars, and that you can completely explain the dependence of 
the width of the infrared oxygen lines from the increase in turbulence in 
these stars. The second point which I think is important is that a couple 
of years ago a paper appeared by Bonsack and Culver who looked at the 
line widths and turbulence in the K stars. This was prompted by Kraft's 
observations of H# as an indicator of absolute magnitude through an 
analogous effect to the Wilson-Bappu effect. They also found that there 
was a correlation of turbulence as derived from the curve of growth with 
the width of H#. Therefore in two cases, namely that of the K stars and 
also the highly luminous F stars, there is some empirical evidence that 
velocities are relevant to the problem and that there is a relationship 
between the observed velocities and various types of luminosity indicators. 

Peytremann — Many people who have tried to interpret the Wilson-Bappu 
effect in terms of velocities have thought that the widths represent 
velocity broadening in a direct sense and did not base their analyses on 
any sort of detailed model calculations to make sure that the broadening 
did not come about indirectly through some other intermediate mech- 
anism. You mention Ha profiles, and I ask how you know that what may 
seem to be velocity broadened widths are really velocity effects. 

Rosendhal — I didn't say Ha was broadened by velocities. I merely 
pointed out that the observed changes in the width of Ha are conelated 
with something which is associated directly with a velocity parameter, and 
that Ha exhibits a behavior analogous to the Wilson-Bappu effect. 

Kippenhahn — The fact that a stellar atmosphere doesn't know about the 
mass but only about effective temperature and gravity has been a basic 
difficulty with the Wilson-Bappu effect. The situation is very similar in a 



148 

quite different field in astrophysics, namely, in the explanation of the 
period4unynosity relationship of the Cepheids. There, as well as here, one 
needs information about the mass of the stars in a given region of the HR 
diagram, information which can only be obtained from evolution theory. 
Evolutionary tracks project the mass-luminosity relationship from the 
main sequence into the region of the evolved star, and, although there is 
some scatter, this procedure brought out the explanation of the mass 
luminosity relationship (Hofmeister, Kippenhahn, Weigert, 1964, Zeit- 
schrift f. Astrophys. 60, 57; Hofmeister, 1967. Zeitschrift f. Astrophys., 
65, 194). What Dr. Peytremann suggested this morning is very similar. 
When he assumed that for the red giant region stars of a given luminosity 
have a certain mass he assumed that there is a mass-luminosity relation- 
ship for evolved stars (which is not the classical mass-luminosity relation- 
ship for main sequence stars). 

I wonder whether one would not get a similar phenomenon for the 
width-luminosity relationship as one encountered already for the period- 
luminosity relationship. In the case of Cepheids we know that stars which 
have undergone a different evolution like the W Vir stars (whose 
evolutionary history is still unknown) have a different mass-luminosity 
relationship when they cross the Cepheid strip and therefore have a 
different period4uminosity relationship. Similarly in the case of stars with 
Call emission: if another population of stars is observed in a certain area 
of the HR diagram they might have masses different from that of 
population I stars in the same region of the diagram. Should they not 
show a different Wilson-Bappu relationship? Can one look for this, or is 
the effect of different masses obscured by the effects due to different 
metal content? 

Athay — There is, I think, an observational way of deciding whether the 
emission extends into the damping wings or is due to a velocity 
parameter. When Skumanich and I looked at the problem several years 
ago we found the same effects that Peytremann has described, but they 
implied that the line wing is producing the broadening, and that there is a 
correlation between the flux in the K emission and the width of the 
emission peak. If you increase the opacity in the chromosphere, that both 
broadens the peak and increases its flux, and I don't see how you can 
avoid that, at least for stars of the same age. Only if you deal with stars 
of different ages would you be able to destroy the correlation. 

Peytremann — I agree that this correlation should not exist for stars of 
the same age, and, indeed, this point will be investigated. 



149 

Jefferies - I think that in fact the answer may be with us already from 
some observations that were shown this morning. There are two things 
that determine the separation of the peaks used in the Wilson-Bappu 
relationship. 

One is the Doppler width and the other is the optical thickness of the 
chromosphere. We should be able to differentiate between these two by 
using profiles of the H and K lines of ionized calcium and magnesium. 
Since these will have the same Doppler (velocity)widths, while the optical 
depths of the chromosphere in the two sets of lines will differ in 
proportion to the relative abundances, I think, therefore, that one should 
be able to determine the major contributor to the width from using a 
little theory and making a comparison of Wilson-Bappu relationships for 
the calcium and magnesium lines. 

Kuhi — The Mg II relationship does seem to have a flatter slope but is 
based on only a few points. 

Linski — An interesting result comes from looking at solar plages 
concerning the Wilson-Bappu relationship. Consider the relation between 
the K Une width, determined say at the half intensity point between K2 
and Ki and the activity of the plage, both the width and intensity 
increase. From a weak plage to a strong plage, the width does not increase 
while K2 does increase. I think the physical explanation of why this 
happens in the Sun would be of great importance in understanding the 
Wilson-Bappu effect. 

Wilson — I would like to ask Jefferies a question about the Ca and Mg 
Magnitude — width relationship he discussed. If you look at two stars 
with the same luminosity but a different calcium abundance, presumably, 
you won't get the same results. 

Jefferies — I can't offhand answer the question of what happens with 
different abundances, particularly with a different Ca to Mg abundance 
ratio from star to star. 

Wilson — If you have one group of stars with a solar Ca abundance and 
another series of stars with, say, only one fifth that much Ca, would you 
expect to get two different magnitude -width relationships? 

Jefferies - To the extent that the position of the bottom of the 
chromosphere isn't dependent on the Ca abundance that may be the case. 
Such a result may seem implausible, but so is the Wilson-Bappu 
relationship. 

Wilson — There are many comments in the Uterature, as you know, about 
possible abundance effects but I think the evidence against such explana- 



150 



tions is quite strong. I will have more to say on this in my talk at the end 
of the meeting. 

Pasachoff - I have suggested in an Astrophysical Journal paper (164, 385, 

1971) one more thing that helps explain the Wilson-Bappu effect in the 

Sun. The Sun is, after all, the star in which one can study how the actual 

' line profile that we measure is constructed. If we look at Figure 11-36, we 




-0.5A 



0.5A 



Figure 11-36 

see profiles of two fine structure elements located about a second of arc 
apart from each other. One can see that each profile for the K line is very 
different from the profile for a neighboring element. These are what the 
supposedly symmetric double-peaked profiles look like under high spatial 
resolution. The K peaks on the violet side of these two profiles appear in 
two rather different locations, a few hundredths of an Angstrom from 
each other. The statistics of how these peaks vary show that there is a 
contribution of several km/sec to the line width of the Sun. Similar 
contributions must also arise in the other stars we see. 

Magnan - I think that the turbulent velocity is only a parameter that is 
put into the calculation for convenience. I think that the best indication 
for velocity fields comes from the asymmetry of the line. I think it is 
important to account for different intensities in the red and blue wings. 

Kandel - I think that from the diagram that Pasachoff showed, the 
velocity differences in the separate cases would be assigned to macro- 
turbulence. 



151 

Pasachoff - We all a%ite that the reason the averaged peaks have their 
observed separation and are asymmetric is still controversial. The simple 
models that just have Doppler shifts one way and the other can certainly 
be challenged on many grounds. While the peak displacements can be 
represented on a velocity scale, it is not necessarily the case that there are 
elements moving at these velocities. 

Jennings — Praderie mentioned in her talk a correlation which has been 
published concerning calcium H and K emission, infrared excesses and 
polarization. Since the initial report quite a bit of work has been done on 
this at Kitt Peak and we have some results which differ from those which 
are in print. We have considered H and K, hydrogen, Fe II and other 
emission lines in late type giants and supergiants and we find the 
following results. If we plot the mean change in polarization vs. the ratio 
of intensity in the K line to that in the continuum we find that the stars 
break very neatly into two groups. Those that are intrinsically polarized 
show no Ca emission detectable at Wilson-Bappu intensity class 11 or 
greater. On the other hand, stars which do not show intrinsic polarization 
do show very strong Ca reversals. There is one" star which tends to bridge 
this gap, a Ori. This star shows very weak polarization, and, as you know, 
Ca reversals. 

Further, Dyck and others have discussed a correlation between polariza- 
tion and infrared excesses, so we can also add infrared excesses to the 
graph. Combining these two pieces of data we interpret this to mean that 
those stars which are surrounded by circumstellar material do not tend to 
show Ca H and K emission. We have also looked at other emission lines, 
notably Fe II and we find that the result holds for these lines; i.e., stars 
with infrared excesses and intrinsic polarization do not show Fe II in 
emission. The only star which does is a Ori. But again tliis is a case having 
very weak polarization, and very weak infrared excesses. It should be 
noted that this particular relationship conflicts with that originally 
mentioned by Geisel who suggested that the presence of Fe II is 
accompanied by infrared excesses. We find this not to be the case. It is 
also interesting to note that among the stars which do not show 
polarization none currently show hydrogen emission nor have we been 
able to find any reference in the literature to hydrogen emission among 
these objects. On the other hand, approximately 50% of those stars which 
are high polarization objects have shown or are showing hydrogen 
emission. Also, this is the strange type of emission which is shown by 
Mira variables, i.e., having a distinctly anomalous decrement. Two cases of 
this type presently in emission are Z Ursa Majoris and RX Boo where we 
find that Ha and H^ are missing, HY is weakly in emission, H6 strongly 
in emission. He is missing, and"H8 through HIO are weakly in emission. 
The explanation for this seems to be that these lines arise far down in the 



152 

photosphere, and are affected by strong overlying absorption. This is the 
current status of the emission line vs. grain indicator correlation. 

Kuhi - In defense of Susan Geisel's comments, I think that in her paper 
she certaiiJy did not mean to imply that 100% of stars that showed Fe II 
emission had infrared excesses. I think her batting average was aroimd 
80%. 

Jennings — Among the late type stars the correlation seems to be exactly 
the opposite. If you find Fe II emission you do not find infrared excess. 

Pecker — Your measurements all refer to rather cool stars, those showing 
the K line, and Susan Geisel picked primarily Be stars. For Be stars do 
you still find the correlation between Fe II emission and the absence of 
infrared excess? 

Jennings — I meant only to say that Susan Geisels correlation is reversed 
in the case of late type stars. Her correlation seems perfectly valid for 
stars of early spectral type. 

Boesgaard — What data do you have for the Fe II emission Unes for 
late -type stars and how many stars did you observe? 

Jennings — Of thirty stars or so, seven or eight showed strong polarization 
and for these we found no iron emission and none seems to be reported 
in the literature. Fe II emission is fairly common among those stars which 
don't show polarization. 

Leash — We do not seem to have directly observable indicators of the 
chromospheres in early type stars. I wonder if Praderie has any opinion 
on whether the lines of Si II at 4128 A and 41 30 A might be a good 
indicator. of chromospheres in B stars? 

Praderie — I have tried to determine the dominant terms in the source 
function for the Si II resonance multiplet at 1808, 1817 A in A and B 
stars. The source function is collision dominated. I don't know the 
situation for Si II 4128 A and 4130 A, and have not considered B stars. 

Heap — I would like to suggest the stars as candidates for having 
chromospheres on the basis of observations by Slettebak in the 1950's. 
Slettebak measured the broadening of Unes in 0-type spectra and foimd 
that there Was no O star whose spectrum shows Unes sharper than about 
75 km sec. His sample was large enough that he should have been seeing 
some of these stars pole-on. He concluded that there was some intrinsic 
velocity broadening, eg, turbulence, present in early stars. Also, AUer's 
plates of planetary nuclei having O or Of-type spectra show at least 75 
km/sec broadening. Hence, there are no O stars, young or old, that have 
sharp lines. This is a serious problem because of velocity of 75 km/sec is 
about twice the speed of sound in the atmospheres of hot stars. 



153 

Underhill — For the O stars there is no difficulty in explaining the 
hydrogen line widths at least, but you are correct in stating that sharp 
lines are not seen in O star spectra. 

Kuhi - Also we must consider the problem of radiation pressure in these 
very hot stars, which may be very efficient in forcing material away from 
the star. This could prevent the formation of a chromosphere. 

Boesgaard — I wish to report on the ultraviolet Fe II emission line in a 
Orionis. It is perhaps too bad to leave the Ca II emission line which is the 
one thing everyone seems to agree on that indicates the presence of a 
chromosphere. Inasmuch as Francoise Praderie implied that the Fe II 
emission lines may be formed in a circumstellar shell, when I talk about 
these Fe II lines I should adopt Olin Wilson's feeling about a chromo- 
sphere: one woman's chromosphere may be another woman's extended 
atmosphere. In any case a Ori offers ample proof of both a chromosphere 
and an extended envelope. It does show the calcium emission and it 
certainly shows blue-shifted circumstellar cores in zero-volt absorption 
lines. These Fe lines were first discovered in 1948 by Herzberg (Ap. J. 
107,94). There are about 17 observable lines from multiplets 1, 6, and 7 
of Fe II. These lines occur in the region 3150 A to 3300 A which makes 
it very difficult to look for them in cool stars since they radiate so little 
energy that far in the ultraviolet. About the best candidates are a Sco and 
a Ori and even these require long exposure times for high dispersion 
studies. Bidelman and Pyper (1963 P.A.SP. 75, 389) looked at something 
like 6 M stars, one MS star and a carbon star for these lines. 

Figure H-37 shows an ultraviolet spectrum of a Ori at 3. 3 A/mm taken at 
the Mauna Kea Observatory 225-cm telescope. The iron emission lines are 
indicated there. Of those 17 lines about 7 are so badly mutilated by some 
kind of overlying absorption that little can be learned from them. (A 
figure in Doherty's talk showed profiles of two Fe II lines: one with a 
strong self -reversal and a second line which has a high laboratory intensity 
but which is too mutilated to give any radial .velocity information.) The 
feature at 3228A looks like a double emission line but is actually a strong 
emission line with a central absorption reversal. The line at 3277 A is an 
example of a strong emission line with a weak self -reversal. The lines in 
the region around 3167 A are among the weakest lines with no reversals. 

I measured the radial velocities on four separate spectrograms taken over 
a period of a year from November 1970 to December 1971. The 
absorption lines give a radial velodty for the photosphere, a Ori is known 
to have a variable radial velocity as the photosphere seems to be 
pulsating. The velocity there is about 21-22 km/sec and shows a range of 
about 4 km/sec. Measurements were made to determine radial velocities 
of the absorption lines, the emission lines, and the self reversals; the 



154 



n— 3167— I Fe I 1 — [3187 r-T^I^^ 

II I.I- - . . I . I I - I i 1 .. 







' ' -■ - I II- -I i iiLiMjja 



-3228 Fe E 3256 



in I II M II I ir; nil I i u.: \' 



Na I 
3277—1 1 Fe E — 3296 3302 

- .,,,., I . . II 




Figure 11-37 

results are shown in Figure 11-38. The first panel' shows radial velocity 
measurements and probable errors on 4 plates for the absorption lines. 
This variation is what is expected for o Ori for the photosphere; it shows 
a range of a total of 4 km/sec. The average velocity is about 22 km/sec. 
The liext part of Figure 11-38 shows the velocities for the emission Unes. 
The large dots at the top are from the seven strongest emission Unes in 
the spectrum; this looks like the velocity is constant for those emission 
lines. The te^on where the emission hues are foimed does not take part 
in the photospheric variations. The four small dots below that are the 
radial velocities of three weak lines. The probable errors are similar to 
those for the strong emission lines but are not shown for the sake of 
clarity. The third part in Figure 11-38 shows the positions of the reversals. 

Now if you have looked at the scale on the left you may be perturbed by 
the fact that these emission lines show a red-shift. That usually indicates 
infalling material. If the chromosphere or envelope is expanding, I find it 
difficult to understand such a shift, but Grant Athay has assured me that 
it is possible, even in an expanding atmosphere, to get red-shifted 
emission lines. If you look at the average of these velocities, the emission 
lines are red-shifted by about 5 km/sec relative to the photospheric lines. 
The reversals, except in the one case of KE-33, are sUghtly blue-shifted 
within the emission features. Tliat we can understand as cooler material 
farther out in this expanding atmosphere. So the reversals are about 3 



155 




26 33 84 410 
ABSORPTION 



26 33 84 410 
EMISSION 



26 33 84 410 
REVERSAL 



Figure 11-38 

km/sec to the red of the photospheric lines or about 2 km/sec to the blue 
of the emission lines. Incidentally, in the same star Olin Wilson long ago 
measured the velocities for the calcium emission and the K2 features are 
also shifted to the red by 4 km/sec. 

Determinations of relative intensities, half -widths, and intensities of the 
reversals have also been made. For Figure 11-39 I have averaged emission 
intensities that are eye estimates on the four plates that I have and 
plotted them against half-width, that is, width at half intensity. There is a 
linear correlation between the intensity and the breadth of the hne. The 
scale shown on the right in the figure is in km/sec; the weakest hnes are 
about 20 km/sec in width and the strongest line has a width of about 85 
km/sec. Figure II40 shows the relationship with the reversal intensities. 
Not all the lines are self -re versed; those are the weak ones and the reversal 
intensity is zero. The medium intensity lines have medium reversals and 
the strong line at 3228 A has a very strong central reversal. This figure is 
again the average intensity from the 4 spectrograms. There are plate-to- 
plate variations so reversal intensities for medium-strength lines range 
between 1 and 3, but none are ever called 4. For individual spectra these 
diagrams show linear correlations without the discontinuities seen in this 
averaged diagram. If we look again at the km/sec scale for the widths, the 
unreversed lines have an average width of about 30 km/sec. The middle 
ones have widths of about 60 km/sec and there is the one strong one at 



156 





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EMISSION INTENSITY 

Figure 11-39 



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EMISSION INTENSITY 



0,2 



0,4 0,6 ' 0,8 
WIDTH (A) 



1,0 



Figure 11-40 



157 

85 km/sec. The width, W^, measured by WUson for the ionized Calcium 
line is 170 km/sec. 

Figure 114 1 depicts profiles of some of the lines. The first one, 3166.7 A 
is an example of a weak line; 3196.1 is one of the medium strength lines 



KE-33 



A 



KE-84 



1 A 
I I 

100 km/sec 



3166.7 



3196.1 



3227.7 



Figure 11-41 

with a self -reversal. Also shown is a strong line, 3227.7 A, with a strong 
self -reversal. The upper and lower set of profiles are from two different 
plates taken several months apart. For the self -reversed lines on KE-33 the 
blue^ peaks are stronger than the red peaks, and the weak line is 
asymmetric. There is some variation with time in the exact structure of 
the iron emission Unes in this star. AU the Unes in KE-84 seem more 
symmetric like the examples in Figure 114 1 . 



158 

The time variation for the Ca line structure is shown in Figure 11-42. The 
solid line is from KE-33 taken on November 14, 1970, while the dotted 



CONTINUUM ? 

1 AK 






100 km/sec 
1 1 

1 1 




Irvv 


V 


\ 


/i i/v. A J\ 


yr 


1/ 

'3922,9 
CLEAR ^^ ^ 


3927,9 
Fe I 


W,v\f 

1^ 3933.7 _ 
Ca n 
3930.3 y 
Fe I 


V 

3941.7 
Co I 



Figure II42 

line is from KE-410 on December 6, 1971, ITiere is a very broad, shallow 
K, and Hi in this star. A continuum point about 17 A to the ultraviolet 
from this line is indicated at the tpp of the figure; the actual continuum 
is probably higher. The line-center position shows that the K3 core is 
slightly blue -shifted. The Kj emission peaks show on either side of K3 . 
Wilson's data give a slight red-shift for jixe emission peaks, +4 km/sec. 
You can see that there are some variations in the Ca intensities and in the 
K2 blue-to-red relative strengths. For KE-410 note that the red peak is 
stronger than the blue. 

There is a large amount of information available about chromospheres in 
the iron lines. There are many lines for one thing, at least 1 that are 
particularly useful and about 17 that give some information. For a Ori 
the photospheric lines show the expected velocity variation while the 
constant-velocity Fe II emission lines are red-shifted by about 5 km/sec 
for the average 6f the strong lines. The weak emission lines are about 
+1.5 km/sec and the reversals are about 2.5 km/sec to the red of the 
photospheric hues. The red-shifts are small relative to the line widths. The 
widths for the weak emission lines are 30 km/sec and that corresponds to 
an average red-shift of 1 .6 km/sec, The stronger lines range from 60. to 85 
km/sec in width which corresponds to a greater red-shift of 5 km/sec. The 
red-shifted Ca II Kj lines have an even greater width of 170 km/sec. The 



159 

line widths eorrelate with eiiiissiofl intensities and with the strengths of 
the selReversals. Another iiitefesting aspect is the time variations that are 
present in both the calcium and iron lines. 

I would greatly appreciate a theoretical explanation of the observed red 
shift. 

Magnan — I would like to describe the profile I call "standard" for an 
expanding atmosphere; Thi§ profile is characterized by a blue-shift of the 
core and an enhancement of the fed emission. The effects are reversed in 
the case of a coii traction. These features are a consequence of a 
differential Doppl^r shift along the path of the photon. This shift is due 
either to a differential expansion in plane-parallel layers or to the 
curvatiife of the layefs in the case of a constant velocity of expansion. 

Underhill - If you take the hydrogen lines in a Be star, invariably the 
strongest Balmet lines ate fed shifted with respect to the others, and the 
velocity of expafl§l0fl is Sdftietiiing of the order of 50-80 km/sec not 
enough for escape. It i§ usually stated that Ha is coming from a region of 
smaUer outward veldcHf: The Fe II lines observations might be explained 
in a similar way. 

V 

Wright - This diagram (Figxifg ii4J) is probably the best example we 
have which shows satellite absorptidfl liiies of the K line obtained during 
the chromospheric phases, prior to first contact j in the spectrum of 31 
Cygni. This series was taken at the time of the 1961 eclipse; we hope to 
obtain another series this summer, chiefly at egress in July. At the 
beginning of the series, the B spectrum fills most of the K line of the K 
spectrum and the Kj and K2 emission features can be seen. The central 
chromospheric absorption, in general, becomes gradually stronger as 
eclipse approaches. A major feature is the appearance of additional 
satellite lines which come and go. Perhaps the most interesting is the one 
shown on August 7-28 which showed in nearly the same position for 
three successive nights when the projected distance of the B star was 
more than two stellar diameters from the limb of the K star. The feature 
disappeared but another one appeared again in September and similar 
effects could be seen right up to eclipse, though after first contact the 
normal broad absorption of the Ca II K Une of the K-type star dominates 
the spectrum. Similar effects have been noted at ecUpses of 32 Cygni arid 
f Aurigae; at times I have suspected three or four satellite lines though 
they are usually weak and sometimes difficult to distinguish from the 
grains of the photographic plate. The explanation in terms of one or more 
clouds of prominences in the outer atmosphere of the K star, moving at 
different velocities, which absorb the light of the small hot B star, still 
seems to me to be reasonable. These observations seem to confirm to a 



160 

INTENSITY 3930 



I 



100 
80 
100 



. V " JULY 9 38 



>Vy^W-< ^ Wv,J< * A < >l^^ 



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3930 3935 A. 3930 3935 A. 

STRUCTURE OF THE K-LINE IN THE SPECTRUM OF 31 CYGNI DURING INGRESS 1961 



Figure 11-43 

certain extent the type of phenomena about which Anne Underhill was 
speaking. 

Boesgaard — One point is that these are small shifts compared to the 
halfwidths. So in fact, there may be more blue-shifted photons since the 
shift is only 5 km/sec while the half -width of the line is 60-80, km/sec 
and the line-profiles are asymmetric. 

Kuhi — One of the problems that has been mentioned is that of mass 
outflow from the star and its detection by specific Une profiles, asym- 
metric Unes, P-Cygni profiles, anomalous line widths, etc. Is there 
discussion on this aspect of the problem? 



161 

Kandel — Are we talking about mass flux as an essential part of a 
chromosphere or only about mass motions of some sort, i.e., velocity 
fields, as being a chromospheric phenomenon? These are two different 
questions. 

Kuhi — In Praderie's talk she specifically avoided discussion of mass loss 
and I think we would Uke to do that as well since that gets into the 
problem of extended envelopes and other questions. I should mention 
Roger Ulrich's defining point this morning, v/hich he didn't get the 
chance to make, that maybe the outer boundary of a chromosphere is the 
point at which the material is no longer gravitationally bound to the star. 
This would eUminate from the discussion all very extended envelopes. 

Cassinelli — I would Uke to point out that it is not necessary to have 
mechanical energy deposition to have supersonic mass loss. John Castor 
and I have recently calculated expanding model atmospheres for early 
type stars. The atmospheres approach the usual static behavior at the base 
and have supersonic expansion farther out. The only form of energy 
deposition required for the flovy is absorption of radiation. 

Pecker - We have been speaking of extended atmospheres and the 
chromospheres of other women — it seems to me that the point is that an 
extended atmosphere is defined by its departure from hydrostatic equilib- 
rium so that what is necessary for making an extended atmosphere is to 
have an additional momentum input, while the chromosphere is distin- 
guished from the photosphere by having an additional energy input. 

Kuhi - Okay, I guess I'll buy that. 

Conti — There are many Of stars for which the X4686 of He II line (34 
transition) is seen in emission and it has always been a mystery why this 
is so. In at least one star, f Pup, the rocket UV observations by Stecher 
also show the Hne He II (2-3 transition) at X1620 in emission. And now 
there have been some observations of the infrared line XI 01 24 of He II 
(4-5 transition) of that same star by Mihalas and Lockwood, and that line 
is also in emission. We have however, the He II . . . Pickering series (4-M 
transitions) in absorption in this star. So some mechanism is over 
populating the ion up to level 5 and then causing cascading down through 
the other levels. According to the recent models of Auer and Mihalas, 
they were unable to get the X4686 line into emission ancf they were 
certainly unable to get XlOl 24 in emission in any kind of plane-parallel 
model. So it seems very clear that at least for f Pup and presumably for 
all of the Of stars in which you see X4686 in emission, you must have 
some sort of extended envelope. If there was a planet from which some f 
Puppians were watching their Sun, and there was a solar ecUpse by an 



162 

appropriate moon, they would certainly see chromospheric emission lines 
in He II, but that's an aside. The main point I want to make is that when 
you see X4686 in emission, there is some sort of extended envelope 
around the star. -. i 

The star I want to talk about now is 0i Ori C. As some of you may know, 
this is the central star of the Trapezium and the star that excites the 
Orion nebula. I have some spectra to show of this star. Figure II44 shows 



6^ ORI C 



U.T. 1971 




the spectral region of X4471 and 4541 of He II. These show just as 
absorption lines on these spectra, taken on five nights during one week. 
Note the appearance of X4686, the first two nights. Then a couple of 
nights later we see an emission at X4686. The emission is violet displaced 
and the absorption is red displaced, and we call this an inverse P Cygni 
profile. As most of you know, a P Cygni profile is one which suggests 
that material is flowing out from the star. Therefore an inverse P Cygni 
profile suggests the opposite. Figure 1145 shows the profile of X4686 on 
the first two nights. The absorption line is undisplaced with respect to the 
other absorption lines and then after three nights we see the emission on 
the violet and the absorption on the red side. What this suggests on the 
face of it is that there is material which is falling into ^i Ori C. 
Sometimes material is accreting and other times it isn't. That is an 
interesting phenomenon for a star that has excited a gigantic nebula 
which is apparent to the naked eye. There are a number of physical 
problems connected with that process, and I think the line formation 
problem is the presence of accretion is in itself an interesting problem for 
astrophysics. The terminal velocity for material falling in is about 1100 
km/sec and the infall velocity, roughly given by the absorption profile, is 



163 




+200 



+400 



KM/SEC 
Figure 11-45 

something like 10 or 20% of that.. So it isn't coming in with full force; 
presumably radiation is braking the fall, but it is definitely accretion. 
That should lead to some interesting problems of interpretation. 

IWlson — Some of those ^jOrionis stars are Binaries, are they not? 

Conti - This star is Usted as a spectroscopic binary. Upon searching the 
literature, you find out it is called a spectroscopic binary by Frost, et al. 
They give it this identification on the basis of "large" velocity variations, 
back in the 20's. Then you find that the senior spectroscopist, Struve, 
(and Titus in 1944 also studied this system) could find no velocity 
variation that could be blamed on binary motion. The plates I have, 
which are these five and another eight or so, aU show no velocity 
variations. 



164 

Mson — That might be why the famous Wolf-Rayet star that was an 
eclipsing binary stopped. 

Conti — Once a binary always a binary. 

Kuhi — Yes, but it stopped eclipsing. 

Conti — But it didn't stop being a binary. 

Pasachoff — Let me show you some observations we've been making with 
the 100-inch telescope on Mt. Wilson, using the 32-inch camera of the 
Coude spectrograph at 6.67 A/mm. Mson and Ali (P.A.SP. 68, 149, 
1956) observed the helium D3 line a few years ago and reported a 
probable detection of D3 in four stars, namely e Eridani, 61 Cygni A, k 
Ceti and X Andromedae. The first three are dwarfs and X Andromedae is 
a spectroscopic binary with a strong chromosphere. However, they were 
able to measure the position of the supposed D3 line for three of the 
stars, and found that they were displaced some 0.4 A or so to the red. 
Since this region is confused by the presence of some water vapor lines all 
around D3 (at X5875.44, 5875.60, and 5876.12, for example, with D3 at 
X587S.64 right in the middle) the evidence was still incomplete. 

Since that time, Vaughan and Zirin (Ap. J. 152, 123, 1968) have 
published a paper with image tube observations of X10830. Thus we now 
know for a variety of stars what the velocities may be. In fact, a 
dominant red shift effect does not appear. Some stars do show such 
velocities, but they are not always in the same sense. Figure 11-46 shows 
the triplet energy diagram. The XI 0830 line comes from the metastable 2s 
triplet state and the X5876 triplet goes from the 2p state, 1.14 eV higher, 
up to the 3d state. 

We have observed a variety of stars, a few A and B stars but mostly G, K 
and M stars. Just as Mson could not specify results for the M stars 
because there were too many lines in this region to know whether what is 
seen is D3 or not, we also had to limit ourselves to the G and K stars. 
But we do not know which stars have strong XI 0830. /3 Draconis, for 
example, a G2 II star, has 1000 milliangstroms of XI 0830 according to 
Vaughan and Zirin. Zirin has some more recent, unpublished observations 
showing twice that equivalent width. Looking at the D3 wavelength on 
Figure 11-47, you see that there is no line there. For P Scuti, similarly, 
there is no D3 radiation. For X Andromedae it is a little trickier. There is 
an iron line about an Angstrom to the red, which could broaden the total 
profile, but there is probably a Une near the basic D3 frequency. X 
Andromedae has 1000 milliangstroms or so of Xi0830 and it is, of 
course, a spectroscopic binary. There is even a hint on one plate of 
possible emission around D3, though that certainly remains to be 
confirmed. 



165 







- 




^3p 7 


_3d_ 


^/ 




- 


7 


/^2p 


_ 


/f^ 






-^s 







eV 

24 

- 23 

- 22 



- 20 



Figure 11-46 

\ Cygni, a K5 lb star, does not show clear D3 in that region. We have to fol- 
low these stars at different times of the year to use the different radial 
velocities to separate out the atmospheric contamination. We are continuing 
this project. 

Figure 11-48 shows some of the spectra. First of all, for |3 Orionis at the 
top, there is a strong D3 line. It is not "chromospheric," according to my 
definition of a chromosphere, for this is a B star and I would tend to call it 
a hot atmosphere. The other stars do not show this line, except for X 
Andromedae, which does show a possible faint line and even possible emis- 
sion on this plate. However, ^ Draconis, a G2 JI star, may have twice the 
XI 0830 of X Andromedae yet it does not show D3 absorption, certainly not 
of the magnitude of X Andromedae. 

So what I would reaUy like are comments on theoretical calculations of 
the relative intensities one expects for XI 0830 and Ds . You rmght expect 
D3 lines to be down by a factor of perhaps 10, calculating with a dilution 
factor of 2 for an atmosphere of about 6000°K. The ratio will change as 
we go to cooler atmospheres, but it would be nice to have some more 
exact model calculations from all the people calculating grids. We would 
also be happy to have suggestions for additional stars to observe in our 
continuing observing program. Elliot Lepler, a graduate student at Caltech, 
has cooperated in this work. 



166 




5865 



5870 



5880 



5885 



5895 



X(A) 



Figure 11-47 



Fosbury — In Vaughan and Zirins' original paper they suggested that you 
are more likely to see 5876 in the slightly earlier type stars, i.e., the F 
stars rather than G. This is the case of Zeta Doradus again. 

I^sachoff — Vaughan and Zirin did comment that they found XI 0830 in 
one F star which surprised them. I have not observed F stars yet for D3. 

Underbill — If you are looking for chromospheres in the F, G, and K 
stars, certainly in the low chromosphere, where there are reasonable 
densities, the most prominent ions are singly ionized metals and some of 
the neutrals. We already found out that non-LTE appUes here because the 
density is a bit too low for LTE to apply. Most of the resonance lines 
that we would want to look at are located in the ground-based region of 
the spectrum. Doherty showed us that it is very difficult to get an 
observable flux in the UV but " there are really not too many low- 



5800 5850 "3 5900 

I 1 1 1 1 1 \ 1— Jh — I — I — I — I- 



167 



5950 6000 ; 

H 1 1 i 1 1 1 ' 



/S Ori B8 




/3 Dra G2 




/S Set G5 




X And G8 




f Cyg K5 




.JOOuiiiOLias 



a SCO Ml 

1:f 



H 1 1 1 1 1 1- 



5800 



5850 



5900 
X 



6000 



Figure 11-48 



chromosphere resonance lines there, so we are not too badly off down to 
about 2000 A which is an easier region to observe than the region below 
2000 A. I think the region 2000 A to 3000 A is important because there 
are a lot of Fe II, Cr II, etc., lines. If you go to the A stars you get Si II, 



168 

C II, between 1000 and 2000 A. So the near ultraviolet is not a difficult 
region for good Observations of stellar chromospheres, and it is tragic that 
we have not got before Us any observational capabiUty for the near future 
to observe such regions. We are going to have to rely on balloons and 
rockets which have limited capabilities. 

Kendo — I would like to point out that high altitude balloons can be 
useful for observations down to about 2000 A and do offer long 
observing periods in comparison with rockets. Residual extinction can still 
be a problem, however, for observations of certain types, particularly near 
2500 A where the absorption due to ozone is high. 

Doherty — It might help if I pointed out that the sHde 1 showed with the 
decrease of many magnitudes was for broad band measurements. In the 
case of the later stars, these results do not show any of the emission lines 
that might "be stronger. The fact that we have a measurement at all of Ly 
a Arcturus is somewhat remarkable and is evidence that Ly a is a very 
strong line in that region. 

Gros — Through an analysis of the observed radiation of Sirius (A LV) in 
two wavelengths located as far as possible in the ultraviolet spectrum, we 
have tried to derive information on the thermal structure of the super- 
ficial layers of the atmosphere of this star. We have used measurements 
made by Carruthers (1968) at X, = 1115 A and Xj = 1217 A. 

• Analysis — Applying the Eddington-Barbier approximation and 
assuming that the source function at the observed wavelengths 
follows the Planck function, we have deduced the temperature 
gradient between the layers (t^^ = 2/3), where the radiation at Xi 
and X2 is formed from the knowledge of the ratio of the observed 
fluxes F(Xi)/F(X2). To get the depths of formation at 5000 A for 
the radiation at the relevant wavelengths, we need a model to start 
with: we have adopted an LTE, non-gray for the continuum, 
radiative equiUbrium one. 

• Application — The fu-st approximation model is homologous to a 
model due to Strom, Ginerich, and Strom (1966), with an effective 
temperature T^^j = 10486°K and a surface gravity of 10*. The 
chemical composition was deduced from the study of lines in the 
Sirius visible spectrum: silicon is overabundant by a factor of 17 
relative to Warner's (1968) solar abundance. The observations 
(Carruthers, 1968, Stecher, 1970, OAO scans) and the theoretical 
spectrum from the Strom et al. model are plotted in the Figure 
II49. We must point out that, in the absence of an absolute 
caUbration for the OAO data, we have related them to the ground 
based observations of Schild, Peterson and Oke (1971). The 



169 



3.0 



2.0 



1.0 



\ 



1. STECHER ROCKET (1969) 

2. OAO SATELLITE, UNPUBLISHED 

3. CARRUTHERS' DATA (1968) 

MODEL I=T(t(5000)) LAW 
FROM STROM et al (1966) 




1500 



2000 



2500 



3000 



4000 



X(A) 



Figure 11-49 

comparison between the observations and the predicted fluxes 
shows that the spectral region around Ly a is well fitted by this 
model, the computed flux is too low between 1300 A and 1520 A, 
and at 1520 A, a discontinuity due to photoionization from the ^P 
level of Silicon is present (A m = 2.07 mag). This discontinuity is 
not shown by the observations. This discrepancy had been pointed 
out by Gingerich and Latham (1969). 

The model allows us to compute the depths of formation for the 
continuum at each X as shown in Figure 11-50. Note that the violet side 
of the Balmer discontinuity is formed at about the same depth as the UV 
radiation at wavelengths greater than 1430 A. This is the main difficulty 
of the application of the present method to stars as hot as Sirius. 

One gets the foUowing results : 
Xi \= 1115A 

Xj •= 1270 A 

^ Te = + i90°K 

Hence we derive an increase of the electronic temperature Tg in the outer 
layers starting at t (5000) = 0.086. 



t(5000) = 0.086 
t(5000) = 0.066 



170 



2.0 



t 1.0 



0.0 



1101 




Figure 11-50 

Figure II-5 1 shows the semi-empirical model obtained from the Strom et 
al - one by modification of T^ (t (5000) above t (5000) = 0.086). The 
characteristics of the predicted flux from this model are shown on Figure 
11-52. 

• A good fit exists for the region around Ly a. 

• Between 1300 A and 1520 A, there is a small excess of flux, which 
is compatible with the presence of strong lines shown by Stecher's 
observations. 

• The computed Si I discontinuity at 1520 A is still too large, but it 
has been decreased by a factor of 2 (A m = 1 .26); the same is true 
for the Si I discontinuity at 1680 A. We have shown elsewhere that 
the discontinuity at 1520 A is blurred by the strong Si II doublet, 
at 1526 A- 1533 A. 

• This ihodel is too hot to fit the observations (OAO spectrum) 
between 2510 A and 3647 A. Moreover the computed Balmer 
discontinuity is too small (D = 0.27), as can be seen on Figure 
11-53. 

We conclude that this attempt is not completely satisfactory in two 
respects: 



171 



16,000 



14,000 - 



12,000 



10,000 



8,000 




-2.0 



-1.0 
LOG 10 (rSOOO) 
Figure 11-51 

• The analysis has been carried out with a purely LTE source 
function for the continuum at 1115 A and 1270 A; at those 
wavelengths the opacity is actually due simultaneously to the wing 
of the Lyman a Une, and to the CI and Si I continua; the total 
source function impUes then the knowledge of the departure 
coefficients in hydrogen, carbon, and silicon atoms. 

• The depths of formation for the radiations we use in our analysis 
depends on the model we choose to start with. If this model has a 
lower temperature T^ at the surface we can hope that the 
concerned layers wiU be higher in the atmosphere and that we will 
so avoid affecting the formation of the blue side of the Balmer 
discontinuity. A complete multiple iteration must be performed. 

We thank Dr. A, D. Code and Dr. R. C. Blen for having provided us a 
•spectrum of Sirius in the region 2000 - 3500 A, from the OAO satellite. 



REFERENCES 

Carruthers, G. R., i968, Ap.J., 151, 269. 

Gingerich, 0., Latham D., 1970, in Ultraviolet Stellar Spectra and related 

ground based observations, ed. L. Houziaux, H. E. Butler, p. 64. 
Schild, R., Peterson, D. M., Oke, J. B., 1971 , Ap. J., 166, 95. 



172 



o< 



<u 






U) 






~-^ 


3.0 


- 


E 






o 






~^ 






Dfl 






k. 






<u 






1 
o 






f— 1 


2.U 


- 


X 






1— 






cr. 






<t 






Ixl 






1- 






< 






X 

•D 


1.0 


- 


_I 






Lx. 




3 



1. STECHER ROCKET (1969) 

2. OAO SATELLITE UNPUBLISHED 

3. CARRUTHERS DATA (1968) 

MODEL-NEW T (t(5000)) LAW 




^-^^.^ 



1500 



2000 

A(A) 
Figure 11-52 



2500 



3000 



Stecher, T. P., 1970,/lp. /., 159, 543. 

Strom, S. E., Gingerich, 0., Strom, K. M., 1966, Ap. J-, 146, 880. 

CONTINUATION OF DISCUSSIONS FOLLOWING 
TALK BY PRADERIE AND DOHERTY 

Underbill - I have some of the observations of Sinus from OAO and 
from ground -based work. The OAO results tend to be overexposed so I 
have not used them. There are Stecher's rocket observations, and Dennis 
Evans from the Goddard Optical Astronomy Division has done an 
absolute calibration of the rocket scans with effectively the same instru- 
ment but with independent absolute calibrations. This material was 
presented last summer but has not yet been pubUshed. Those two sets of 
measurements £^ee within' the uncertainties of transfer to absolute 
intensity, within 15%, say. The OAO results for this star can't be 
caUbrated as well as rocket data. I have not heard from Savage in 
Wisconsin what he thinks of my revision of his sensitivity curve based on 
the rocket data. 

Sacotte - In the preceeding talk, M. Gros had some observations in the 
Lyman a range and she obtained some models. In this work, we are 



173 



5.0 






— - GROUND BASED OBSERVATIONS 


D«t 


V 




FROM R. SCHILD.D.M. PETERSON, 


o 

a* 






J. 8. OKE (1971) 


|4.0 


\ 
\ 
\ 

\ 

\ 
\ 

\ 




X MODEL 


b 


\ 
\ 

\ 






f 3.0 

< 

<: 


\ 
\ ■ 

\ 

\ 






x: 

§ 2.0 


X 

X 




'\ 




V \ 




,N 



3000 4000 5000 6000 7000 8000 

A (A) 

Figure 11-53 

departing from models. We compute some synthetic spectra and compare 
them with observations in the range 2000 - 3000 A, and then use character- 
istics of the models for comparison. We used the OAO results and believe 
the calibration is accurate to about 20%. To compute a synthetic 
spectrum we compute the emergent flux every 1 A or 0.5 A and then 
convolute the emergent flux by the apparatus function, and we obtain a 
spectrum directly comparable to the OAO spectrum. Line calculations are 
made in LTE. We assume that the source function is the Planck function 
and we use atomic data from various sources. We use a broadening 
constant 2 times the classical value plus the effect of broadening by 
hydrogen and heUum. The first graph. Figure 11-54, shows the OAO 
spectrum and the comparable synthetic spectrum. The model used is by 
Strom, et al. From 2000 A to 2500 A we have an important dis- 
agreement, but in both spectra we notice important absorption features. 
At X2500 A, we introduce in our Une computation the data on Fe II by 
Warner and the agreement is much better as a result. The level of 
observed flux is reached and every feature is well reproduced. The second 
graph. Figure 11-55, shows a similar computation based on the model of 
M. Gros, and here the agreement still is not good. We can reproduce 
various changes in the spectrum but the flux levels are not in agreement, 
and we can see some emission levels in our calculation. All we can deduce 



174 



uT^ 





1K 


SIRIUS 

OBSERVED « OAO H 
COMPUTED • «eff = 0.48 


2.0 


\S\ 


aCONTINUUM 

^"vY \ ^~~ "~~~ •*=* -— 


1.5 


- \ 
\ 
\ 
V 

1 


xi «' V 

1 



2 1 00 A 



2500A 
AA 



3000^ 



Figure 11-54 



2.5 






I 
o 



2.0 



1.5 



SIRIUS 




210pA 



A& 



. OAO E OBSERVED 
« M. GROS COMPUTED 



/' 



^^,r^^ 



CONTINUUM 




2500A 2950A 3000A 



Figuie II-5S 



175 

from the calculation perfoimed with the semiempiiical model of M. Gros 
is that the location and the importance of the rise in temperature 
deduced from the Ly a region in a Al Star have very sensitive effects 
redward of 2500 A to the Balmer discontinuity. 

Giuli - I would like to amplify a comment made earlier by Kondo on the 
use of balloons in UV astronomy to about 2000 A. Current operational 
balloons can carry telescopes with easily twice the light gathering power 
that any Aerobee type rocket can carry. At altitudes of something like 40 
km the signal strength or recorded signal per unit time is just as strong as 
that of a rocket and on top of that you have the advantage of an entire 
night's observing time. For some reason astronomers seem to have missed 
out on many of the recent developments. Cosmic ray physicists have been 
using balloons for a long time, but there are really only about three 
astronomy payloads that have seriously considered ballooning for ultra- 
violet astronomy. I would like to encourage those of you who are 
seriously interested in ultraviolet astronomy from balloons that there are 
several places aroimd the country which can offer advice, based on 
experience, such as the Gehrels Polariscope group in Tucson or our group 
at the Marmed Spacecraft Center. 

Bonnet — We have also been using balloons to perform ultraviolet studies 
of the Sun. 

Peytremann — Such balloon experiments have been carried out for many 
years by smaller countries with limited research budgets, and these were 
often considered secondary relatively unimportant experiments compared 
to the orbital ones. There is perhaps some irony in the renewed interest 
shown here in ballooning. 

Giuli - Yes, my comments have been directed to the American astro- 
nomers. It is ironic, but understandable, how balloon astronomy has been 
neglected in this country. Our space program was funded suddenly, and, 
as a consequence, funds were suddenly available for rocket payloads. 

AUer — Can balloons take payloads above the ozone? 

Giuli - Reliable balloons can carry 500 kg payloads to 4042 km. Smaller 
telescopes could be carried reliably to 44 km, but to go much higher 
requires a tremendous increase in balloon volume, and hence cost and 
risk. Also, the larger balloons obscure a larger portion of the sky about 
the zenith. 

Kondo — It is also important to realize that the state of the art in 
carrying out these experiments has advanced significantly in recent years. 
Sophisticated pointing and stabilization systems used in our experiment 
are examples of such an advance. One can also benefit greatly from the 



176 

capability to monitor in real time the spectrum being scanned, using only 
the integration time needed for this purpose, and then moving on to 
observe other objects. The flexibility we now have in carrying put 
observations was not available a few years ago. 

Kuhi - That's an. important point; ballooning is not restricted to 
photographic recording of data. • 

Underhni — I agree with these possibilities for good observations dowii to 
2000 A or so. Most of the emphasis in ultraviolet astronomy has been on 
the hot stars and on the wavelength range below 1700 A. 1 haye felt Uke 
a. voice crying in the. wilderness saying that more stars can be observed 
and more interesting things in the 2000-3000 A range than have received 
attention so faj;. But let us not, please, lose sight of the fact that you 
really need a spectroscopic satellite, such as we have described as SAS-D, 
up there to observe all sorts. of stars for a long time. Balloons and rockets 
have their place, biit sateUites are required for comprehensive observing 
programs. 

Bonnet — I would like to add a comment on balloon spectroscopy. We 
took advantage of balloons to look at the solar spectrum but had no 
means at that time to look at stars, due to the lack of a good pointing 
system. It appears possible to observe at balloon altitudes in the range 
below 3000 A down to 2700 A. Below that wavelength you have a strong 
absorption by ozone and at lower wavelengths competition betvyeeri 
absorption by molecular oxygen and ozone. However, there is a reasona- 
bly transparent region between 1900 A and 2300 A and, furthermore, this 
region of the- solar spectrum is very interesting because of the presence of 
the carbon emission hne at 1994 A. Detailed observations of this line 
shows that it is emitted in very limited regions, probably correspondirig to 
spicules on the Sun. If this is confirmed it would be possible to look for 
spicules in stellar spectra by observing the carbon line using balloon 
spectroscopy. This line is quite strong and might help in identifying a rise 
in temperature in the outer layers of a star as well. 

Jefferies - In Hawaii we have been making ultraviolet spectra of the Sun 
from a rocket, and with a resolving power of about 200,000. One of the 
lines that we have observed is a line of S I; this displays a very curious 
distribution over the Sun. It is extremely strongly Umb brightened in our 
spectra. 1- forget the exact wavelength, but I was wondering if any of the 
stellar observers have seen this. It is a reliable observation and seems 3 
definite indicator of some sort of chromospheric emission. 

Kuhi — Apparently no stellar observers have seen this line. 



177 

Fosbury — Can I comment on the point that Jefferies just made. Let us 
refer to the diagram for the Ca H and K lines — and the Mg II emission 
lines. I am trying to find out whether it is a Doppler effect or an opacity 
effect. I know there is an Fe line blending with the H lines, but can you 
not do that with the H and K lines separately? You have a factor of 2 in 
oscillator strength. 

Jefferies — In principle you should be able to do so, but, in practice, 1 
don't think it will work. I think that we need a much larger factor than 2 
between the optical depths to show a difference of the kind you mention. 
I think that the factor should be about 10 between Mg and Ca. 

Fasachoff — May I make a plea for not confusing the spectroscopic 
notation for H and K, which refer to Calcium. I suggest that we find 
other nam'es for the Mg resonance lines. 

Kendo — We are provisionally calling those lines the 2795 line and the 
2802 line. However, we might also consider alternative ideas such as use 
of "h" and "k" suggested by Skumanich. 

Kuhi — Fraunhofer's notation ends up by P, so we could use P and Q. 
They are resonance lines and the least confusion is caused if we refer to 
them by wavelength rather than by the Fraunhofer notation which has 
caused enough confusion. 



Page Intentionally Left Blank 



PARTffl 



MECHANICAL HEATING AND ITS EFFECT 
ON THE CHROMOSPHERIC ENERGY BALANCE 



Chairman: Andrew Skumanich 



179 



Page Intentionally Left Blank 



MECHANICAL HEATING IN STELLAR CHROMOSPHERES 
USING THE SUN AS A TEST CASE 

Stuart D. Jordan 

Laboratory for Solar Physics 
Goddard Space Flight Center 

INTRODUCTION 

The remarks in this talk will apply only to chromospheres of compara- 
tively late type stars which have significant convective envelopes. This is 
not to imply that mechanical heating does not occur in other stars, but 
only that, to the best of my knowledge, little or no satisfactory progress 
in applying mechanical heating theories to the outer atmospheres of 
non -solar type stars (without convective envelopes) has been madei 
Indeed, practically all of the progress that has occurred has been in solar 
work, so most of my remarks will pertain to the Sun. 

The serious work on solar atmospheric heating began in the late 1940's 
and, since then, has included treatments of wave modes which might be 
involved and the development of observational techniques to detect them. 
Definite results up to the mid-1 960's included strong theoretical support 
for some kind of gravityrmodified sound wave as the source of at least 
some heating via shock dissipation, and the earliest observations of the 
now well known (but still not well understood) 300 sec periodic 
variations in the line central brightness and position of many upper 
photospheric and low chromospheric Hnes. 

Comparatively recent efforts in the past six years have emphasized more 
detailed numerical calculations, including some non-linear effects, to 
determine the generation, propagation, and dissipation of various wave 
modes for more reaUstic solar atmospheric models. In, addition, the 
corresponding observational work has been directed toward studying 
phase relations among oscillations at different heights (using lines of 
different strengths) and toward getting both high spacial (1 arc sec) and 
time (5-10 sec) resolution spectra, in the hope of inferring directly from 
the observations information on the heating and the. associated velocity 
fields. 

With that backgroimd, I'd Uke to offer a brief review of the principal 
wave modes proposed and studied for the heating, along with where they 
are generated and how they propagate. Then I'll review the solar heating 
picture as it stands today. 

181 



182 

WAVE GENERATION AND PROPAGATION 

The general problem of wave propagation in a compressional atmosphere 
with gravity and a magnetic field is treated by Ferraro and Humptori 
(1958) and many others. Since it is difficult to solve the propagation 
equation with all the terms in it, the usual procedure has been to obtain 
solutions for simpler cases where one or more of the three basic 
parameters (medium compressibility, magnetic field, and gravity) are left 
out. For the moment, I'll ignore the magnetic field parameter. 

Extensive studies of the gravity-modified sound wave have resulted from 
the original suggestions of Biermann (1946) and Schwayschild (1948) that 
these waves heat the outer atmosphere by shock dissipation. In particular, 
numerous appUcations of the Lighthill (1952) theory for generation of 
sound waves by isotropic turbulence have followed his pioneering work. 
One comparatively recent and important contribution by Stein (1968) 
included several calculations of both the total acoustic power generated 
and the frequency distribution of the acoustic emission. To do this 
calculation, it is necessary to know the turbulent velocity ampUtudes and 
also the turbulence spectrum (spacial and frequency dependence) in the 
generating region. Since these parameters are currently difficult to infe^ 
from observations, reliance on a convection zone model and theoretical 
turbulence spectra is necessary. Stein, like many others before him, had 
to use an admittedly rough model for the convection zone, based on the 
earlier Bohn-Vitense (1953) mixing length theory. He then did the 
calculation for several different turbulence spectra. His results demon- 
strated that the total acoustic power output is highly sensitive to the high 
frequency tails of these spectra. This situation, added to the already weD 
known sensitivity of the result to the turbulent velocity amplitudes (the 
acoustic emission varies as the fifth power of the turbulent Mach 
number), introduces considerable uncertainty into the computed acoustic 
flux. Stein's computations yielded an uncertainty of about an order of 
magnitude in the acoustic flux, but the further uncertainties in the 
convection zone model and in the method used for the calculation, which 
ignored the interaction between sound and turbulence, suggests an even 
greater final uncertainty in the results. 

In spite of all these difficulties in this extremely elaborate treatment. 
Stein's results are important for two reasons. First, even if his lower limit 
for the upward flux of sound waves is an overestimate by an order of 
magnitude, this flux would still be of the order of 10* ergs cm"^ sec"', 
which now seems adequate to balance the net radiative losses in the lower 
chromospheric region by dissipation of weak shocks. Since the empirical 
evidence of the solar granulation, as well as simple theoretical arguments 
based on Rayleigh and Reynolds numbers, lends continuing support to 



183 



this general picture of sound wave generation at the top of the convection 
zone, Stein's results are encouraging. Second, the calculated frequency 
dependence of his acoustic emission exhibits a peak far above the critical 
angular frequency cj^ = 7g/2cj (7 = specific heats ratio, g = gravity 
acceleration, Cg = sound speed) below which all sound waves are reflected. 
If this were not true, vertical transport of the sound waves through the 
temperature minimum could not occur. This important result was true for 
all turbulence spectra used. Figure III-l is a graphic demonstration of this 
second conclusion, where acoustic flux spectra are graphed for the three . 
turbulence spectra used by Stein. An immediate consequence of this 



10^ 



t 



(A 

k 
u 

« 



10' 



EE (EXPONENTIAL) 




SE (SPIEGEL) 



0.01 0.1 

— u (sec-i) *■ 

Figure III-l Steins solar acoustic flux spectrum. 

result was that people working on the chromospheric dissipation of waves 
generated by turbulence in the low photosphere returned to their work 
with renewed confidence that they were doing something relevant to the 
Sun. The general picture of chromospheric heating now seems still more 
involved than when Stein's results appeared, as we shall see presently, but 
the two main conclusions mentioned still stand, to the best of my 
knowledge. 

So far, I have deliberately avoided mentioning magnetic fields. We know 
they must play some role in the heating problem. One has only to note 
the strikingly different behavior in the temperature sensitive H and K 



184 

lines over plages and the so called normal chromosphere. What role do the 
magnetic fields play? 

This is a difficult question to answer, because the introduction of the 
magnetic field complicates the mathematical problem considerably, partic- 
ularly by introducing significant non-linear terms into the propagation 
equation (Pikel'ner and Livshitz, 1965). Understandably, less progress has 
been made here than in treating the simpler case of zero magnetic field. 
Fortunately, there is one rather strong statement that can be made. It 
may be possible to ignore the magnetic field and still obtain a relevant 
model for the solar chromosphere. By relevant, I mean an approximate, 
one -dimensional, theoretical model, based on a mechanical heating theory 
which ignores magnetic fields, and yet, which is in substantial agreement 
with one -dimensional models derived from observational data. If this 
proves true, it would have direct bearing on the theoretical treatment of 
chromospheres of non-solar, main sequence stars with convective enve- 
lopes. Difficult as . it may be to devise ways of computing non-radiative 
equilibrium models for these stars with a relatively simple heating theory 
it would be extremely difficult to do it with the non -linear (and, possibly, 
multi-dimensional) aspects the problem would assume with strong mag- 
netic fields. 

To demonstrate this simplifying possibility, consider the dimensionless 
parameter 



= K 



where c^ and c^ are the Alfven and sound speeds, respectively, and B, p, 
and T are the magnetic field strength, mass density, and kinetic tempera- 
ture. The quantity K is an almost constant function of the mean 
molecular weight and the specific heats ratio. From the wave equation for 
propagation in a medium with magnetic field, we can readily see that, 
when Cji^/Cj < 1 , the wave propagates more like an ordinary sound wave as 
the ratio becomes progressively smaller. In the language of Osterbrock's 
(1961) well known study, the fast hydromagnetic mode becomes the 
sound mode. But it is easy to substitute the appropriate numbers to see 
that this is exactly what happens in the solar low chromosphere and 
photosphere outside of plage and spicule regions, which comprise a small 
fraction of the total gas mass at these heights in the atmosphere. So, 
barring the possibility that the magnetic structure of the bulk of the gas 
is a small scale, unobservable, high-fields-of-opposing-polarity situation, it 



185 

follows that, below and possibly within much of the transition region, the 
heating occurs mainly in regions of negligible magnetic field. 

These remarks are meant only to show one way in which the magenetic 
field might be negligible in treating one part of the heating problem. As 
chromospheric densities drop rapidly with height, we soon enter a 
situation, somewhere in the transition region, where cpjc^l, even for a 
field of one gauss. Also, any treatment of heating in plages and spicules 
requires inclusion of magnetic field effects. Finally, the magnetic field will 
play some role, perhaps a vital one, in wave generation (cf. Kulsrud, 
1955), again, where c^/Cg^l. So the current research on how to treat 
various hydromagnetic modes and their interactions with each other and 
the non-uniform propagation medium is very important and should 
certainly be pursued vigorously. On the other hand, the comparative 
insensitivity of the solar wind to the solar cycle (Hundhausen, 1968) 
suggests, though it does not prove, that at least the total amount of 
steady state mass and mechanical energy flux from the subphotospheric 
regions is constant and, thus, not strongly dependent on magnetic 
activity. Perhaps many (important) details of the steady state heating will 
prove to be strongly dependent on the magnetic field, while the total 
magnitude of the heating will not. These are major questions for which 
we currently lack answers. 

Another wave mode that has been treated extensively as a possible 
heating mode is the gravity wave, the relatively low frequency, long 
wavelength, two dimensional wave characterized by elliptical (rather than 
longitudinal, as in the case of sound waves) particle motion in the vertical 
plane passing through the wave propagation vector. This mode represents 
one possible solution of the wave equation, leaving out the magnetic field, 
but including medium compressibility and gravity. Given a suitable 
perturbation, this mode is certainly present in the solar atmosphere 
wherever the radiative relaxation time is not too fast to suppress it. 
Whitaker (1963) injected the gravity wave into the solar heating problem 
because sound waves with (relatively low) frequencies characteristic of 
photospheric granules (Bahng and Schwaszschild, 1961) could not propa- 
gate through the temperature minimum region. This was before Stein 
showed that the frequencies for sound waves generated by the Lighthill 
mechanism lay much higher than the critical cut-off frequency ygl2c^. 
Thus, Whitaker's original motivation for proposing the gravity wave no 
longer exists. 

This situation can be illustrated by the diagnostic diagram in Figure III-2 . 
This diagnostic diagram is simply a plot of the dispersion relation F(ci;, 
kjj) = for different vertical wave numbers \ii and a set of physical 
parameters characterizing the solar temperature minimum region. (Mean 



186 



.04 



03- 



o 

<u 02 



.01 







1 

k,=2xl0 


^ 


f 


1 




1 1 

Te=5000°K 
r = 1.2 


_k,=0 ' 


y 


/w=kxCa 






wa =.0233 sec-i 
cj =.0174 sec-i 






=2 |V 


^ 


ao- 


-8 


-^ 


rS3^^ : 


^^^ 


■-' 


k^=10 
1 


1 




1 1 







2.0 



4.0 6.0 8.0 
kxXlO-8{cm-i) 



10.0 12.0 



Figure III-2 Diagnostic Diagram for Tg (min) region. 

molecular weight unity is also used.) The values given are those chosen by 
Whitaker, but, although Tg should be lower, it doesn't change the general 
picture, cjg is the Vaisala-Brunt frequency above which vertical propaga- 
tion of gravity waves cannot occur. It is given by cjg = g(7 - ly^h^- The 
straight line solution w = k^Cg is a pure sound wave in a zero gravity 
medium, that is, a horizontal sound wave in the Sun. The solutions in the 
upper left-hand comer represent the gravity modified sound waves which, 
as we see, cannot propagate vertically for oyCio^ = .0233 sec"' . Thus, for 
example, a 300 sec sound wave could not propagate up through this 
region. Of course, now we believe that 30 sec is a more representative 
period for the high frequency sound wave, and this latter period lies well 
below the limiting value for vertical propagation. The gravity waves, on 
the other hand, have dispersion relations more like those of the photo- 
spheric granulation with which Whitaker seems to have identified them. 
Hence, we see his preference for gravity waves. In addition to the fact 
that the gravity waves no longer seem necessary in the low photosphere, 
there -is a more serious objection to associating them wdth this region. 
That is, as Souffrin (1966) pointed out, the rapid radiative relaxation 
time, of the order of one second, would quickly eliminate these oscilla- 
tions in this region. 



187 

It would seem that gravity waves play no role in solar atmospheric 
heating and that the preceding discussion is somewhat irrelevant, but this 
is not necessarily the case. There is now convincing observational (Frazier, 
1968) and theoretical (Moore, 1966) evidence that a significant convective 
flux penetrates above the rather artificial boundary separating the convec- 
tion zone fiom the radiative equihbrium photosphere to heights wKere the 
radiative relaxation time has increased enough for the atmosphere to 
support gravity waves. Given a reasonably high efficiency for gravity wave 
generation (and this is predicted), it is still quite possible that the gravity 
wave flux might be as high as 10* ergs cm~^ sec"'. Although no known 
dissipation mechanism makes these slow, low frequency waves a candidate 
for chromospheric heating, they must still be considered for coronal 
heating, where various 'frictional' and conductive processes may liberate 
the energy over a long path length, or where conversion to a different, 
hydromagnetic mode may occur. In addition, the possibility exists that 
the penetrative convection, in the presence, of magnetic fields of 10 gauss 
or more in the low chromosphere, might give rise to torsional oscillations 
which propagate upward along magnetic lines of force, dissipating their 
energy by Joule heating of the atmosphere. Howe (1969) performed a 
linearized calculation and concluded that such a mechanism could account 
for spicules, although the conclusion is highly tentative and illustrates the 
difficulty of treating problems where medium compressibility, gravity, and 
magnetic field may all play a role. 

It is safe to say that, while Whi taker's original ideas on gravity waves in 
the Sun have not stood up, the gravity mode and other modes generated 
by penetrative convection in the upper photosphere and low chromo- 
sphere are probably present, and that they may play an important role in 
heating both the corona and chromospheric, particularly in regions of 
magnetic field strength exceeding 10 gauss. 

A discussion of waves in the chromosphere would be utterly incomplete 
without a consideration of the 300 sec velocity field oscillations which 
have actually been directly observed, in contrast to the high frequency 
sound waves, hydromagnetic modes, and gravity waves for which the 
evidence is, at best, more indirect. Ever since their chief characteristic 
features were first described by Leighton, Noyes, and Simon (1962), the 
question has been raised as to what role these oscillations might play in 
heating the outer atmosphere. Frazier (1968) obtained power spectra for 
both velocity and intensity fluctuations in three lines spanning the 
photosphere from the top of the convection zone to the temperature 
minimum, with sufficient resolution and observing time to break up the 
300 sec oscillation into two, long duration, constant period velocity 
fluctuations of 265 sec and 345 sec. Furthermore, the amplitude ratio of 



188 

the short to the long period oscillation was found to grow with height. In 
addition, a strong, low frequency, convective component of the velocity 
field was found to persist right up to the temperature minimum. Finally, 
the duration of the velocity fluctuations suggested little or no correlation 
with the granulation. The implications of these and other observations 
analyzed during the past few years have stimulated a new round of 
theoretical activity which we are still experiencing right now. 

It was immediately recognized that the granulation, which is our observa- 
tional evidence for the turbulence which we believe generates the 
relatively high frequency acoustic spectrum studied by Stein, is in no 
direct way connected with the 300 sec oscillation, in contrast to the 
earlier notion that granule "pistons" might be dd'/ing them. Also, the 
observational evidence for penetrative convection at the, temperature 
minimum kept alive the possibility that gravity waves might play a role in 
atmospheric heating, as already mentioned. 

The most significant development to follow Frazier's work, however, in 
my opinion, is the two studies by Ulrich (1970) and Leibacher (1971), in 
which what seems to be a plausible mechanism for the 300 sec oscilla- 
tions is discussed, and where the resulting eigenmodes are followed 
through much of the photosphere and chromosphere, where they begin to 
lose their energy rapidly through non-linear (shock) dissipation. 

Ulrich's work concentrates on the generation of the oscillations; Lei- 
bacher's, on the propagation and dissipation. Both agree that the observed 
oscillations in the photosphere cannot be standing waves in the sense of 
running waves constructively interfering as they move back and forth 
between reflecting boundaries. The critical frequency for sound wave 
propagation is too high in this region, as we have already noted. In the 
absence of a forced, but decaying, oscillation pumped by the granulation, 
what are we really observing in the photosphere? Ulrich may have 
suppUed the answer by recalling that small pertubations can lead to 
overstable oscillations in the presence of a superadiabatic temperature 
gradient in the presence of radiative cooling, a condition which is 
described by Moore and Spiegel (1966) and applies to the top of the solar 
hydrogen convection zone. Given this situation, Ulrich noted that the 
upper convection zone could trap standing acoustic waves, which would 
then drive the photosphere at the appropriate eigenfrequencies determined 
by the boundaries of the resonant cavity below. Although the waves 
could not propagate as running waves into the "forbidden" region around 
the temperature minimum, it is easy to show that the decay distance for 
the energy density 1/2 pv^ (v = material velocity) is quite long there. 
(The notion of reflection at the boundary follows from ray acoustics and 
is highly approximate here, as the ratio of the very long, > 1000 km, 



189 

wave length to scale height is quite large.) Detailed calculations show that 
attenuation is not too rapid. Indeed, the velocity amplitude actually 
increases with height in the atmosphere, so small is the density scale 
height. 

The reason for the trapping follows readily from a cursory examination of 
the dispersion relationship for waves in a compressional atmosphere with 
gravity (again zero magnetic field for simplicity). It is necessary to apply 
this relationship, which follows, to a non-isothermal atmosphere such as 
the top part of the convection zone. The dispersion relationship is 






where all the quantities were defined in discussing Whitaker's work, 
except here, 



2 / 7 - 1 ^ 1 dT 



should be used for the Vaisala-Brunt frequency in this non-thermal 
situation (cf. Kuperus, 1965). The lower boundary occius where the 
inwardly increasing temperature decreases the first term on the right hand 
side of equation (1) so that, for a given finite (non-zero) value for the 
horizontal wave number k^, it becomes equal to the second term, which 
will be of opposite sign for oJa^coKcji)^, the frequency range in which the 
observed oscillations lie. Thus, k2 = results, defining a lower reflecting 
boundary. The upper boundary occurs where the two terms again cancel, 
this time because, for a given co, the outwardly deaeasing temperature 
causes a correspondingly increasing coj to approach o) in value. The result 
is a resonant cavity for eigenmode (cj, kj^), given a model for the upper 
convection zone and photosphere. 

To actuaUy obtain eigensolutions, one must, of course, solve the appropri- 
ate wave equation with boundary conditions which depend on the 
eigensolutions (w, k^). Ulrich obtains a simple, workable, lower boundary 
condition from equation (1), by noting that cjg ^0 as one goes into the 
convection zone. Then he determines the upper boundary by finding the 



190 

mode which has the smallest velocity amplitude above the temperature 
minimum, on the grounds that this mode should be distorted least by 
shock formation in the upper atmosphere and, thus, provide the most 
reliable boundary matching. His eigensolutions include a fundamental 
mode and first -overtone mode which pass through the peaks of Frazier's 
published power spectra. To establish that these oscillations are over- 
stable, Ulrich is forced, by his method of handling the outer boundary 
condition, to consider the energy balance. When he does this, he finds 
that the fundamental mode and first two or three overtone modes are 
overstable. In addition, he estimates the outward energy flux in these 
oscillations is greater than 10^ ergs cm"* sec"* , or roughly in agreement 
with estimated net radiative losses from the outer atmosphere reported by 
Athay (1"966). Although 1 would take issue with his speculations as to 
what happens to the waves as they heat the outer atmosphere (conversion 
to heat through some hydromagnetic interaction), it seems to me that 
Ulrich has come closer than anyone, to date, to providing insight into the 
origin of the 300 sec oscillations. In addition, he concludes his article by 
outlining the kind of observations necessary to further check some of 
these ideas. 

Leibacher, on the other hand, while concluding independently that the 
mechanism of subphotospheric standing waves is responsible for the 
observed photospheric oscillations, concentrates on the properties of the 
observed "evanescent" oscillations themselves. He shows how the evanes- 
cent waves become propagating waves once more, due to the chromo- 
spheric temperature rise, and calculates the atmospheric heating through 
non4inear dissipation. Further results which ITl mention in a more 
detailed treatment of the heating make this seem very plausible. That is, 
there is good reason to believe that 300 sec progressive waves wiU develop 
very quickly into strong shocks, so that complicated hydromagnetic 
interactions are unnecessary. Therefore, these interactions, mentioned by 
Ulrich would seem less likely to be important in heating the upper 
chromosphere or transition region, at least, outside of plages and spicules. 
The position of the evanescent waves in an isothermal temperature trough 
is shown on the diagnostic diagram of Figure III -3, which appears in 
Leibacher's thesis. We see immediately that their range of (co, k^), which 
corresponds to observed values, is quite incompatible with propagating 
acoustic or gravity waves. They are on the other hand, completely 
compatible with the picture provided by the more recent work. 

This concludes what I want to say about the 300 sec oscillations. There 
isn't time to review past theoretical efforts to understand them. Most of 
these efforts have run into serious objections, often as refined observa- 
tions clarify what the Sun is doing. An earlier effort by Moore and 



191 




2Hk, 



Figure 111-3 Evanescent waves on solar diagnostic diagram. 

Spiegle (1964) suggested the evanescent wave interpretation, which now 
seems promising, without offering the explanation of underlying standing 
waves. Time and better observations, particularly of phase relations in two 
dimensions, will permit us to check the more recent work of Ulrich and 
Leibacher. 



SOLAR ATMOSPHERIC HEATING 

Keeping all these remarks on wave modes in mind, I'd like to turn to the 
heating question. Since most of the quantitative work on this question 
has been restricted to the chromosphere, it is useful to start there and 
work up. 

The earliest idea, already discussed, was that sound waves generated by 
turbulence at the top of the convection zone would build up into shock 
waves, as they propagate out into the sharp negative density gradient, and 
rapidly give up their energy, thus producing the 'abrupt transition to 
coronal temperatures and heating the corona itself. Recent detailed work 
(cf. Ulmschneider, 1970, 1971 a,b), using the theoretical acoustic spectra 
of Stein — Figure III-l again - has modified the original picture in several 
ways. 

By following the growth of the sound waves from their point of 
generation up through the photosphere and low chromosphere of a 
typical solar atmospheric model, Ulmschneider has shown that a fully 
developed shock wave (crest of an initially sinusoidal wave has caught up 



r 



192 

with the trough) develops after the wave has traversed a few scale heights, 
i.e., several hundred kilometers. This particular conclusion is in substantial 
agreement with several earlier studies. The result is important in insuring 
that significant shock heating will occur around or slightly above the 
temperature minimum, where, as we shall see, some mechanical heating 
appears to be necessary. A departure from the original picture occurs, 
however, when Ulmschneider solves the weak shock propagation equation 
for these waves. He shows that, for the relatively high frequencies of the 
Stein acoustic spectra (typically 30 sec period), the diock Mach number 
remains small enough in the low chromosphere to preserve the validity of 
the theory; and this permits estimates of the local mechanical heating to 
be made by using it. He then calculates the heating in this way, and finds 
good agreement between the heating and the local net radiative losses due 
to H", which are corhputed using the same model. This is illustrated in 
Figure III4. Earlier studies either ignored the situation in the low 



10" 



\ 



I 



10' 



10" 



,s- 



FLUX CALCULATED BY 
ULMSCHNEIDER USING 
STEIN'S EE ACOUSTIC 
1 SPECTRUM CALCULATED 

RADIATIVE 

LOSSES 



110 km 




(FLUX CURVE CALCULATED 
USING STEIN'S SE SPECTRUM'' 
LIES ONLY SLIGHTLY LOWER) 



_L. 



_L. 



_L. 



-Iff-' 



10-=' 



10-^ 



I 

m 

^ 



10^ 



300 600 900 1200 ISOO 1800 
— h (km) » 



Figure III-4 Mechanical flux and dissipation in chiomospheie 

chromosphere or treated it very approximately. Furthermore, the earlier 
notion that the waves generated by the turbulent convection are responsi- 
ble for the chromosphere-corona transition and the high coronal tempera- 
ture now seems wrong. It is the low chromosphere, alone, below the 
sharp upward temperature transition, where these waves seem to be 
effective. Higher up, we appear to need the 300 sec progressive waves 
and, possibly, other modes. 



193 

The importance of Ulmschneider's results can best be seen, I feel, if we 
keep two things in mind. First, it is useful to recall that, if the low solar 
chromosphere does require mechanical heating, as now seems well estab- 
lished (Athay 1970), the net radiative losses from this region of almost 
negligible extent (compared to, say, the corona) are probably equal to the 
sum of all the other net radiative losses from all other sources in the 
entire outer atmosphere beyond the temperature minimum. This is due, 
of course, to the relatively high densities in the chromosphere compared 
to the corona, notwithstanding the much higher coronal temperature. This 
observation, though reported often, does not seem to have made much 
impression on some astronomers who talk about the heating problem as if 
coronal heating were the sum of it. Obviously, a region, however smaD, is 
fundamentally important if (1) much of the heating must, ultimately, 
occur there, and if (2) the waves responsible for heating all the higher 
regions must pass through it. Incidentally, this problem of energy balance 
in the chromosphere is a principle reason for energetic efforts to 
determine, from observations, the optical depth, breadth, and value of the 
minimum temperature. These efforts, which sometimes involve consider- 
able expense— for high altitude infrared observations, for example— are 
certainly worthwhile. 

Consequently, Ulmschneider's rather satisfactory treatment of the low 
chromosphere has importance in its own right. Looking ahead, it keeps 
alive the hope, already mentioned, that a relatively simple heating theory 
may be applicable to building one-dimensional non-radiative equilibrium 
atmospheric models for a large class of late type stars with convective 
envelopes. 

This brings us to the upper chromosphere and/or the transition region.* 
What causes it? This is certainly still an unanswered question, but recent 
work on shock theory offers one interesting possibility in the magnetic 
field free regions. Several recent calculations show that the relatively low 
frequency waves associated with 300 sec oscillations will develop into 
strong shocks in the upper chromosphere, and the sudden release of a 
large burst of energy in this way could cause the transition to coronal 
temperatures, if the atmosphere cannot lose the energy over a shocking 
cycle under chromospheric conditions (Jordan, 1970). This mechanism 
raises as many questions as it attempts to answer and says nothing about 
the complex spicule phenomenon, but it has the merit of simplicity and, 
recently, some additional support, both from the theoretical picture of 
the 300 sec oscillations and how they develop when they become 
progressive Waves, as well as from some recent observations from the 



Til use these two terms interchangably. Usage varies. 



194 

OSO-7 satellite (Chapman et al., 1972). These satellite data give evidence for 
periodic changes in upper transition region conditions, as inferred from ap- 
proximately 300 sec periodic changes in intensities of lines from He II, Mg 
VIII, and Mg IX. These changes could be caused by periodic temperature 
fluctuations due to strong shock waves passing through this region, consist- 
ent with Leibacher's theoretical calculations. 

One of the serious problems that the strong shock hypothesis runs into is 
refraction and, to a somewhat lesser extent, reflection from the sharp 
temperature rise. These effects could reduce the outward flux in these 
waves below the value required to balance energy losses in the corona. 
Even more to the point here, the sharp temperature rise implies a strong 
conductive flux from the corona back down into the chromosphere. All 
of these processes will be further comphcated where there are magnetic 
fields. 

These compUcations do not preclude shock heating in the transition 
region, but they do show that the total heating picture is probably much 
more involved. In particular, until we have a reliable observationaUy 
determined temperature model of the transition region, it will be difficult 
to determine the conductive flux at various points and, hence, the 
conductive heating. One real hope for progress soon is that planned high 
resolution satellite spectra in transition region lines will provide us a 
sufficiently good model to permit the shock heating and conductive 
heating calculations to be made there. Then we can not only discriminate 
better among various possible transition region heating modes, but also 
determine better what waves can continue on into the corona. 

One summary picture of solar chromospheric heating, consistent with the 
work reported and restricted to that great bulk of gas for which the 
magnetic field is negUgible (< 10 gauss), might appear as follows: Sound 
waves are generated by turbulent convection in the low photosphere and, 
thanks to their comparatively high frequencies, they pass through the 
temperature trough and develop quickly into weak shock waves. As such, 
they deUver their energy to the low chromosphere, balancing the net 
radiative losses in H~ and a number of medium to strong spectral Unes, 
and then pass into the transition region where their behavior is less well 
known, but their residual energy flux, and hence their effect, is small, 
perhaps negligible. On the other hand, the 300 sec periodic oscillations in 
the temperature trough have been transformed, by the outward rise in 
low chromospheric temperature, from non-propagating, evanescent waves 
into progressive sound waves and develop quickly into strong shocks, 
capable of producing a rapid temperature rise by heating the gas (ionizing 
hydrogen) beyond its capacity to remain thermally stable at low chromo- 
spheric temperatures. A significant conductive flux back-down will result 



195 

from this rapid temperature rise, and the heating associated with this flux 
will, along with the strong shock heating and the radiative cooling, 
determine the final temperature structure and energy balance of the 
transition region. 

Since this summary picture is necessarily tentative, it might be useful to 
mention several critiques of the above ideas. Ill then indicate why the 
above picture still seems the most compeUing to me. 

First, we cannot discount completely the possibility that the temperature 
rise in the low chromosphere is produced in radiative equilibrium, 
eliminating the need for mechanical heating there (Cayrel, 1963). Some of 
us, including myself, felt that this idea was fundamentally incompatible 
with the non-LTE situation in the H" continuum, but this proved to be 
wrong, due to the non-coherence of the continuum scattering (Skuma- 
nich, 1970). Thus, it was evident that only detailed calculations could 
settle this issue. In particular, given a reasonable density distribution for 
the chromosphere, and the effects of Une blanketing on the temperature 
there, the question becomes: will a radiative equilibrium, blanketed model 
exhibit temperatures as high as those obtained from current observation- 
ally determined models. Athay, (1970) did this calculation and concluded 
that, although no mechanical heating would be needed to produce a 
temperature minimum of 4400° K at Tc (normal optical depth at 5000 
A) = KT'*, mechanical energy would be required above this point. This 
agrees with a calculation I have done, using Athay's blanketing functions 
and a formulation of the problem similar to Gebbie and Thomas (1970). 
At this stage, it appears that the cooling due to Une blanketing above the 
temperature minimum more than offsets the tendency of the non-LTE 
Cayrel mechanism to increase the temperature. Consequently, mechanical 
heating will be necessary to produce a temperature rise in the low solar 
chromosphere. 

I might mention here a subject 1 am not competent to evaluate, but one 
which is very important. This is the possibility of radiative equiUbrium 
temperature rises in early type stars, discussed briefly in Mihalas (1970) 
and, in greater detail, in a series of papers by Mihalas and Auer which 
appeared in the Astrophysical Journal over the late 1960's. If this rise 
occurs in radiative equiUbrium, up to the color temperature of the 
background continuum (otherwise, the second law of thermodynamics is 
violated), this could reduce the requirements for mechanical heating 
significantly. Finding a source of mechanical energy is a serious problem 
for these hot, early type stars, as they have radiative, not convective, 
subphotospheric envelopes. 

Another possibiUty for the solar chromosphere, advanced by one of the 
participants, is the suggestion by Ulrich (1972) that radiative dissipation 



196 

of sound waves might produce the temperature rise. Ulrich questions the 
shock hypothesis on the grounds that evidence for the waves is lacking, 
but it is not obvious that we have taken the observations or properly 
analyzed the data to confirm or rule out the shocks. Quite to the 
contrary, this is the object of several current research programs. It is 
probably premature to judge the radiative damping mechanism, which 
depends strongly on such parameters as wave frequency, radiative relaxa- 
tion time (hence, non-LTE effects), and material velocity in the chromo- 
sphere. Nevertheless, given the sharp negative density gradients in the low 
chromosphere, and considering the granulation evidence for a turbulent 
region 'in which the necessary high frequency sound waves can be 
generated, not to mention the results of weak shock calculations, it would 
seem that the shock heating mechanism still offers the most natural way 
to heat the low chromosphere. 

Subject to these alternate possibilities, the shock heating picture looks 
very promising. In view of this, it might be worthwhile pointing out what 
form of the weak shock theory is valid for chromospheric calculations, 
where the Mach number does not greatly exceed unity. Some conflicting 
results have appeared in the literature, and it is now clear how this 
conflict arose. 

Osterbrock (1961) is the first person to pubUsh an appUcation of what we 
call weak shock theory to the chromospheric heating problem, to estimate 
mechanical heating as a function of height for a given temperature-density 
model. As we have seen, his conclusion that weak' shocks probably heat 
the low chromosphere seems as likely today as it did then. On the other 
hand, much else has changed, and it is somewhat ironical that this original 
conclusion still stands. First, current chromospheric models have a much 
smaller density scale height than the van de Hulst (1953) model used by 
Osterbrock. Second, we now beUeve that wave periods around 30 sec are 
more apt to characterize the turbulence generated sound that the 100-300 
sec range used prior to Stein's (1968) work. Third, it is easy to show 
that, for these short period waves in the chromosphere, the approxima- 
tion used by Osterbrock to evaluate the mechanical flux integral leads to 
serious over-estimates in computing the growth of the shock strength and 
the dissipation. 

Ulmschneider, in the studies referenced earlier, has performed the evalua- 
tion correctly, provided the shock is truly weak. Such a weak shock is 
represented by a P(t) curve calculated by Schwartz^ and Stein (1972) for 
an initially sinusoidal disturbance of period 100 sec under low chromo- 
sphere conditions. The P(t) relation behind the shock front is almost 
linear. This linear relation is equivalent to assuming that the relaxation 
phase of the wave's passage can be represented by a simple wave in a 



197 

perfect gas (cf. Landau and Litshitz, 1959, p. 367). This is not unreason- 
able if the entropy change during the relaxation phase is not too abrupt 
(in marked contrast to the initial "shocking" phase). So by assuming a 
linear P(t) relation over a shocking cycle, one can evaluate analytically the 
mechanical flux integral 

ttF^ (mech) = y /^ (P(0 " V "W^*' (2) 



where Pq is P(t=0) and T (here) is the period, for a given, simple rest frame 
velocity u(t), usually chosen to be a sawtooth N-wave. In fact, it can be 
shown that" the result of integration is almost independent of the ratio of 
the velocity relaxation time to the period, as long as this ratio does not 
become much smaller than 1/3. Using the resulting expression for rrF+ 
(mech) in the shock propagation equation, it can be solved for a given 
atmospheric model. This is what Ulmschneider did. His results confirm 
Osterbrock's original conjecture, but only because the tendency of new, 
smaU scale height models to cause explosive growth of the shock is offset 
by the shorter period and less approximate method for evaluating the 
mechanical flux integral. We have come full circle in a decade. 

The work of Schwartz and Stein, just mentioned, and its antecedent 
(Stein and Schwartz, 1972) bear directly on this question of ranges of 
validity for the weak shock theory. They show that, as expected, for a 
relatively short period wave (100 sec vs. 400 sec), where weak shock 
theory begins to become applicable, a careful treatment of the growth of 
the initially sinusoidal disturbance is necessary to prevent an overestimate 
of the heating low in the atmosphere, and the weak shock theory will 
seriously underestimate the heating as the Mach number approaches 2. 
Fortunately, Ulmschneider's calculations exhibit a lower Mach number 
throughout the low chromosphere. 

It seems that periods of around 100 sec (corresponding to roughly twice 
the acoustic cutoff frequency a;^) represent the upper limit for a weak 
shock treatment of chromospheric waves. Figure III-5 shows the results of 
a calculation I did, using the Harvard Smithsonian Reference Atmosphere 
(Gingerich, Noyes, and Kalkofen, 1971) and solving the shock propaga- 
tion equation exactly as Ulmschneider did. We see that, for a 30 sec 
shock, the shock strength parameter rj remains almost constant with height 
as Ulmschneider concluded. For a 95 sec shock (the velocity relaxation time 
Tq differs by a negligible amount here — it was varied during the calcula- 
tion), 7j grows rapidly with height and eventually exceeds the range for 
validity of the weak shock theory, thus yielding spurious values for the 



198 
3.0 

2.0 



1.0 
1.0 



r.= 300, T= 300,,,, — "" 


^ 


■^^"^ m —^ ''~~'~~ 



0.5 



/ 


T,=90, T= 95 




- — 


-/ 




To = 30, T = 30 


■7(139 KM) =0.32 


_( 1 r 1. 


1 1 1 , 



0.0- 

100 300 500 1000 

h (KM) — »- 

Figure 111-5 Shock stiength parameter ij(h) vs. H for HSRA model and 
different periods t (sec). 

dissipation, as noted by Schwartz and Stein. Finally, for a 300 sec shock, 
the wave, once assumed to be fully developed, grows explosively, and 
cannot be treated by the weak shock method, consistent with the 
previous work of all of us. 

This concludes a survey of the situation in the chromosphere, including 
the transition region, and brings us into the solar corona. What heats the 
corona? We don't know. It's even hard to make an educated guess, 
because there are problems with all the wave modes proposed. 

The Alfven mode is the favorite candidate of a number of authors, for 
several reasons. First, one important effect of a magnetic field will be to 
couple the different wave modes in the chromosphere, leading to a 
transfer of energy from the fast mode (which, you will recall, is just a sound 
wave in a zero magnetic field) into the Alfven mode, in regions where the 
Alfven speed exceeds the sound speed. Since the Alfven speed is given by 
c. = B/\/^'fP> aiid since density drops off faster than temperature 
increases up to the transition region (or, more to the point, c^t faster 
than Cj t as h t), we see that this situation will exist everywhere in the 
chromosphere where B > 10 gauss. The Alfven mode has the right 
propagation properties for coronal heating too; namely, it can penetrate 
to the corona without appreciable dissipation. This is largely due to the 
non-compressible feature of the Alfven wavej which will follow magnetic 
field lines up into the corona. The problem is that no one, to my 



199 

knowledge, has offered a satisfactory dissipation mechanism for these 
waves in coronal gas, whose low densities appear to make the various 
collisional mechanisms inefficient. 

A similar problem exists for the gravity mode, which Frazier's (1968) 
observations suggest should be present due to the presence of penetrative 
convection near the temperature minimum. Again, how is the energy 
dissipated in the low density corona? The long wavelength and low 
frequency gravity wave does not lend itself to shock dissipation there, and 
and linear dissipation processes appear too inefficient. 

One useful bit of information bearing on this problem would be to 
determine, once and for all, if the quiet solar corona, observed at sunspot 
minimum, is a phenomenon of only regions of significant magnetic field 
strength, with material at essentially interplanetary densities between the 
magnetic regions (cf. Billings, 1966, Chapter 3.). If this proves true, it 
would restrict our search to waves and heating mechanisms effective in 
these regions. In particular, it would favor the Alfven wave hypothesis, or, 
perhaps, the one proposed by Howe (1969) and mentioned earUer over 
heating by ordinary gravity waves. 

A popular hypothesis over the years has been that the progressive waves 
generated near the top of the convection zone heat the corona by shock 
dissipation. This raises just the opposite problem from the Alfven and 
gravity modes. Dissipation by shocking could heat the gas, but getting 
these progressive waves into the corona with an adequate energy flux 
looks difficult. The high frequency soimd waves which are likely to heat 
the low chromosphere dissipate practically all of their energy there, 
according to all our recent calculations, which are of course, model 
dependent. The 300 sec waves may carry sufficient energy to the base of 
the transition region, but refraction and reflection off the sharp tempera- 
ture rise probably reduce this flux several orders of magnitude, so, while 
these waves can easily heat the transition region right up to the 10* °K 
corona, they may not have sufficient vertical flux to balance the various 
coronal losses. Again, this conclusion is model dependent, and could 
change as we get better models for the transition region. 

CONCLUSION 

It should be evident from these remarks that one of the crucial 
theoretical problems is the behavior of a system of waves under chromo- 
spheric conditions in the presence of a magnetic field. How do they 
interact with the medium and with each other? What new modes appear 
as a result of this interaction? Frisch (1964) has addressed himself to this 
problem, which involves some unpleasant non-linearities, and. finds that 



200 

with a WKB approximation the rotation of the magnetic field couples the 
modes. Stein and Uchida, among others, are working on the problem 
now, and many of us await their results eagerly. 

Ill close this survey of solar atmospheric heating on the optimistic note 
that, thanks to the high spacial resolution possible on currently flying and 
planned future solar satellites, coupled with good time and spectral 
resolution, we can confidently expect to learn much more about oscilla- 
tory velocity fields and general chromospheric and coronal structure in 
the 1970's. The two pointed experiments on OSO-I, scheduled for an 
early 1974 launch, will obtain simultaneous spectra in a large number of 
uv lines, with spacial resolution approaching 1 arc sec, time resolution of 
10 sec, and spectral resolution of .05 A or better. This will permit us to 
do many things, like testing the chromosphere for the presence of high 
frequency waves in the region where the core of the strong Mgll 
resonance doublet is formed. This is the very region where we expect 
strong dissipation from these waves. 

For those of you interested mainly in non-solar stars, I hope this review 
has demonstrated two things: (1) The shock dissipation hypothesis still 
seems the most attractive for the Sun, outside of, possibly, the corona. 
(2) Nevertheless, there are stiD other candidates for the heating, so great 
caution must be exercised in treating chromospheric/coronal heating of 
non-solar stars with strong convective envelopes by some shock dissipation 
theory . 

Several efforts have been made to treat late-type stellar atmospheres in 
this spirit over the past decade. In this afternoon's discussion, I'll attempt 
a critique of one of the latest and most comprehensive of these studies. 

REFERENCES 

Athay, R.G. 1966, Ap. J., 146, 223. 

Athay, R.G. 1970, Ap. J., 161, 713. 

Bahng, J., and Schwarzschild, M. 1961,^p.7.,134 312. 

Biermann, L. l946,Naturwiss., 33, 118. 

Billings, D.E. 1966, "A Guide to the Solar Corona," New York: Academic 

Press. 
Bohm-Vitense, E. 1958, Z. Astrophys., 46, 108. 
Cayrel, R. 1963, Comp. Rend. Acad. Sc. Paris, 257, 3309. 
Chapman, RD., Jordan, SJ., Neupert, WM., and Thomas, R.J. 1972, Ap. 

J., 174, L97. 
Ferraro, V.C A., and Plumpton, C. 1958, Ap. J., 127, 459. 
Frazier, EN. 196S, Ap. J., 152, 557. 
Frisch,U. 1964, Ann.d' Ap., 27,224. 



201 

Gebbie. K.B., and Thomas, RJ^. 1970,161, 229. 

Gingerich, O., Noyes, R.W., and Kalkofen, W. 1971, Solar Physics, 18, 

347. 
Howe, M.S. 1969, Ap. J., 156, 27. 
Hulst, H.C. van de, 1953, chapt. 5 in "The Sun," ed. G.P. Kuiper, 

Chicago: Univ. of Chicago Press. 
Hundhausen, AJ. 1968, Space Science Rev., 8, 690. 
Jordan, S.D. 1970, Ap. J., 161 , 1 189. 
Kulsrud.RM. \9SS,Ap.J., 121,461. 
kuperus, M. 1965, "The Transfer of Mechanical Energy in the Sun and 

the Heating of the Corona," Dordrecht, Holland: Reidel. 
Landau, L.D., and Lifshitz, E.M. 1959, "Fluid Mechanics," London: 

Pergamon Press. 
Leibacher, J. 1971, Thesis, Harvard University 

Leighton, R.B., Noyes, R.W., and Simon, G.W. 1962, Ap. J., 135, 474. 
Lighthill.MJ. 1952, iVoc. Roy. Soc. London, A211, 564. 
Mihalas, D. 1970, "Stellar Atmospheres," San Francisco: Freeman. 
Moore, D£., and Spiegel, E.A. 1964, Ap. J., 139, 48. 

. 1966, ibid, 143,871. 
Moore, D.E. 1967, part II C in "Fifth Symposium on Cosmical Gas 

Dynamics" ed. R.N. Thomas, London: Academic Press. 
Osterbrock, D.E. 1961, Ap. J., 134, 347. 

Pikel'ner, S.B., and Livshitz, M.A. 1965, Soviet Astronomy, 8, 808. 
Schwartz, R.A. and Stein, R.F. 1972, to be published. 
Schwarzschild, M. 1948, Ap. J., 107, 1. 
Skumanich, A. 1970, v4p. /., 159, 1077. 
Souffrin,P. 1966, ^n«. d'Ap., 29, 55. 
Stein, R.F. 1968, Ap. J., 154,297. 
Stein, R.F., and Schwartz, R.A. 1972, to be published. 
Ulmschneider, P. 1970, Solar Physics, 12,403. 
. 1971a,yls/ro«. & Ap., 12,297. 
. 1971b, ibid, 14,275. 
Ulrich, R. 1970, Ap. J., 162, 993. 

. 1972, to be published. 
Whitaker, W.A. 1963, Ap. J., 137, 914. 

DISCUSSION FOLLOWING THE INTRODUCTORY TALK BY JORDAN 

Skumanich — I would like to ask a question about the zeroth order 
atmosphere for which you are doing the calculation of this heating. Do 
you start with the models that we radiative transfer types give you? 

Jordan — Yes. The calculations in my talk were done for a number of 
models including a current version of the Harvard-Smithsonian Reference 



202 

Atmosphere, which is, I think, the best current model. In general, one 
sees that the results for the heating are almost model independent, as the 
crucial parameter, the scale height, is not strongly model dependent. 

Skumanich — Keeping in mind that these are average models, where do 
we look to better understand heating in the light of these theories, in the 
network or in the cells? 

Jordan — We look in the cells. What is really interesting, however, is the 
fact that when we calculate mechanical dissipation rates with the weak 
shock theory in the low chromosphere, using these average models, and 
compare the results with computed values for the net radiative loss due to 
H", or even make some rough approximation to the blanketing by using 
the Athay -Skumanich blanketing functions, we get surprisingly good 
agreement. I think that this is good evidence that the weak-shock theory 
is a good first approximation theory for the heating in the low chromo- 
sphere. 

Beckers — In connection with the observation, several years ago, I took 
observations in the K and H lines on the disk with a time resolution of 5 
sec and a spatial resolution of one or two arc sec. I never saw any 
periodic phenomena— varying with periods less than 100 seconds. 

Ulrich — In your relation between pressure and velocity, did you include 
the effect of radiative dissipation? 

Jordan — No. 

Ulrich — As I shall discuss later, this could be important. 

Stein — Would you really expect to see waves of such high frequency, 
since the spectral lines you used to study the oscillations are formed over 
a certain atmospheric depth? The velocity profile goes from maximum to 
minimum over a period in a nearly linear way, or the variation is slow, 
whereas the pressure goes from maximum to minimum rather steeply. The 
question is, then: Is the perturbed atmospheric region small compared to 
the region over which the line is formed? Can the oscillation even be 
detected? 

Athay — I've computed the width of the contribution function in the 
chromosphere for the K line for a region making about equal contribution 
to the intensity. It comes out to 300400 km. This is the same order as 
the wave length you are talking about. 

Skumanich — But the velocity field is going to be weighted most heavily 
by the emission at the head of the wave, so it's not a simple question. 

Jordan — And you must keep in mind that high time resolution is 
necessary if there is to be any hope at all, as the time of a single 



203 

observation must be short compared to a wave period or we won't see 
any periodic variations. Both high time resolution and a careful analysis 
will be necessary to settle this question. 

Sheely - I'd just like to point out that we do have data to answer some 
of these questions. Time resolutions of 5, 10, 15 sec and high spatial 
resolution in a great number of lines: Ha, the K line, etc. 

Thomas — I'd like you to clarify once again what region of the 
atmosphere most of your remarks pertain to? 

Jordan - The cell. The non-magnetic chromosphere above the supergranu- 
lation element. Not the sunspoi. Not the plage. Not the spicule. 

Thomas — Why do you restrict yourself to this region? 

Jordan — Because there is where we think the bulk of the chromospheric 
gas is located. The good correspondence between calculated dissipation 
and net radiative losses as a function of height throughout this low 
chromospheric region suggests that these simple, one -dimensional models 
which ignore the magnetic fields may liot be too bad. Thus, though we 
admit, or at least I do, that we can't do the heating calculation in the 
presence of magnetic fields yet, this may not be too serious for the solar 
chromosphere. 

Skumanich - In doing this you're avoiding the coronal heating problem. 

Jordan - More. You're avoiding the role of the transition region, which 
could produce a large conductive flux down. This could be serious. 

Skumanich — I'm worried about the fact that, in the results you showed, 
the shock strength parameter becomes imcomfortably close to unity. I 
recall the value 1/3. 

Jordan — But 1/3 is not uncomfortably close to one in this theory. First, 
the coefficient's of the higher order terms are very small. More reassuring, 
laboratory experiments show that the theory is very accurate in this Mach 
number range. 

Frisch — Why is the knowledge of the temperature structure not 
sufficient to determine the conductive flux? 

Jordan - If we write down the usual expression used to compute 
conductive flux, where this flux varies as the 5/2 power of the tempera- 
ture, you might think that all we had to do was to differentiate this 
expression to get the heating; but that's not necessarily true. We don't 
know the value of the coefficient, which depends upon, among other 
things, the magnitude and direction of the magnetic fields. 

Skumanich — But we know about these fields in the network. 



204 

Jordan - But that's not the region we're talking about. What about 
strong, as yet unobserved, horizontal magnetic fields over the cells, above 
where the weak shock heating occurs, yet in the transition region of 
strong conductive flux? This is a real possibihty. 

Jefferies — You went over coronal heating rather swiftly. What seems to 
be the essence of the problem? 

Jordan — Among other things, I don't think we really know what wave 
modes exist in the corona. There may be some who would take issue with 
that statement, but if you accept it, then you can see that it would be 
rather meaningless to estimate the heating theoretically. Estimates based 
on observations have been offered, of course, equating necessary heating 
to net radiative losses, conductive losses down, and convective losses out. 

Stein — I think the problem goes deeper than that. I believe that in the 
near future well be able to say what wave modes exist in the corona. But 
there is the further problem that the total amount of energy needed to heat 
the corona is small compared to the total energy in the waves when they are 
generated lower down. When you consider the errors inherent in esti- 
mating the energy generated, the dissipation lower down, and the energy 
in waves produced by wave-wave interactions, you find that these enors 
are of the same order as the amount you need to heat the corona. 

Thomas — Are you saying that most of the energy of these waves is lost 
before they reach the corona? I'm not sure of the picture. 

Stein - All I'm saying is that estimates of the amount of energy needed 
to balance coronal radiative losses, conductive flux, and the solar wind are 
small compared to the amount originally generated. We can estimate the 
amount of energy in the 300 sec oscillations, for example, and then when 
we consider the errors in this estimate, they might be of the same order 
as the amount of heat needed in the corona. 

Skumanich — I think you fluid mechanics people are avoiding the 
question of reproducing the dissipation that can be inferred from the 
temperatures which we spectroscopists derive for the corona and the 
transition region. The real problem is that you are unable, with your 
theories, to predict the observed flux divergences high enough in the 
atmosphere that are infened from spectroscopically determined tempera- 
ture distributions. 

Schwartz — But you're talking about the difference between two very 
large numbers, and this difference can be very small. 

Thomas — If I understand the picture correctly, we have not ohe, but 
two competing mechanisms operating here in the low corona just above 



205 

the transition region. In addition to the conductive flux down, we have 
also the convection outward, both in that region where mechanical 
heating due to some mechanism is taking place. This is a more complex 
picture than the one you're talking about Andy. 

Skumanich — That's right. 



Page Intentionally Left Blank 



THEORETICAL UNDERSTANDING OF 
CHROMOSPHERIC INHOMOGENEITIES 

Philippe Delache 

Observatoire de Nice 

"By assuming that the atmosphere is 
homogeneous at each depth, we are 
immeasurably adding to the numerical 
tractability of the problem at the 
expense of ignoring 80 years' worth 
of data on chromospheric inhomogeneities" 



LINSKY and AVRETT (1970) 



INTRODUCTION 



To the spatial inhomogeneity, Linsky and Avrett could have added the 
variations with time which are also well known, well observed character- 
istics of the solar chromosphere. Let me quote also Praderie (1969): large 
asymmetries are observed in stellar K2 components which vary with time, 
"so that it seems difficult to think of any interpretation of the K line 
profile that would ignore motions and inhomogeneities in the atmosphere 
of those stars". And let me borrow a conclusion from Thomas (1969): 
"So what we need are ingenious ideas for empirical inference; or 
theoretical generalization from experience with the solar case". I wonder 
if the solar experience is sufficient at the present time to permit any 
theoretical generalization, as has been the case for the solar wind. In 
order to simplify, 1 shall restrict the scope of this contribution to the 
quiet solar chromosphere, and focus only on spicules. It is quite possible 
that, in ignoring plages and active phenomena, we miss an important clue 
to the understanding of inhomogeneous structures. But we also have to 
"add to the tractability of the problem". 

Now, one basic observed property of the solar chromosphere is undoubt- 
edly its inhomogeneous structure; at the present time, the basic physical 
property seems to be the mechanical energy deposited. So a first question 
could be: how fundamental is the relation between mechanical energy 
deposition and inhomogeneities? The answer is not clear, since the way is 
very long which has to go from the origin of mechanical energy, it's 
transport (or propagation), it's deposition, it's effect on the state param- 
eters, on the macroscopic structures, and then the prediction of escaping 



207 



208 



radiation, which is what we observe. We must not forget that we have at 
our disposal numerous studies where the inhomogeneous structure is an 
essential starting point (or conclusion) together with completely homo- 
geneous theories, some of which are successful. Our question could then be 
replaced by the following: in neglecting the temporal and spatial factors, 
do we loose a significant amount of the physics? and how complicated 
would it be to include the (t, r) parameters in the existing theories? 

The chromosphere-corona transition region should obviously be included 
in our study, since its structure is continuously connected to the 
chromosphere. This continuity, essentially with respect to mass flow, has 
been stressed by Zirker (1971). 

In the following, we shall start from the observations. As we shall see, it 
has been possible to infer from them some empirical models, in which, 
very often, a great many theoretical considerations are embedded; gener- 
ally, the transfer problems are partially solved, whereas the dynamical 
equations are not considered. 1 shall call this type of approach "descrip- 
tive theories". "- 

Then we shall consider the mechanisms of some dynamical models that 
have been proposed to explain the machinery which is responsible for 
inhomogeneities. 

After having stressed that, with little effort, we have at our disposal some 
simple tools for studying inhomogeneities, I shall give a brief account of a 
recent work in which the inhomogeneous structure of the chromosphere - 
corona transition region shows up very simply, from dynamical considera- 
tions applied to observations averaged over the whole disk of the Sun. 

OBSERVATIONS - DESCRIPTIVE THEORIES 

Spicules can be seen on the limb, and also on the disk, even if there still 
exists some disagreement on the correct detailed identification. They form 
families (brushes, coarse mottles) lying at the boundary of the supergranu- 
lation cells, where the magnetic field is known to be relatively strong. 
Most of the available information on spicules can be found in the very 
extensive survey made by Beckers (1968). More recent observations, 
essentially pertaining to the H and K problem, have been made with high 
resolution (spatial, temporal, spectral); for example by Bappu and Sivara- 
man (1971) who propose that the boundary of the supergranulation 
should obey the Wilson-Bappu relationship. It is possible to construct 
simple models for individual spicules and for the chromospheric back- 
ground (sometimes called "interspicular" matter). As Zirin and Dietz 
(1963) mentioned, this kind of descriptive model may account for the 



209 

observations, but generally it does not answer the fundamental questions: 
what is the heating mechanism, and what makes spicules? Recently Krat 
and Krat (1971) deduced that the classical model of a rotating spicule 
made of a Ca II core with a Helium envelope is still adequate for the 
interpretation of their high spatial resolution observations in Ha, H|3, D3 , 
H and K. The question of the dynamical state of such a structure is 
avoided in saying simply that it is compatible with the model of Kuperus 
and Athay (1967). Going to the chromosphere-corona transition region, 
Wthbrbe (1971) also gave a crude description of a spicular structure that 
is needed to explain center-to-limb XUV observations. Beckers (1968) also 
gave a descriptive model of a two component chromosphere, and very 
carefully made warnings on the vaUdity of such an approach. First, he 
obtains a pressure inversion in the interstellar region. (Note that Delache 
(1969) has given a possible interpretation in terms of momentum 
transported by the heating waves.) Second, he questions the validity of a 
statistically steady state; as an example, the recombination time for a 
proton and an electron (Tg =15 000°, Hg = 10'*cm~^) to the first and 
second level is 1.0 or 2.5 min respectively. Similarly the quasi-static 
behaviour of the radiation field could also be questioned. The random 
walk of a photon in an optically thick spicule can take a long time! 
Preliminary work shows that the process can be described in a diffusion 
approximation (Delache, Froeschle, 1972; Le Guet, 1972). 

Since, clearly, one cannot avoid going to the dynamical models, let me 
Ust some observational requirements, as given by Beckers (1968): 

• A spicule moves up (= 25 km s"'), slows down, and approaches a 
standstill; "it is likely that it returns to the photosphere after it 
becomes invisible". 



• 



At two different heights, the accelerations are practically simultane- 
ous: the accelerating force propagates with velocity v > 500 km 



• Spicules appear in the magnetic regions which outline the solar 
supergranulation (B«s 25-50 gauss). 

• Spicule diameters, birth rates, and lifetimes are similar to that of 
the granulation. 

• Temperature Tg is nearly constant above 2000 km. 

• Before the death of a spicule, its diameter increases. 

• LefJ and right hand sides of a spicule are different, possibly 
indicating a rotation. 



210 

SOME DYNAMICAL MODELS 

The first step in trying to put another kind of physics, besides just 
radiative transfer, into what I have called descriptive theories is, of course, 
to look at the energy problem. Thus, the various dynamical theories differ 
essentially in the heat supply. If mechanical energy is deposited in an 
inhomogeneous, time dependent pattern, this can be due to either (or 
both) of two reasons: 

• Th6 amount of energy available for absorption depends on £^ and t. 

• The process by which the energy is absorbed depends on i, t. 

In both cases, the currendy accepted heating mechanisms can be responsi- 
ble for the spicular structure; some of them have been studied in the 
homogeneous case, like shock wave dissipation, or heat conduction, 
together with the departure from radiative equilibrium. A recent review 
by Frisch (1972) describes the results obtained in coupling the heating 
mechanism with the radiation field in a stratified atmosphere. This kind 
of mechanical energy may, or may not, be available in an inhomogeneous 
pattern. For example, Kuperus and Athay (1967) propose that spicules be 
driven by the conductive heat flux. The latter is inhomogeneous from the 
very beginning due to the magnetic structure of the transition regions. On 
the contrary, Defouw (1970) describes a local instability sensitive to the 
magnetic field, which borrows the energy from a constant homogeneous 
source. 

Other types of energy sources have been described which are basically 
inhomogeneous, as the kinetic energy of horizontal motion in the 
supergranulation, or the Petschek mechanism of magnetic line recoimec- 
tion, as proposed in a qualitative manner by Pikel'ner (1971). As there is 
no reason why the starting inhomogeneitiea would be similar to one 
another, it is hard to see why the resulting spicules are so alike . However, 
the role of local parameters in fixing thej, t properties of the dissipation 
are not excluded, and again, it seems worthwhile to study in some detail 
the "local machinery" that may lead to a relaxation, or unstable 
situation. 

For Kuperus and Athay (1967), as we have said, the heat conducted 
backward from the corona in ,the steep temperature gradient of the 
transition region is responsible for the onset of a Rayleigh-Taylor 
instability. The authors describe the instabihty as caused by the upward 
pressure force in the dense layer, replacing the downward gravitational 
field of the classical instability. The quantitative analysis is missing; in 
fact Defouw (1970a) concluded their picture would lead to a stable 
situation. 



211 

In his paper, Defouw describes "thermal instabiUty" but does not deal 
with the real heating mechanism. He assumes simply that there exists a 
heat loss function £ (energy loss minus energy gain per unit mass per unit 
time). The rate of energy input is assumed to be constant. Then, the 
instability is described. The initial idea goes back to Thomas and Athay 
(1961): if the hydrogen plasma is heated, it may become less and less 
able to get rid of its internal energy by radiation. Defouw finds that, 
depending on the temperature range, the temperature gradient, and the 
value of the density, one can have unstable situations. The presence of 
magnetic fields reinforces the instability. Growth rates, temperatures, and 
electron densities are in satisfactory agreement with the spicule observa- 
tion. However, the radiation field is treated in the quasi-static, effectively 
thin approximation, and the energy supply is left unspecified. 

At this point, I would like to make a general comment on "descriptive" 
and "dynamical" models, which comes from the coronal experience. 

If one takes into account the energy equation, and the hydrostatic 
equilibrium for a fully ionized plasma, one can predict a static spherically 
symmetric solar corona (Chapman, 1959). One needs only to specify Tg, 
ng at a boundary point, e.g., at the base of the corona. But this corona 
has a finite pressure far away from the Sun; one needs an artificial wall to 
sustain it. Once the wall is removed, the static corona is no longer stable. 
Is it going to show relaxation into inhomogeneous structures? This seems 
to be a very complicated idea. One has only to allow for a sphericafly 
symmetrical expansion; we add the mass conservation equation and wait 
for the steady state to establish itself. We do not have to impose any 
further physical boundary condition. In particular, the velocity v at our 
boundary point is fixed. The solution (Parker, 1965) is thus viewed as the 
asymptotic behaviour of a time dependent problem. 

Thus, precisely because we think that the chromosphere can be locally 
unstable, the mass motion should be taken into account from the very 
beginning. In a following paragraph we shall see how this simple principle 
can yield to some interesting ideas in the chromosphere<orona transition 
region, possible connected with spicular structure. 

SOME TOOLS FOR THEORETICAL STUDIES IN 
CHROMOSPHERIC INHOMOGENEITIES 

In this section I would like to show, with three examples, that the tools 
that we need to begin are available or can be found with little effort in 
the existing Hterature. 



212 



FIRST EXAMPLE: 



Local description of the instability condition by Defouw: after some 
calculations, one finds that a necessary criterion for instability is: 



^ = (^-T4rM(^'-T^.)-K-^x„)(..-^^^<o 



(£ is the heat loss function, "7 is the number of ionizations per unit mass 

per unit time, p, t, x are the density, temperature, ionization degree, 

and £^ stands for 1£, etc.) 
9 X 

This result has a simple local physical interpretation. In the equilibrium 
state, a given mass element has well defined energy E, number of parti- 
cles M, and volume V. This reads: 



E = cst 


->■ 


£(x,p,T) = 


H=cst 


-> 


J(x,p,T) = 


V = cst 


->■ 


P(x,p,T) = P^^, 



(P is the pressure of the mass element, P^^Js the "external" pressure.) 

What is the condition for the existence of an equilibrium (neutrally 
stable) X, p, T? (Which is the starting point for a discussion of thermal 
instability, as in Souffrin, 1971 .) 

The answer is straightforward: 6jC = 5 J = 5P = 0, i.e. 
£ 8x + £ 8p + £ 8T =0 
jr^Sx+ J8p + J8T = 



^"t ll+x p T 



= 



(sincePa(i+x) pT). 



213 

A solution for 6x, 8p 6T different from zero can be found only if A = 0. 
Thus A = is the condition for marginal stability. A closer examination 
will show which side has the instability .(*) 

This does not mean that the complete calculation made by Defouw is use- 
less. On the contrary, it is really necessary for a detailed description. 
This was intended simply to show that it is often possible to extract 
simple descriptions imbedded in stratified geometries or abstract calcu- 
lations. These simple descriptions can be more than qualitative and can 
give valuable support to the intuition. 



This example is non-local, and mixes the heating process together with 
radiative transfer. Frisch (1970, 1971) has solved numerically the problem 
of radiative and conductive coupled transports in a stratified atmosphere. 
In her results, there seem to appear two regions; as a matter of fact it has 
been shown by Cess (1972) that an approximate solution can be found 
analytically within the framework of singular perturbations; the boundary 
layer can be treated separately from the interior. Again, from detailed 
results, it has been possible to infer an approximate, but much simpler. 



(*) Note added in the final manuscript after a remark by R. J. Defouw. 

The question is not really very simple: for example Defouw (1970b) interprets the 
procedure in the following way: Suppose that 6T=«P=0 and we calculate SjCas a func- 
tion of 6T. 



6X = 



P ~r 5T, 



^x " TTir -'''' 



as ^ <0, X = 0, the thermal instability criterion _ < is equivalent to A < 0. 

One can object that it also seems legitimate to calculate SCT as a function of 6x if 
SX = §p = 0. 



Then 



6 J = ^ 6x, 

■£ -P. JC„ 



as Xq < 0, jC >0, one finds that if A >0, >0 which seems to also yield an un- 
stable situation. 



6 7 

6x 



Obviously in both cases we are not dealing with the correct proper perturbations 
corresponding to eigenvalues of the damping constant (or growth rate). 



214 

description of the physical process. Obviously, the stratified medium 
assumption is no longer fundamental in Cess's treatment. 

TfflRD EXAMPLE: 

This last example is well known. It is simply the non-LTE radiative 
transfer problem, and the concept of thermalization length A, first 
introduced by Jefferies (1960). 

In Mihalas's recent book (1970) the rather simple result obtained by 
Avrett and Hummer (1965), namely 

A« J- ; 1_ ; ^ (Doppler, Lorentz, Voigt), 
e 9e 9e 

results from long calculations whose physical meaning is not obvious. 

While the physical usefulness of A was demonstrated, for example by 
Rybicki (1971), for rapid calculations of non-LTE multilevel transfer 
problems, Athay and Skumanich (1971) succeeded in calculating orders of 
magnitude for A from very simple physical considerations. Notice again 
that the validity of this kind of procedure is demonstrated only because 
the "exact" solution in known! A series of papers by Finn and Jefferies 
(1968) and Finn (1971, 1972) also has to be mentioned; it deals with the 
probabilistic interpretation of radiative transfer. It is interesting to see the 
amount of formalism decrease while the physical insight given to the 
reader increases. The present tendency seems thus to eliminate most of 
the algebra, especially that connected with plane parallel geometry, and 
concentrates on the physical meaning of the local parameters. For 
example Athay (1972) proposes that the optical depth t has to be 
replaced by the "mean number N of scatterings that a photon has to 
suffer before it escapes". Obviously there is a one to one correspondence 
between N and t, but N is not related to a particular geometry. 

In conclusion, I think that one can be optinustic about the possibiUties 
that we now have to attack the problem of understanding the local 
machinery which makes the spicules, if we are careful to consider the 
right local parameters, and if we first try to get good local descriptions of 
physical processes. 

INHOMOGENEITIES IN THE CHROMOSPHERE - 
CORONA TRANSITION REGION: MASS FLOW? 

This paragraph is a brief account of a recent work (Delache, 1972) based 
on the two principles that have been stressed in the previous paragraphs: 



215 

Try to define the local quantities which stand at the midpoint 
between observations and theoretical predictions. The proposal is to 
take the temperature as the independent variable (instead of altitude 
h, or optical depth), and to study the "thermal differential emission 
measure" f(T) defined by 

f(T) dT = n2 dh. 



• Relax the condition of a static atmosphere. 

The equations are very similar to that of solar wind theory, except for 
radiative losses which are taken into account. In a first step, they are 
treated in a one dimensional analysis. The value of the velocity v, or mass 
flow UgV, at a boundary will be physically fixed by the steady state, as 
usual, and will depend on the amount of energy deposited in the corona 
(I assume no energy deposition in the transition region).' As this is outside 
the domain of the study, one will need the observations to infer v, either 
"local" observations (XUV spectrum or radiospectrum) or extrapolations 
of the solar wind flow. 

First, one finds that f(T) is, in fact, simply related to observations, either 
XUV or radio. If the pressure is assumed to be nearly constant in the 
transition region, then f ^ (T) °^ T^ ^ ; this last quantity is not very 
different from T^l^ ^ , which is the expression of the conductive flux. 
Thus, it is not surprising that simple reductions of observations lead so 
often to simple predictions of this flux. For example, Chiuderi et al. 
(1971) proposed a simple parametric representation of the radio obser- 
vation. One can show that this particular form necessarily implies a 
constant conductive flux! 

But the main result is the following: f(T) can have two very different 
kinds of behaviour, depending on the value of the mass flow: 

• If the mass flow is in the "low regime" (which would correspond to 
the solar wind flow, or less) then f(T) « ,^7, thus leading to a 
constant conductive flux and agreement with XUV observations for 
Unes emitted at T > 2.10* °K. This confirms Athay's previous 
result (1966), and is represented by the straight lines on Figure III-6 
which is taken from Pottasch's classical work (1964). However, as 
can be seen on the figure , this behaviour does not match the 
observation for low values of T, nor does it match the radio 
observations (Lantos, 1971). 

• If the mass flow is in the "high regime" (say 50 times higher than 
the prediction of a spherically symmetric extrapolation of the solar 



216 



10 



JO' 



10 



-s n- 



-C tt 

t— n' 



E-i 

—Si m— ' 

\ 
(— n— I 
I — SI n— < 
\ 
I — N m — I 
h-si ly-i 




Mg X 



xir- 



Al XI-l 



' Al K/ 

i-^SiX-H 
MgE-l 



Tean 



\ STZI 



_L 




-S E— I 



(—0 HI — 



I 



10,000 30,000 100,000 300,000 

TEMPERATURE "K 



1,000,000 



Figure III-6 



wind), then f(T) « T^'^ (T-Tq)"^ which agrees with radio observa- 
tions and XUV observations for T < 2-20^ °K as shown on the left 
part of Figure III-6. 

The two regimes can be reconciled in a single model in which the vertical 
coordinate is guided by the magnetic field. The cross section of the 
magnetic tubes of force open to the solar wind flow is increasing from 
the bottom (chromosphere) to the top by a factor of 50. Thus the mass 
flow HgV can be large locally, while it remains constant when integrated 
over the whole solar surface. This sort'of morphology for the magnetic 
structures is known from observations of course, but it is striking that it 
can be deduced from observations which integrate the complete disk. The 
picture can be quaUtatively completed: in regions of closed magnetic lines 
(i.e. the two ends are connected to the solar surface) the conduction 
perpendicular to the field is lowered; the outflow is prevented; the 
transition region should be very iow in the atiiiosphere and very thin; it 
does not contribute to the emission measure for T < 2 10* °K. 



217 

In this model, the transition region structure is dominated by the 
conductive flux for T < 2 10' °K above spicules (open field regions) and 
for all T in the closed field regions. Below T = 2 10' °K, in the open 
field regions, the enthalpy flux plays a major role. The motion of matter 
is important. (It has already been noticed by Kuperus and Athay (1967) 
that the energy flow due to motions in spicules was important.) The 
temperature gradient is not so steep. The amount of material in a given 
temperature range is increased. 

CONCLUSION 

It seems that we are now in a position of starting detailed physical studies 
of inhomogeneities. Local theories are being developed in dynamics as 
well as in radiative transfer. The mass flow has to be taken into account, 
as it is almost certainly a consequence of energy deposition. The 
momentum equation should also be looked at in detail, as the energy 
flow and deposition lead nearly always to momentum flow and deposi- 
tion. (Pressure is exerted by the heating waves, especially in inhomoge- 
neous structures, where they can be refracted.). The stability problem has 
to be solved after the non-static steady state is fully described. In the 
previous paragraph we have seen a crude theory starting on those basic 
principles, applied to a region where dynamics and radiative transfer are 
disentangled; one is really tempted to connect what is described there 
with spicular structure. 

REFERENCES 



Athay, R.G.: 1966 Astrophys. J. 146, 223. 
Athay, R.G. : 1972 preprint 

Athay, R.G. and Skumanich, A. : 1971 Astrophys. J. 170, 605. 
Avrett, EH. and Hummer, D.G. : 1965 M.N.R.A.S. 130, 295. 
Bappu,M.K.V. and Sivaraman, K.R. : 1971 Solar Phys. 17, 316. 
Beckers, JM. : 1968 Solar Phys. 3, 367. 
Cess, R.D. : 1972 Astr. and Astrophys. 16, 327. 
Chapman, S. : 1959, Proc. Roy. Soc. London A 253, 462. 
Chiuderi, C, Chiuderi Drago, F. and Noci, G. : 1971 Solar Physics 17, 
369. 



Defouw, R.J. 
Defouw, RJ. 
Delache, Ph. 



1970a Solar Physics 14, 42. 

1970b Astrophys. J. 161, 55. 

1969 in' Chromosphere-Corona Transition Region NCAR 



Publication, Boulder, Colorado. 



218 

Delache, Ph. : 1972 preprint. 

Delache, Ph. and Froeschle, C. : 1972 Astron. and Astrophys. 16 348. 

Finn, G.D. and Jefferies, J.T. : 1968 J.Q.S.R.T. 8, 1675. 

Finn, G.D. : 1971 J.Q.S.R.T. 11, 477. 

Finn, G.D. : 1972 J.Q.S.R.T. 12, 149. 

Frisch, H. : 1970 Astron. and. Astrophys. 9, 269. 

Frisch, H. : 1971 Astron. and Astrophys. 13, 359. 

Frisch, H. : 1972 Solar Physics, to be published. 

Jefferies, J.T. : I960 Astrophys. J. 132, 775. 

Krat, V. A. and Krat, T;V. : 1971 Solar Physics 17, 355. 

Kuperus, M. and Athay, R.G. : 1967 Solar Physics 1, 361. 

Lantos, P. : 1971 Ph. D. Thesis - Paris University. 

Le Guet, F. : 1972 Astron. and Astrophys. 16, 356. 

Linsky, J.L. and Avrett, E.H. : 1970 Publ. Astron. Soc. Pac. 82, 169. 

Mihalas, D. : 1970 Stellar Atmospheres, Freeman & Co. 

Parker, EJSI. : 1965 Space Sci. Reviews 4, 666. 

Pikel'ner, S.B. : 1971 Comments on Astrophys. 3, 33. 

Pottasch, S.R. : 1964 Space Sci. Reviews 3, 816. 

Praderie, F. : 1969 1.A.U. Colloquium n°2. Commission n°36N.B.S. Pub. 

332 p. 241. 
Rybicki, G.B. : 1971 preprint 
Souffrin, P. : 1971 Theory of the Stellar Atmospheres Ed. Observatoire 

de Geneve - Suisse 
Thomas, R.N. and Athay, R.G. : 1961 Physics of the Solar Chromosphere 

Interscience, New York. 
Thomas, R.N. : 1969 lA.U. Coloquium n°2. Commission n°36 N.B.S. 

Pub. 332 p. 259. 
Withbroe, G.L. : 1971 Solar Physics 18,458 
Zirin, H. and Dietz, R. : 1963 Astrophys. J. 138, 664 
Zirker, J.B. : 1971 The Menzel Symposium, Ed. Gebbier, K.B., N.B.S. 

Pub. 333 p. 112 



DISCUSSION FOLLOWING THE INTRODUCTORY 
TALK BY DELACHE 

Souffrin — I would like to ask where are the large and the small 
ampUtude velocities that you talk about? 

Delache — You may have "large" values for the boundary condition on 
the velocity, which means really a "large" value of the mass flux, if it 
would cover the whole Sun, while the numerical value for the actual 
velocity remains small. This is what happens in the lower part of the 
transition region. 



219 

Thomas — In other words, you end up with a small mass flux down 
below and a large mass flux up above. 

Delache — The important condition is that the mass flux over the whole 
Sun remains constant. Also, I don't want to go into detail about the field 
structure. This whole picture I've given is very macroscopic. 

Thomas — I haven't pushed you to open or closed fields. I've just pushed 
you to large or small mass fluxes, that's all. 

Cayrel — Is it not true that if you multiply the mass of the spicules by 
the appropriate velocity you get the same order of magnitude as the mass 
flux of the solar wind? 

Delache — Yes, I think Beckers has the answer, which I believe is yes. 

Beckers — The upward transport in the spicules is two orders of 
magnitude greater than is required to balance the solar wind; but the 
energy available from the spicules is two orders of magnitude less than 
that required to balance the losses of the corona due to conduction down 
and other losses. So the spicules can easily provide the coronal mass 
losses, but not the coronal energy losses. 

UnderhiU — I'm wondering if this has any relevance to a fairly commonly 
observed phenomenon in stars. In certain late type stars with extended 
atmospheres, you see what are called clouds. These clouds refer to the 
fact that one day you see two or three displaced calcium absorption lines 
and the next day you don't. This common type of observation can be 
explained qualitatively by irregularities in a more or less steady flow. 1 
wonder if this solar-type flow you're describing here might be what is 
taking place? Could this kind of thing develop irregularities? 

Delache — Yes, we know that this kind of thing can develop irregularities 
because the magnetic field structure is changing with time, often very 
rapidly. In the solar case, you must go to the filamentary structure. In 
observations of coronal streamers made from balloons, you see the 
structure changing in two or three hours. 

Pecker — I'm a little troubled by the temperature picture that comes out 
of your model. The temperature within the spicules and the temperature 
outside the spicules seem to vary at such rates that it implies little 
connection between the thermal structure and the magnetic structure. 

Delache — This is not really a complete model. For consistency, you have 
to demand something like pressure equilibrium between the two columns. 
That would require a further step than I have taken. 

Skumanich — I think what all of you are saying is that some systematic 
flow is needed. On the other hand, this avoids the question that Thomas 



220 

raised long ago of the possible role of spicules in heating the corona. We 
lend to view the spicules now as though they arose from energy deposited 
in the corona and conducted back down into the chromosphere; but what 
about the possibility that they arise as a result of some hydromagnetic 
effect. We don't know what this effect may be, of course. We wave our 
hands and say Petcheck mechanism or induction mechanism, but the 
point is, couldn't some magnetic field effect be responsible for the 
spicules and might they not play some role in coronal heating? Do we 
have to go all the way down to the convection zone for the source of 
heat for the corona? Can we deduce anything from the ending of chromo- 
spheres along the main sequence? Can we say anything about how this 
convection decays as we go off the main sequence? Does the type of self 
excited instability that Ulrich has studied prevail along the main 
sequence? How does this scale? 

Athay — One thing that excites me in your work is that you've taken 
data which have no spacial resolution and inferred an inhomogeneous 
structure for the Sun. This has important impUcations for stellar work. 
It's interesting that in the case of the Sun people working from a 
different direction arrive at the same results you discuss. 

Pecker — I was intrigued by Anne Underhill's earlier comment. I wish she 
would make more clear to us exactly what stellar observations are relevant 
to these ideas of Delache. 

Skumanich — I would like to know more about structure in extended 
atmospheres. 

Underhill — The most pertinent observations are those given by Petore 
McKellar, and Wright on the 31 Cygni type stars. Regarding irregularities 
in the flow, you have variations in the tops of emission Unes in the 
Wolf-Rayet type stars. Also in Be stars and B supergiants, when you can 
scan the profiles rapidly. You find they're changing in a matter of 
rninutes, or at least a half hour. You just have to conclude from looking 
at the data that inhomogeneities exist. 

Wright — The figure I discussed yesterday (Figure 11-43) represents 
probably the best example we have of the satellite ,lines in the K line of 
31 Cygni. This is a series taken during the eclipse of 1961, and I hope to 
observe a similar effect before May of this year. Here we have the normal 
K type spectrum with the emission produced by the Kj and K2 , and 
superimposed on that are the chromospheric lines as you come into 
totaUty. This series started in July of 1961, and by the time we got into 
August we saw evidence for these clouds or whatever you want to call 
tiiem. This particular one lasted for three full days, August 6 to August 8. 
Then it disappeared and there was only a single component. Then in 



221 

September the additional chromospheric lines appeared again. Not in the 
same position, but since these are just velocity effects, this is probably 
diie to the fact that different portions of the atmosphere are moving with 
different velocities at different times. Hence, the interpretation as prom- 
inences or clouds, whatever you want to call them. Sometimes you see 
several components. It doesn't show up too well here, but in 32 Cygni, 
particularly in 1965 and later on, 1 have suggested that they may be as 
many as four or five components at a single time. I'm not too positive 
about some of the multiple-component lines, but they do seem to be 
present. When you get deeper into the atmosphere, the lines tend to 
broaden out, and I am interpreting this broadening as the sum of several 
components. Finally, as you come out of totaUty, you begin to see the 
damping wings and get the true K line of calcium. But these must be 
velocity effects, I think. You have broad Unes getting narrow and then 
broad again, all of which is evidence for the type of clouds that Anne 
UnderhiU was talking about. 

Skumanich — Couldn't this be a binary effect, i.e., a gravitational 
perturbation, rather than a structural difference in the atmosphere? 

Wright - I don't think so with these stars, you have the atmosphere 
extending out three stellar diameters, with the B type star just a Uttle 
thing. There's no evidence 1 can find for mass exchange in 31 Cygni or 
Zeta Allrigal, for which we have this kind of data. There does seem to be 
mass exchange in UV Cephei, however, and it therefore qualifies as a 
close binary. 

Pecker — 1 think those observations are exceedingly interesting, and I 
would be tempted to react in the same way Anne did. But this kind of 
thing could not be observed on the Sun at a distance, because the spicules 
are too small and numerous. So if you are to see the kind of thing 
discussed here, the elements must be of a sufficiently large size. So I ask 
the question to Phihppe Delache of how one can apply the equations and 
conditions of energy, momentum, and mass conservation to these objects, 
keeping in mind the fact that much of the flow may occur out the side 
of the spicule-like inhomogenities. 

Delache - I don't think you can do it, because the magnetic field is 
needed to confine the flow, and we don't know anything about the 
magnetic field stfucture of these stars. 

Pecker — But the magnetic field only confines the flow. It does not alter 
the general picture regarding conservation of mass, momentum, and 
energy in the flow. 



222 

Thomas - The magnetic field only establishes the boundary physics - 
not the internal or overall physics. 

Ulrich - I have a somewhat different point of view on this. I feel that 
the granule size or scale is governed by the pressure scale height 
somewhat below the surface of the Sun. Now the pressure scale height in 
these late type stars is a much larger fraction of the total radius of the 
star than in the case of the Sun. If you scale the granulation up 
proportional to the pressure scale height, you conclude that a granule in 
these stars is something like 8% of the radius of the star. Therefore the 
spicules are going to be very large objects. This does assume that the 
spicules are rather directly associated with the granules. Consequently, 
you don't necessarily have to have something like prominences to explain 
the observations; it could be something associated with the granulation. I 
would say that the case of 32 Cygni, the grazing eclipse, is an example of 
this. 

Skumanich - A caution about scaling. As Dumey has discovered in his 
work with Leibacher, one cannot always scale solar to stellar results, at 
least with the solar wind. They found that, in trying to scale the solar 
wind to late type supergiants, the sonic point was reached inside the 
radius of the star. So the wind there is more than the corresponding solar 
wind would be. It's a very dominant feature of the atmosphere. Although 
it's very useful to use the Sun as a standard, we should be particularly 
careful when we go off the main sequence. There are many changes to be 
taken into account. 

Cayrel — In looking at the components of these K lines, I would like to 
ask what part comes from the main component of the atmosphere and 
what part comes from interspicular material? 

Peterson — Isn't that really what Pasachoff has been observing? When we 
observe the K line with high resolution, aren't the changes due to the 
different chromospheric components we are observing? 

Skumanich — I would be very cautious about that. I've looked at 
Pasachoff s results, and if we take, as as measure of the region we are 
looking at, the energy in the line over a one Angstrom band, we find that 
he was looking at only one network region. This problem of statistics 
does plague us, and we must be careful that we are looking at a 
representative solar region. Most of Pasachoff's data are from the cells. 
They are not from the network boundary. On the other hand, everyone 
has seen pictures of the Sun in Ha, .6 Angstroms from line center. Here 
we see Uttle fingers which, if we identify them with spicules, show that 
they tend to cluster around the network boundary, presumably where the 
magnetic field is strong. Thus, you can see the K line from above without 



223 

having superimposed on it the time dependent spicule contribution. If 
not, we have a harder problem to solve. If we cannot assume a steady 
state, then we have to solve a dynamical transfer problem, and that is 
difficult. 

Underhill - That's saying that you have radiative irregularities as well as 
spatial inegularities. 

Skumanlch — More than that. It's saying that while we've let the 
dynamicists worry about the time variable, we've ignored it in the transfer 
problem. I think that, in the network, that's all right. But in the spicules, 
that may not be all rigiit. The spicules are a dynamic phenomenon, v/ith 
time scales comparable to the reaction rates of interest. 

Underhill - I can imagine a situation where you see the spicule for 
a while, and then you don't; so you think it has gone away. But maybe if 
hasn't, really. Rather, the spectral feature you were observing to detect 
the spicule has faded. 

Skumanich — May I now call for more detailed questions on the two 
introductory papers. 

Defouw — I'd like to make a comment on the first paper first. Jordan 
noted that shock waves may begin at an altitude of 1000 km. This is the 
altitude at which there is an abrupt temperature jump, and he implied 
that this temperature jump may be caused by this shock formation and 
the subsequent dissipation. I'd like to point out that the amount of 
dissipation that is required is not determined by the temperature but by 
the radiation rate. That is, an abrupt increase in temperature does not 
imply an abrupt increase in the heatirtg rate. In fact, you can have an 
abrupt jump in temperature even if the heating rate is uniform through- 
out the whole atmosphere. To show this I will make an elementary 
calculation using the net heat-loss function, L, which is the cooling ?ate 
(in ergs cm"' sec"* or ergs gm~' sec"' ) minus the heating rate . The energy 
equation in which I am interested is L = 0. I would like to consider the 
simplest case where L depends only on the local values of the electron 
temperature, T, and the gas pressure, P. If we differentiate the heat 
equation L(T J*) = with respect to height, h, . . . 

Skumanich — Excuse me. Just for clarification, what is in your heating 
function L? 

Defouw — I'm going to consider the heating rate in L to be a constant. 
The funtion L includes the mechanical heating but is otherwise unspeci- 
fied. 



224 

Skumanich - Do we know how to differentiate it? 
Defouw - I'll differentiate it as follows: 



dL dT ^ 3L ^ ^ Q 



31 dh aP dh 



Now I'm going to ignore momentum transfer by waves. Which Delache 
likes to include. If we just consider ordinary hydrostatic equilibrium 
(dP/dh =-pg), we find that the temperature gradient is 



dT 9L/9P 

— = pg 



dh aL/ai 

By the assumption L = L(T,P), I've assumed an optically thin atmosphere. 
I'll draw on the board the radiation rate for an optically thin gas as a 
function of the electron temperature for a fixed value of density. This 
curve was first calculated in essence^by Pottasch and most recently by 
Cox and Tucker. You have a maximum around 20,000 K due to 
hydrogen emission and a maximum around 100,000 K due to emission 
from ions of carbon and oxygen. 

Skumanich - At what density? 

Defouw — At any fixed density. If we consider fixed pressure, which is 
what we want for the derivative dL/9T, the cooling curve is similar but 
the maxima are shifted to slightly lower temperature. 

Skumanich — Is there any particular density you would use? 

Defouw — No, as long as the gas is optically thin. 

Skumanich - I come back to my comment during the first day. That is 
not sufficient, there is a length scale that has to come into the problem. 

Defouw — In this case, I'm just assuming an optically thin atmosphere. I 
don't believe the chromosphere is really optically thin. This is just an illus- 
trative, calculation. Now, the numerator (3L/9P) of the above expression 
for dT/dh is always positive because it is essentially a density derivative of 
the radiation rate. The sign of the denominator (3L/9T) is determined by 
which side of a maximum in the cooling curve you are on. If you are on 
the low-temperature side of one of the maxima, the denominator is positive, 
and the temperature must increase with height in order to keep the radiation 
rate equal to the heating rate. As you get closer to the maximum, the 
radiation rate becomes less sensitive to the temperature, and therefore the 
temperature has to increase more rapidly with height. Finally, at the maxi- 
mum, 3L/3T vanishes and the temperature gradient becomes infinite. By 
this time conduction has become important. 



225 

If you look at models such as the one Vernazza presented the other day, 
and early models of Thomas and Athay, you see two temperature juinps 
which I think you can associate with the two maxima in the cooUng 
curve. I admit that optical thinness is not a valid assumption near 
T= 10* °K, but I think it is reasonable to assume that the temperature 
dependence of radiation will show a maximum due to hydrogen emission. 
The first temperature jump near T = 10'' °K, should be attributed to this 
hydrogen maximum while the chromosphere-corona transition is due to 
the carbon -oxygen maximum in the cooling curve. The largest tem- 
perature gradient occurs where the maximum in the radiation rate is 
found. It follows that we are not jumping to coronal temperatures 
because we need more efficient radiation-we are already at the maximum 
of radiation efficiency. Because we are at the maximum, the denominator 
in the above expression for dT/dh vanishes, and we have an infinite 
temperature gradient. That is my first point. 

Now I'd like to comment on the model of Delache. This comment may 
be wrong because I'm not sure I understand the model. If so, please 
correct me. We have the large conductive flux from the corona. How do 
you dispose of this flux? Radiation cannot dispose of it because the 
temperature gradient near T= 10^ K is so large that the large conductive 
flux from the corona is deposited in a shell only a few kilometers thick. 
This problem was first pointed out by Giovanelli in 1949. Now, what 
Delache proposes to do is to balance this conductive flux with an 
enthalpy flux associated with some fluid flow. He finds first, doing a 
one-dimensional calculation with no horizontal structure, that, if the 
enthalpy flux is to be large enough, you need a fluid velocity of 50 
km/sec, or several tens of km/sec. The mass flux you get for these 
velocities is much larger than the mass flux in the solar wind. To get 
around this, he says that the velocities are occurring just over a fraction 
of the disc, to reduce the mass flux. So he still has velocities of 50 km/sec. 

Skumanich - I think 10 km/sec was the value. 

Defouw - OK. 10 km/sec. As I understand it, he has not done the energy 
calculation for this new configuration. One thing he is obviously going to 
have to include is what Kopp and Kuperus pointed out. The conductive 
flux is also going to be channeled by the magnetic field and it's going to 
be magnified by the same factor that the mass flux is reduced. So it is 
not at all clear to me that the enthalpy flux associated with the mass 
flow vvill still balance the conductive flux. 

Delache — I think that the answer is yes, that the kinetic flux is 
channeled by the magnetic field, but you must realize that you do not 
necessarily have conservation of the whole conductive flux, as is the case 
for the mass flux. 



226 

Defouw — Then is it true that you are no longer balancing the enthalpy , 
flux with the conductive flux? 

Delache — If we include radiative losses, that is true. As I said, you are 
increasing the gas conductivity and lowering the temperature gradient, 
which increases the omission measure and the amount of material which 
can emit radiation. 

Defouw — Now do you think the radiation can take over? 

Delache — No, it can only partially take over. 

Defouw — Have you done the complete calculation for the configuration? 

Delache — As 1 have said, this model is very naive, with one thing on top 
of another. We have to go through this region with a variable cross 
section, which I have not done-yet. But in this discontinuous model, the 
basic quantities are conserved: mass flux, and energy (flow, conduction, 
radiation). 

Defouw — My last comment is that I no longer beUeve in my theory of 
spicules. The reason I don't is that the temperature of spicules seems to 
be going down. The most recent estimates are about 8000°K. For 
thermal-convective instability you need at least 12,000°K. 

Skumanich - They are 8000°K if steady state is assumed. So we are 
hiding a sinner in the basket, for, if steady state does not hold in spicules, 
the estimate of the temperature may be in error. I don't know by how 
much, but I don't feel that your suggestion is necessarily thrown out by 
current low temperature values based on a steady state assumption. 

Defouw — I beUeve that my explanation of the temperature jumps is 
essentially correct, although some details like opacity effects and 
the height dependence of the true heating rate will require some 
modifications. 

Ulmschneider — It seems to me that observations show radiation losses in 
Lyman a, and so on, that are much greater than the C, N, and 
radiation loss. 

Defouw — But the observed Une intensities depend on the temperature 
gradients in the respective regions of Une formation. 

Ulmschneider — This curve that you plot here should be such that the H 
peak should be very large and the C, N, and the peaks quite small, on 
the tail of the H. (Editor's note: This curve does not appear in these 
Proceedings.) 



227 



Defouw — You can't proceed from observations on this matter, because 
the observed intensity of a Une depends on the thickness of the region of 
line formation. 

Skumanich — Well, that's not quite correct, because I think we do have 
to accept the spectroscopic model of Mr. Vemazza. 

Defouw — I think that in Vemazza's model, Lyman a is produced in a 
region 100 - 200 km thick, whereas the important carbon and oxygen 
lines are formed around T= 10^ °K, where the length scale is only about 
5 km. 

Schwartz — Let me make a comment on what Defouw just described in a 
quaUtative way for a constant heating rate, and say that it probably 
occurs even in a more realistic situation. Figure IIL? shows the results of 
a calculation showing, in a quasi-reaUstic way, the heating and cooling of 
this region. It is a numerical experiment, where you take the atmosphere 



en 

< 

UJ 

i ° 

UJ 20 

cr 

13 

Q. i5h 

Z r 

UJ 



1 1 1 1 r" 

T = 50 sec 

RAD + ION 

— ION 

— - ADIABATIC 



. >T----r 




1 1 1 1 1 1 T 1— 

T = 200 sec 

- RAD + ION 

- ION 

- ADIABATIC 






1000 2000 3000 4000 5000 
HEIGHT (km) 



Figure 1II-7 



228 

and tickle it from below, and then watch and see what happens. The 
upper curve is for a half-sine pulse with a width of 50 seconds (for a full 
sine wave it corresponds to a 100 sec period). The first pass at the 
problem didn't include any radiation at all to cool the atmosphere. We 
just set the radiative cooUng equal to zero, and the temperature just went 
shooting up as soon as the shock was formed. When we put in the sort of 
cooling that Defouw talked about, the temperature rise was rather modest 
until you got to something like the transition region; then the temper- 
ature shot up again. However, the net dissipation of mechanical energy as 
a function of height was nearly the same for these two calculations. You 
see that the inclusion of radiation causes a rather radical change in the 
temperature distribution. 

Skumanich - It sounds as though the mechanical dissipation is temper- 
ature insensitive. 

Schwartz — The dissipation was fairly temperature insensitive, but the 
temperature rise produced by that dissipation is affected very much by 
the radiation. 

Stein — I would like to make three comments about shocks, before Bob 
Schwartz continues with the results of our computer experiments. First, 
an isolated pulse and a train of waves behave very differently. For an 
isolated pulse the shock strength increases indefinitely as the wave 
propagates outward. In an isothermal atmosphere, 

eZ/2H 

(M-1) = (M-l)o- , 



4ii(M -l)o (e^/2H.i-) + 1 

^■0 



V4 



where M is the Mach number and the subscript indicates initial value. 
When the atmosphere has a more compUcated structure, corresponding 
formulas can be obtained, but 1 just want to show the simplest case. For 
a train of waves, however, the shock strength, instead of increasing with 
height, approaches a constant asymptotic value'. 



M-1 = (M-l)o 



eZ/2H 



4-S_ (M-l)o (e^'^^-l) +1 



So the first thing you should decide when making a model is which is the 
realistic situation for the Sun. 

Second, weak shock theory is an infinite frequency theory. It includes 
stratification, but neglects the dynamic effects of gravity. This effect is 
dramatically illustrated by some of our results which Bob will present. 



229 

Finally, even for high frequency waves, weak shock theory gives incorrect 
dissipation. A wave must propagate some distance before it forms a shock 
and begins to dissipate, so weak shock theory which assumes that a shock 
already exists cannot be appUed starting at the place where the wave is 
produced. On the other hand, after a shock has travelled a distance, 
non-Unear effects increase the dissipation above the weak shock value. 

Skumanich - Does what you say depend on the temperature structure of 
the atmosphere? 

Stein — Not really. Weak shock theory with these simple formulas is for 
an isothermal atmosphere. The same thjng happens if the atmosphere has 
some noniso thermal temperature structure, but then the formulas come 
out in terms of an integral over height. Qualitatively, the behavior is the 
same. 

Ulmschneider — I would like to make one comment. Until now, the weak 
shock theory was only applied a considerable distance above temperature 
minimum to insure that the shock would be fully developed. Therefore 
the dissipation is naturally too large at low heights, if weak shock theory 
is erroneously used there. 

Skumanich — So what you are saying is that you can "fudge" where you 
put the energy by where you introduce the shock. Is that correct? 

Ulmschneider — Yes, to date, when we used a fully developed weak shock 
theory, we didn't start from the temperature minimum, but started from 
an observational point further up. 

Skumanich — How can you justify that? What is the reason for putting 
the boundary where it is? -^ 

Ulmschneider — Because I know that the shock is not developed lower 
down and that you cannot expect the result of a fully developed weak 
shock to be correct there. 

Jordan — I agree with Ulmschneider that one can invoke fully developed, 
weak shock theory in the maimer he indicated and still obtain reasonable 
dissipation estimates above the temperature minimum. This is because, 
from independent studies, it is just above the minimum that we expect 
significant departures from radiative equilibrium, largely due to H", and 
also because the shock strength settles down to a value of about 1/3 over 
most of the low chromosphere, rather independent of the initial value tJq 
for the strength chosen (in a reasonable range of 0.1 <t?o < 1/3). Thus, 
any overestimate would be confined to a narrow region just above the 
minimimi. Furthermore, one can follow the development of an initially 
sinusoidal sound wave from the low photosphere, where it is generated, to 



230 

the chromosphere. Many independent studies suggest that these waves will 
become fully developed shocks (for short period waves with period 
T < 100 sec) by the time they have reached the low chromosphere above 
the minimum. 

Skumanich — It seems to me that the correct solution is to get Vernazza's 
model. He gives you the mechanical flux gradient without the conduction 
term taken into consideration; but he presumably can put that in. The 
question is, are you getting that kind of dissipation of energy with height, 
or with density, as Vernazza suggests, or not? It is not clear that you are. 
You seem to put the lower boundary wherever it suits your purpose. 

Jordan But if the computed net radiative losses as a function of height 
correspond to the computed mechanical dissipation as a function of 
height for the same model, as the calculations we have done with the 
HSRA so far indicate, then this is reason to believe that the initial 
formulation chosen for the problem is not too urueasonable. This is the 
criterion you have just stated. 

Schwartz — Let me tell you where to put the boundary. If you start at 
height zero with a wave of initial velocity Vq and period equal to t, then 
the wave goes a distance AZ = 2Hln(l + 7/2(7+ 1) • gr/v^) before the 
crest of the wave has caught up with the trough and it has formed (in 
some sense) a fully developed shock. If you start off the wave with a 
given velocity ampUtude, then this formula tells you at what height you 
can begin to apply these weak shock formulas. 

Souffrin — Is that the distance where you start pushing the gas? 

Schwartz — That is where the. shock is formed. 

Souffrin - You put in Vq and you get the shock at some distance? 

Schwartz — That's correct. 

Souffrin - In the distance travelled in a period or two, you reach the 
place where the shock forms? 

Schwartz — That's correct. This says if you take longer periods the wave 
gets higher up before it shocks. But remember this is an oversimplification 
which neglects gravity. 

Skumanich - What are the free parameters in this? It looks like they are 
Vq and the height at which you hit the atmosphere with v^, with an 
infinite plane wave. 

Schwartz — This is for an isothermal atmosphere which is the only 
condition in which you can work it out analytically. 



231 

Skumanich - But what are the parameters? v^ , the height at which you 
start the pulse, and what else? 

Stein — In the Sun, essentially nothing. Even the height at which you 
start is rather unimportant because, once you get into the convection 
zone, the density scale height becomes large and, therefore, starting the 
wave deeper in the convection zone will not change very much the height 
at which the shock forms. 

Schwartz - In other words, this formula fails, because the atmosphere is 
not isothermal below the top of the convection zone. 

A. Wilson - If 1 give you some numbers, I wonder if you can tell us what 
that Az would be under those circumstances. Try a period of 10-20 sec, 
and an amplitude of 1.2 km/sec. What is Az? 

Stein - We didn't actually do it for a 20 sec, but for a 50 sec, pulse in 
our paper and it came out to be TiVi scale heights. This is the point at 
which you start getting dissipation. 

Skumanich — Where does that put you relative to h = on the limb? 

Stein - A few hundred kilometers higher. 

Skumanich — But isn't that too low? 

Stein - No, not for a high frequency, like the 50 sec pulse represents. 
Longer period waves, on the other hand, don't form shocks until they 
reach greater heights. 

Ulrich - I want to make a general comment about all of this sound wave 
heating. I think unless you put some treatment of the radiative interac- 
tion in the dynamics of the sound wave you are not likely to get the 
correct answer. This is a very dominant effect. It makes the calculations 
messy. I don't know how the energetics work out. I would be surprised if 
you got the same results. 

Stein — We also did the calculation with radiation. We included H"and 
hydrogen recombination to excited states in an optically thin approxima- 
tion. Direct radiative damping of the waves occurs in the photosphere and 
low chromosphere, and can remove up to 2/3 of the wave's energy. The 
rate of shock dissipation is insensitive to radiation, but instead of the 
temperature increasing this energy goes into ionization and radiation. The 
temperature rise is small untU hydrogen is ionized. 

Souffrin — Regarding what you just said, and what Uhich just said 
before, about pulses and wave trains. It is somewhat like the difference 
between an initial value analysis and a boundary value analysis. Consider 
the question of dissipation. It turns out that it is just impossible to guess 



232 

ahead what effect radiation will have on either analysis. If you look at 
the initial value problem, you have some motion given at an initial time. 
Then suppose you have some radiative damping. It turns out that 
radiation smooths out the motion in a given time. If you look at the 
boundary value analysis, you just can't guess, due to stratification, 
anything about the spatial damping in the wave train problem just by 
looking at the time damping in the initial value problem. It is very 
important in all these questions concerning heating to have a good idea 
about the physics of the excitation of the observed motion. 

Schwartz — For the weak shock theory, which Jordan just talked about, 
we did another numerical experiment. This time we excited the atmo- 
sphere with a wave at the bottom with a period of 100 sec. and let it run 
for about 40 periods to let the transients die down and enable the 
atmosphere to achieve something like a steady state. The velocity profile 
is shown on Figure III -8. This resembles a classic N wave, as everybody 
has assumed in treating this problem. However, you will notice that the 




40 60 

TIME (sec) 



Figure III-8 



233 

pressure variation is much more sharply peaked than the velocity varia- 
tion. That might be of interest for people who look for oscillations in 
(intensity. Figure III -9 shows the same calculation for a wave with a 
period of 400 sec, about half the acoustic cutoff frequency, twice the 
critical period. This is in the non-propagating region in the low chromo- 
sphere. Here, at 1000 km above the photosphere, it still looks very 
sinusoidal, and the pressure variation is very smooth. You will notice that, 
in this wave, the pressure is out of phase with the velocity. Look at the 
relationship Jordan wrote down this morning for the energy propagation: 
energy flux = 



•'0 



(P-Po)V<»t 



E 
>• 



O 0.0 



T 1 1 

VELOCITY 

PRESSURE 




^^' 



100 200 300 400 

TIME (sec) 

Figure IH-9 

Since the pressure and velocity are 90° out of phase, then the wave is not 
propagating energy; it is like a standing wave. 

Figure III-IO shows the dissipation caused by the first wave (100 sec 
period).. The dotted line is the fully developed weak shock theory and the 
soUd curve is the result of the actual non-Unear numerical calculation. 
Although it has the same asymktotic form, it still disagrees by an order of 
magnitude in the asymptotic regime, even though this is the regime where 
you might expect the weak shock theory to" hold. Of course, as 



234 




T =100 sec 
- NON LINEAR STEADY STATE 
• WEAK SHOCK 



ICXK) 
HEIGHT (km) 



Figure IIMO 

Ulmschneider just remarked, the weak shock theory gives excess dissipa- 
tion in the lower atmosphere, because it assumes a fully developed shock 
at all heights. 

Ulmschneider - Nobody has done a calculation down there using the 
weak shock theory. 

Schwartz — That's correct, for the reason you pointed out. You know the 
weak shock theory wiU give the wrong result down there. 

Skumanich — What, exactly, are you comparing to what? 

Schwartz — I am comparing the weak shock theory to the exact 
integration of the equations of motion, for this particular model, the 
isothermal atmosphere. Whether or not it has anything to do with the 
Sun or not is another question. However, in this example, the heating 
which is given by the weak shock theory above 1200 km. is an order of 
magnitude less than the exact solution which the weak shock theory 



235 



purports to approximate. If you think this is bad, look at Figure III-ll. 
That gives results for a long period wave, the 400 sec one. We see the 




Figure IIMl 

weak shock result for the dissipation here, and the steady state result for 
the non-linear calculation down below by 5-6 powers of ten. So the 
application of the weak shock theory to waves with periods longer than 
the acoustic cutoff is nonsense, even qualitatively. 

Ulrich - May I please ask whether your exact equations of motion 
included the radiation curve? 

Stein — In this particular case, to make comparisons easier, the compari- 
sons were between the weak shock and an exact integration of the 
equations of motion for an isothermal wave in an isothermal atmosphere. 

Schwartz — We have obtained results which include radiation, in the 
optically thin approximation. 



236 

Souffrin - For an isothermal shock in an isothermal atmosphere there is 
an isothermal deformation, and the dissipation goes to zero. 

Schwartz - If you have a shock you have dissipation. 

Souffrin — For an isothermal wave, its dissipation goes to zero. Gamma is 
one. 

Schwartz — No, it is /Tds and the entropy changes across the shock. But 
you assume, by saying it is isothermal, that this is a very unphysical 
radiation shock. As soon as you raise the temperature slightly above the 
ambient temperature, the system gets rid of all the energy by radiation as 
fast as you dump it in. That is physically what this means. But it's not a 
physical result. 

Skumanich — What you are saying is that you are throwing away the 
entropy generated by the shocks, so it doesn't go into internal energy. 

Schwartz — That's right, but you are keeping track of the total amount 
you have thrown away; that is what this dissipation is. This is admittedly 
an unrealistic case, but it was the only case for which we could write 
down an analytic formula for the solution of the weak shock equations to 
compare it to the numerical results. 

Skumanich — I infer that you are then saying, "Don't trust weak shock 
theory." Now, do the weak shock theorists want to stand up and say 
something in rebuttal. 

Ulmschneider — This work was done with waves of higher period. The 
weak shock theory is mostly done with waves of about 25 sec period. 
This is a factor of four below the waves discussed here. So I would 
suggest that by extrapolating in Schwartz's graphs from the 400 sec to 
the 100 sec and from there to the 25 sec waves that the weak shock 
result would be much better for the higher frequency waves. 

Jordan. — To that, I would like to add something that has already been 
pointed out; namely, in the application of this theory, we do not have to 
assume a fully developed shock at the zero point on those graphs. So I 
would completely agree with everything on Schwartz's graphs, and, yet, I 
think that the weak shock theory does have a useful range of vaUdity for 
high frequency waves in the low chromosphere. • 

Skumanich — Then the question is; are they high frequency or low 
frequency waves? 

Stein — In the discussion this morning, Beckers talked about the 
observations and said that they had looked at phenomena with good 
enough time resolution so that if there had been shock waves with 
periods of about 50 sec they should have seen them, and they didn't. 



237 

Thomas — Wait a minute. You have given a shock wave and you should 
predict what you should expect to see. Then you ask whether Beckers has 
seen it or not. 

Stein — Wolfgang, Kalkofen and I are in the process of doing that. 

Schwartz - It should be noted that it is a bit misleading to talk about 
high and low frequencies in this context. Although a wave may be 
thought of as starting out with a certain frequency or superposition of 
frequencies, the situation is altered once the shock forms. Since the shock 
travels faster than the sound speed, it catches up whatever waves may be 
present ahead of it and converts some of their energy into shock energy. 
Thus, although you may have, for instance, some transient low-frequency 
waves present in the atmosphere which would never form shocks by 
themselves, that does not preclude their contributing to the strength of a 
shock by this nonlinear interaction. 

Ulmschneider — By considering what kind of mechanical flux you have, 
you find that the amplitude of the shock wave is not very large. You 
don't expect a very high velocity of the shock. You expect a shock 
velocity that is almost equal to, the sound velocity. In that way the shock 
doesn't eat up the other distrubances. It appears that the high frequency 
waves which have periods of around 10-20 sec develop into shocks first at 
low heights. You can get an idea of how such a shock develops out of a 
sound wave by considering the simple wave theory. This shows that if 
you assume the same initial flux, then a wave of high frequency will 
develop into a shock earUer. This was the basis for my work, in which I 
assume that at low heights, 200 km above the temperature minimum, 
high frequency shock waves are formed. In the case of short period 
waves, as we just saw, 1 suppose it isn't too bad to assume weak shock 
theory. I think everything is self consistent and consistent with the 
computation of acoustic flux done by Stein. The graphs shown by Jordan 
show that a large part of the acoustic flux comes in short period waves. 
Now, why don't you see them? I think, because of the contribution 
function, the height interval in which you contribute to the line emission 
is about 300 km. But if you have a 10 sec period wave and a 7' km/sec 
sound speed, then you have a wavelength of 70 km. This fits several times 
into 300 km, so you shouldn't see it. You shouldn't see effects of high 
frequency sound waves in spectral lines. It will add to the micro tur- 
bulence of the medium, so you see a broadened profile. But will not see a 
periodic shift of any kind. So I don't think this is an argument against 
high frequency waves. 

Thomas — But how much can it add to the microturbulence? You had a 
very high frequency weak shock, so how much does the material velocity 



238 

change across that shock? If it's not much, then it doesn't do anything to 
the micro turbulence. 

Ulrich — There must be a sound speed difference across the front or it's 
not a shock. 

Thomas - An infinitesimally weak shock has no material velocity 
amplitude, and that's what I measure. The propagation velocity is the 
sound velocity, but not the material velocity change. 

Souffrin — There is a difference between turbulent excitation and pulse 
excitation. If you think of just one shock traveling, then, after some time, 
the initial situation is restored. Now from a stationary excitation there 
must be a stationary structure, something that is not a traveling shock. 

Skumanich — One comment. We have been talking about two modes of 
excitation. One is from the turbulent convective region, and it propagates 
and then undergoes non-Unear interaction. The second one is just like a 
piston hitting bottom of the atmosphere with some characteristic time. 
Which one is involved in producing these high frequency waves? Also, will 
the mechanical energy theorists please give the observationalists some 
guide as to what they should be observing. The theorists have to constrain 
the domain of applicability so that some observational parameters can be 
found. 

Ulrich — There are four main points I wish to make. I will start off by 
some discussion of shock waves, because 1 think the evidence in favor of 
them is weak from the observational standpoint. At least for the longer 
period oscillations, the observed line core intensity fluctuations are too 
small to be compatible with shocks. If there are shocks, they must occur 
at higher frequency. I think this particular effect was demonstrated by 
the observations of Simon and Shimabakuro (Ap. J., 168, 525), who 
looked at the electron temperature of the gas somewhere about 2000 km 
above the temperature minimum. They found that the brightness of this 
gas showed only a slight correlation with five minutes. Their time 
resolution probably was not able to provide useful results for periods 
shorter than 100 sec. 

Concerning the power spectra calculated by Stein, I would point out that, 
in the region of the frequency diagram between 100 and 300 sec, it gives 
exactly the wrong slope compared to the observed power. Anyone using 
this theory should find a reason for this error and come up with another 
power spectnmi which is more in agreement with the observations. Until 
this is done, I, for one, will remain a Uttle skeptical of this peak at 50 
sec. That is something that the high frequency shock people must do in 
order to make their theory more beUevable to me. 



239 

In talking about heating today, we have had a good deal of discussion 
about the derivative of the mechanical flux. Figure III-12 illustrates some 
of the relevant expressions. Most people have used the first expression for 



CHROMOSPHERE HEATING WITHOUT SHOCK WAVES 
F = FLUX OF ENERGY ASSOCIATED WITH OSCILLATORY MOTIONS 
16aT3pTj(T-Tj = -- 



dF ACOUSTIC ENERGY BECOMES 

., ■ RADIATIVE ENERGY 



WHAT IS F? THE CIRCLED QUANTITIES ARE CLAIMED TO BE F. 

Da ^-^ 

ECKART : p ^+ V" (Pu> pg • u + pq 

Dt ^-^ 

LANDAU & ^ , e,^„ r Lj\ 

: — (pS)+ V-(pHu)=pq 

9t 



LIFSHITZ 



WHERE £ = y2|u|2 + E+gz 

q = -16aT3„(T-Tj 



Figure III-12 

the mechanical flux. I have tried to find the source of this expression, 
and the references lead to the book by Eckart on "Hydrodynamics of 
Oceans and Atmospheres" in which this equation is indicated. This is the 
total derivative of the energy per gram of the fluid following the motion. 
This equation seems perfectly valid. However, I think it's hardly clear that 
the circled quantity is a proper flux since the divergence of this must 
follow the motion of the fluid. Additionally, there are two extra terms. 
Landau and Lifshitz, on the other hand, derive this equation, and point 
to this term where the script H is the enthalpy and claim that this is the 
mechanical flux. On the left hand side is a time derivative fixed in space 
so that Landau and Lifshitz's flux looks like a more legitimate flux since 
the divergence of it gives a time derivative of the energy density. I have 
adopted this as my definition of the mechanical flux. In the case of 
non-adiabatic oscillations this expression gives and additional entropy 
derivative which must be included in the flux. Another thing to notice in 
this equation is that I have written the emissivity schematically in a crude 
form. It is precisely this same quantity divided by the density which 
appears in the equations of motion of the sound wave. 



240 

I have studied the propagation of acoustic waves in the presence of a 
temperature gradient and radiative interactions. Figure III-13 shows the 
assuinptions that I have used to get a tractable dispersion relationship. 
The critical assumption here is that the opacity is given by LTE. 





ASSUMPTIONS 


1. 


SMALL AMPLITUDE OSCILLATIONS ABOUT A 




PLANE PARALLEL MODEL IN HYDROSTATIC 




EQUILIBRIUM. 


2. 


PERFECT GAS EQUATION OF STATE. 


3. 


OPACITY GIVEN BY INSTANTANEOUS LTE. 


4. 


NO VISCOSITY. 


5. 


tjT3 = CONSTANT. 



Figure III-13 

Relaxation of that assumption would give a different radiative cooling 
rate and possibly a phase shift. This assumption of LTE says that the 
radiative cooling goes towards wiping out a temperature difference 
between the average medium and the displaced parcel. 

Now for the second point. I want to demonstrate that overstability is 
possible whenever the temperature gradient exceeds a critical value which 
is less than the adiabatic gradient. As a way_ of convincing you that this is 
at least possible, I would like to present the following rough argument. 
Consider an atmosphere initially in hydrostatic equilibrium. Label mass 
shells in this atmosphere by their undisplaced altitudes z and consider 
plane parallel displacements |(z) about these altitudes. The continuity 
equation then gives 

Ab. = 11 

' -p az ' 



241 
and the momentum equation gives 

_32| ^ dAP 
9 12 3 z ' 

The quantities AP and Ap are the changes in pressure and density 
following the rhotion. In the case of an isothermal atmosphere and 
adiabatic displacement, the solution to these equations is well known and 
is (see Lamb, 1940, "Hydrodynamics," § 309) 

3(P^0 =, (<^ 



3z 



) /cu^-jo^y ^v, 



where co is the frequency of the wave, cJq is the acoustic cutoff 
frequency and c is the adiabatic sound velocity. At to = cJq we see that 
3(jo'^|)/9z = 0. Therefore 9|/Pz = |/(2H), where H is the pressure scale 
height. Using the continuity equation we conclude that 

J^ = -J- 
P 2H ■ 

This implies an adiabatic temperature change of 

The condition for overstability in the case of slow radiative heat exchange 
requires that the rate of change of the temperature in the blob | YT/^ I 
exceeds the rate of change of temperature in- the surroundings I dT/dz | . 
In terms of the logarithmic temperature gradient this condition is 



which is always weaker than 



V > 



V > 



7-1 

2 '. 



7-1 



This condition differs from the usual condition for the onset of con- 
vection because the pressure in the displaced blob of rhatter is not equal 
to the average pressure. I find this same condition from the correct 



242 

solution to the equations of motion with a temperature gradient in the 
case of slow radiative heat exchange. In the case of a very rapid radiative 
heat exchange I find the condition is 

but at present I do not have a short derivation of this condition. 

The third point I want to make concerns the temperature rise. After 
computing the divergence of the flux associated with an acoustic wave, 
you can determine the temperature rise required to dispose of this energy. 
The equation I find is 

T-W.,„,, = 350=k{(v,,.).k(^_^).^}, 

where v^^^ is the material velocity in km sec"* , K is a function which 
varys in value according to the graphs of Figures III-14 and IIM5 as a 
function of radiative damping parameter /J and the ratio cj/a;^ , Cp is the 
specific heat at constant pressure, (R is the gas constant, and ju is the 
mean molecular weight. The largest values of K occur for the lowest 
frequency and w and the smallest values of /3. At small ^ and low 
frequency you get a fairly large factor. If you put in an rms velocity like 
4 km/sec, and if this value occurs at low frequency, then you get a very 
large temperature rise from this formula. 

Another thing to note is that, for small 0, T . T^^^^ equi.) i^ independent 
of p. At small j3, if the medium can dispose of the energy quickly, then it 
gets a large share of the acoustic flux which comes by. On the other 
hand, a section ^of matter which cannot radiate easUy does not get a very 
large share of the passing acoustic flux. This type of heating seems to be 
a rather democratic process where those who pay (radiate) receive a large 
share of the money (energy) and vice versa. 

A final point which concerns the five minute oscillations is something of 
a puzzle. If you believe that the 5 min. oscUlations are heating the 
chromosphere, then you have the disconcerting observation that the 
amplitude of the five min. oscillations is less under plage regions than 
under quiet regions. This means that you are generating less energy, since 
the energy generation in overstable acoustic waves is proportional to the 
square of the amplitude. Yet, there seems to be more emission in the 
higher layers. This is a puzzle. I think one possible explanation is that in 
a magnetic region, the required emission is redistributed and it is easier 
for an upper layer to radiate the energy which is being generated. So you 
need a smaller ampUtude to drive the whole thing. This explanation does 



243 



^ 3.0 




Figure III-14 

not seem very satisfactory, however, and, yet, I don't have a better one. 
Possibly there is another energy source over plage regions which is 
dominant. 

Skumanich — What is the reservoir from which the work comes, is it the 
radiation field? 

Ulrich — It's the oscillations in the convection zone. Ultimately, that is 
the source. The energy emitted locally in the low chromosphere and 
observed as a temperature excess has as its immediate source the pressure 
variations of the underlying layers. These in turn are generated by the 
interaction of the radiation exchange and the temperature gradient. The 
temperature gradient permits a displaced parcel of fluid to be cooler than 
average when it is in the compressed portion of the oscillation cycle. As 



244 



0.15 - 



0.10 - 



0.06 - 




Figure III-15 

long as the matter gains thennal energy at this phase, then the oscillations 
will be driven as in a classical heat engine. As far as the immediate source 
of energy for the excess radiation is concerned, it doesn't matter what 
drives the acoustic waves. Also I should say that, at this point, I haven't 
said anything about the overall energy balance of the oscillations. This 
must be considered to determine the amplitude. 

Thomas - I don't understand that remark. 

Ulrich — In terms of the 5 min. oscillations, I think the analysis must be 
essentially non-linear, such as that done by Leibacher. 

Thomas — What is your basic coupling mechanism between the aero- 
dynamics of the motion and the radiative energy balance in the electron 
continuum? 

Ulrich ~ This is just the work which is done over a cycle by the 
compression. 

Thomas — So if I have a big radiative energy loss, I can hold this 
amplitude down. 

Ulrich — If you have a big radiative energy loss, then, for the same 
ampUtude of oscillation, you get a larger portion of the work out of it. 



245 

Thomas — I am talking about the temperature amplitude now. If I have a 
big radiative energy loss, I can hold this amplitude way down. I can't see 
from your equations where you have these things put in. There must be a 
coupling term somehow. 

Ulrich - Perhaps I can clarify a crucial aspect of the temperature rise 
calculation. I write that 

T ( z,t ) = Tre. ( z ) + [ T„ ( z ) - Tr E.( z )] 

+ [ T ( z,t ) - T„ ( z )] 

The radiative heat loss by the matter is then proportional to 

/3 [ T ( z,t ) - Tre. ( z ) ] = H T„ ( z ) - Tr.eX z )] 

+ /3 [ T ( z,t ) - T„ ( z )] 

The time -independent portion of this expression is caiicelled by the 
divergence of the acoustic flux which is a second-order average of the 
first-order solution to the equations of motion. The radiative heat 
exchange terin which enters the equations of motion and effects phase 
relations is then the . second term on the right hand side which is a 
first-order. As you say, a large value of p will hold down T(z,t)-To(z). 
However, for ^ ~ cj, the divergence of the acoustic flux is proportional 
to ^, so that T0(z)-tR E (z) is independent of j3. Finally, an important 
point I haven't included in all this is that the coupling constant could be 
complex. In this case, you get phase lags between compression and 
cooling. I am almost sure that you will get this in the non-LTE regime. 

Thomas — Your work just seems to lead to an awfully big temperature 
amphtude on the right hand side of the T-T(r3d. equi.) equation. 

Souffrin - To go back to the problem of wave generation, I would like 
to make a statement concerning the physical picture for the excitation of 
the 300 second waves. Where does the instability come from? I understand 
it as a mechanism which can be traced back to Chandrasekhar and Cowling 
as a general possible cause of pulsational instability. Its relationship with 
acoustic modes was clarified by Spiegel and later by Spiegel and Moore. It 
works the following way. To give rise to that instabihty, a system needs 
three kinds of things. It needs a superadiabatic temperature gradient, a 
mechanism providing a restoring force, and a dissipative process such as 
heat conduction. A system with these three properties can exhibit 
pulsational instabihty. The convective zone has the right temperature 
gradient. Radiation gives the necessary smoothing of temperature 



246 

differences. The extra restoring force can be due to, say, a gradient of 
molecular weight which enhances the density stratification, or to a 
magnetic field, or to anything else you want. In the case considered here 
it is provided by compressibiUty, i.e., by the acoustic or pressure modes. 
That acoustic modes provide a restoring force inside a convective zone 
amounts to the fact that high frequency acoustic modes exist and are 
stable in such a zone. That is to say, for instance, that one can make 
noise inside a convective zone. 

Let me sketch now how the mechanism works. Suppose an element of 
material is pushed out of its equiUbrium position. Let the restoring force 
due to pressure prevail over the buoyancy force so that the system is 
dynamically stable, although the Schworzschild criterion indicates insta- 
bility. The parcel is then decelerated and ultimately turns back towards 
its initial position. Due to, say, radiative transfer, the temperature of the 
parcel tends to reach the temperature of the surrounding material, so that 
the parcel experiences a buoyancy force (upwards) at any level, which is 
smaller when it comes back towards its equilibrium position than when it 
first went up. Since the restoring pressure forces are not much altered by 
the heat exchanges, it is immediately seen that, along half a cycle, the 
balance between the pressure and the buoyancy forces is modified to 
produce a situation which is clearly pulsationally unstable. My beUef is 
that the one very clear mechanism for producing the 300 sec oscillatioris 
is the one considered by Ulrich in his numerical calculations, appUed to 
the convection zone. 

Ulrich — The only point I want to make is that resonant acoustic waves 
are basically pressure modes, where the pressure variations are large 
compared to the average pressure. In the more familiar gravity modes you 
have described, the pressure variations may always be neglected. 

Kippenhahn - If I understand your mechanism correctly then it is the 
same which produces overstabUity when V = d6nT/d£nP fulfills the condi- 
tion Vj^ < V< Vad + dCn /i/dCP (p. molecular weight). But then Vad is 
the gradient critical for the problem while you have this puzzling 
factor 2. 

Lin^y — I'd like to make a conunent to Uhich about interpreting data, 
namely spectroheliograms taken in the cores of strong lines. There seems 
to be a strong tendency for the various elements of the solar chromo- 
sphere to segregate themselves into two camps— the brights and the darks. 
There is no true gray gradation between Ught and dark regions. I suspect 
that bright regions, in general, have higher densities and temperatures, and 
that an instability is indicated by the spectroheUograph data. Namely, a 
region that is slightly overdense absorbs more acoustic energy and 
becomes overheated relative to the rest of the chromosphere. 



247 

Scumanich — We want an interaction with the radiation transfer people. 
We want to find what are the key observations which fix the free 
parameters in the dynamical theory. 

Souffrin — I ask for the following observations. The observations are to 
discriminate between the theories by locating the energy at any level in 
the atmosphere in terms of frequency and horizontal wave number in the 
(k,w) plane. This is not bound directly from observations. But the 
analysis of the observations in k and w is the only one useful for the 
theory. 

Skumanich — So you suggest that a variety of lines at different heights 
should be observed. 

Souffrin - Any line at any one height is good, if you can tell us how 
much energy of oscillation you find, not only at a given frequency, but 
also at that frequency and horizontal wave number. Space-time observa- 
tions, two dimensional observations, at any altitude are what we need. It 
would be even better if you could give the density in the diagnostic (k,a;) 
plane, with anpHtude. This would make it possible for us to say if the 
unstable oscillation of Uhich is real. If it turns out to be real, it could 
give us a lot of information about the stratification ' of the adiabatic 
gradient, as Ulrich mentions in his paper. 

Skumanich — You said that we need simultaneous space, time observa- 
tions, i.e. in the (k, cj) plane. 

Sheeley - He is saying that the meeting place between the observational- 
ists and the theorists is on the (k, co) plane. 

Skumanich — But you can't see this, whether you like it or not you are 
born in the (x,t) plane. 

A. Wilson — Nobody seems to point out that Frazier has already done 
this. This data already exists. 

Souffrin — But we need it even better. 

Skumanich — It is unfair to say as good as you can get it, because there 
are compromises that the observationalists have to make. So we really 
need to know where one should struggle very hard, and where it's not so 
essential. 

Ulrich — Regarding the (k,ta) plane, I would like to point out that the 
long horizontal \yavelengths are the most important, because these are the 
ones which penetrate the deepest in the convective zone. I would caution 
the observers who are looking for evidence for long horizontal wave- 
lengths that they must be sure that they don't have some power at short 



248 

wavelengths, where the amplitude seems to be greater, mixed up with 
their observations. This could be most confusing. 

Underhill — Talking about observations to prove a theory, theory is 
supposed to represent a fundamental behaviour of material. I would like to 
point out that the non-solar stars are useful. It is not necessary, as far as I 
have understood the suggested mechanism, that it occur only in a few 
thousand km long lengths near the surface of the Sun. If the mechanism 
is universal, it seems plausible that, under conditions on a star with 
different gravities and radiation fields, the scale may be larger. If so, then 
you could look at the stars and find brightness variations, in selected 
wavelength regions, of these short periods. Rather rapid pulsations of 
certain stars are known. Whether they are relevant to this mechanism or 
not I don't know. I haven't quite got the physical picture. But I think it 
is worth exploring. The mechanism might operate under different scales, 
and then occur on the appropriate stars. 

Skumanich — You do give up space resolution when you do stellar 
observations. If the concern is, in fact, to use the space scales to pin 
down which of the mechanisms is operating, this could hurt you. 

Underhill — I have not understood from the discussion that they have 
said they need a tiny space scale. 

Stein — Two types of observations are possible: a statistical approach 
which looks for the location of power in the (Kjjoriz ^) plane, and the 
analysis of individual wave packets. Studies of individual wave packets 
could determine the polarization relationships between Au, AB, AP, k, 
Bo, as well as the vertical and hoizontal propagation velocities, and the 
shapes and sizes of the packets. The directions of Au, AB, Bq and k can't 
be easily determined, but their relative amplitudes, and the variation of 
the relative amplitudes with height and from center to limb can be 
observed. Because the magnetic field, B^, is more or less vertical in the 
network in the chromosphere, and because the ratio of Alfren to sound 
speed changes with height, such studies will give information on the type 
of wave. 

Skumanich — Why do you people give temperature increases, and not the 
rate of energy dissipation? 

Stein — We have that. You would begin to see a temperature rise where 
substantial dissipation begins, if there were no radiation. Radiation has 
little effect on the dissipation. The wave is still dissipating the same 
energy, but that energy is now going into ionization and radiation, not 
heating. 



249 

A. Wilson — The point I got out of today's discussions was that there 
are two schools of thought about the heating problem. These are either: 
(a) We need high frequency, short wavelength acoustic waves with very 
large amplitudes (1-2 km/sec). No mechanism for generating such motions 
has been suggested and they are not detectable observationally. (b) The 
main cause of the heating above the minimum is the energy dissipation of 
the running wave component of the 300 sec oscillation. A small amoimt 
of energy in the form of high frequency waves may be needed lower 
down with small amplitude (.25-.5 km/sec). 

These two alternatives bring us face to face in the Sun with a most 
important contemporary . problem in the study of stellar atmospheres. 
What is microturbulence? As you know every line in the solar spectrum 
shows an increasing width towards the limb. No theory of line formation 
predicts this effect. It is always ascribed to microturbulence. The micro- 
turbulence has an amphtude of 1-2 km/ sec and is on a small enough 
spatial scale to evade detection by wiggling line bisectors, etc. 

Apart from the intrinsic interest of the heating problem, it throws a great 
deal of light on the subject of microturbulence. If the velocity field 
postulated in suggestion (a) can be shown to be really necessary to heat 
the atmosphere we must accept that microturbulence exists. We then have 
a rather stiff hydrodynamic problem; that of working out how it is 
generated and propagated. If suggestion (b) wins the day, as I think it 
will, we have a rather interesting situation. Firstly, the 300 sec oscillation 
will not give rise to the anisotropic microturbulence required in the 
photosphere because: its amplitude is too small, its z dependence is 
exponential, not sinusoidal, and it is a primarily vertical oscillation. 
Secondly, any ^ small wave motions required to start the heating at low 
heights will have far too small an amplitude to act as microturbulence. 

As you know,- the history of microturbulence is very unhappy. It was 
operationally defined in the days when our understanding of line forma- 
tion wasn't even roughly correct. Microturbulence is simply a discrepancy 
factor. Its importance lies in the fact that it plays a central role in 
methods of determining element abundances. 

Now suppose that we can heat the solar atmosphere adequately without 
using a microturbulent velocity field. What then causes the increase in 
width of the lines towards the limb? We can look for breakdowns in our 
descriptive scheme at two points: 

• In the theory of line formation: Here we can ask if the assump- 
tions of a frequency independent and isotropic line source func- 
tion are adequate. Any discussion of these questions must rest 
on our ability to obtain the radiation field bathing the atom and 



250 

the redistribution function for scattering in the atom's rest frame. 
The problem of obtaining the redistribution function has now been 
solved. We have discussed that of obtaining the radiation field 
bathing the atom below: Now let us consider the second independ- 
ent source of error in our theory. 

• Error in the description of the solar atmosphere: Here we can ask 
the following question: Does the present assumption of a homo- 
geneous atmosphere with anisotropic microturbulent motions pro- 
vide an adequate description of the inhomogeneous state of the 
actual atmosphere? 

Clearly any attempt to form the radiation field bathing the atom by directly 
analyzing observational data must solve the inhomogeneity problem first. 
Recent work of mine has shown that: 

• No self consistent explanation of the core profiles of the D lines is 
possible if the solar atmosphere is homogeneous and does not 
contain microturbulance. 

• No consistent explanation of the center limb variation of the 4571 
102 A of Mgl is possible in a homogeneous atmosphere. One is 
forced to the conclusion that the inhomogeneity of the atmosphere 
is not well approximated, using the microturbulence model. There- 
fore the development of the subject should be as follows: (a) 
Observationally , we must obtain sufficient spatial resolution to 
obtain limb darkening curves at each point in the structure pattern 
of the inhomogeneity. (b) These limb darkening curves must then 
be inverted to yield a first order structure. The inversion will 
assume the simplest line formation physics. 

But we have now returned again to the problem of self consistency of the 
source function (which of course now depends upon position in the 
atmospheric structure). Only when our data set closes along all resolution 
axes have we any right to expect adequate agreement between our theory 
and the observations. Until this time we shall be plagued by non 
uniqueness arising from insufficient resolution in wavelength, space or 
time. 

Finally I should like to emphasize again the importance of microtur- 
bulence in the solar atmosphere. If it is present, it is by far the dominant 
part of the velocity field. It does absolutely everything. It looks as if solar 
hydrodynamicists have aheady tacitly assumed it does not exist, as they 
have made no attempt to explain its generation on propagation. The 
majority of the lines used in abundance analysis fall on the flat portion of 
the curve of growth, and are very sensitive to the value of microturbulent 
velocity adopted. Until the present confusion about the nature of 



251 

microturbulence is cleaied up, we can have little idea of the accuracy of 
the abundances estimated from such lines on the accuracy of our line 
formation theory. 

Skumanich — I would like to suggest a possible experimental, observa- 
tional test in stars, as Arme Underbill would like us to do, for whether 
you have a convection driven heating, or a self excited heating, that 
presumably exists along the main sequence and is not due to the presence 
of a convection zone as I am guessing. As Wilson suggested, lets look at 
the diagram of the b-y index versus the absolute power emitted by the 
Call chromosphere. This is the actual power output; it is not normalized 
to the luminosity of the star. You have a curve, for example for the 
Hyades; that is still rising near where the observations become difficult 
and disappear. Does this continue to rise? Do we find, very close to here, 
the rapid turnaround, because the convection zone is disappearing? I 
don't think the evidence is yet in. 

The spectral types here are F6, F7 etc. There is a difficulty in obtain- 
ing measurements as we go to earUer stars, because the continuum 
is rising rapidly. The Une itself is being affected by the higher effec- 
tive temperature, and the ionization changes the Une opacity, but we 
should see the turnaround if it is there. 

0. Wilson — I started the Hyades at just an arbitrary point. Perhaps I 
didn't go far enough towards early type stars. 

Skumanich — From looking at your data, I couldn't find evidence of even 
saturation. 

0. Wilson — I think it is because we didn't look there, we didn't go there. 

Skumanich — I am then repeating your suggestion that we should look at 
this end of the main sequence, and see if there is a turnaround where we 
beUeve convection is dying out. 

Wilson - I think it dies out very rapidly, if you find where rotation 
ceases. 

Underbill — But that doesn't mean that you don't have a chromosphere, 
because you could have these mechanical pulsations excited in another 
way. You .could have shearing on rotation. You just need some httle 
disturbance in density to have it grow. 

Skumanich — The only two mechanisms I have heard about have been the 
overstability, and the convection zone driving an oscillation field. I don't 
know much about rotationally driven overstabiUties. You may possibly be 
right. This may not be a test of these ideas. It would certainly be 
interesting to know whether there is a turnaround or not. 



252 

MIson — You know about this point on the main sequence, which is a 
(b-y) of 0.28. You no longer see strong chromospheric activity. But 
Procyon does have weak chromospheric acitivity. It lies above the cutoff 
of rapid rotation. If that power point marks the onset, or the end of deep 
convection, then you still have some chromospheric activity above that, 
but it is very weak. But we are looking here at a rather narrow range of 
spectral types. Procyon is F3, and the cutoff point is F4 or F5. As it 
refers to (b-y), it's a little early. 

Skumanich - It's also a subgiant. 

0. Wflson — It lies in the main sequence band according to Stromgren. 

Skumanich — That's true, but is there evidence that it is going hori- 
zontally across? 

O. Wilson — This I don't know. 

Underhill — This comes back to the problem of defining chromospheres. 
We've got to stick to the definition of a temperature increasing outwards. 

Skumanich — My definition would include my guess that whatever 
produces calcium emission on the Sun produces it in the main sequence 
stars of earlier type. I am using an homologous shift of the Sun up and 
down the main sequence. 

Cayrel — Is the Lighthill theory able to predict the magnitude of the 
mechanical flux of energy coming from the noise in the convection zone? 

Skumanich - I have looked at the work in the field, so I will try to 
answer the question. The Lighthill theory was first done by Proudman 
and he got a factor in the coefficient on the order of 50. Stein did it 
again and found that the power put into the tail of the turbulence 
spectrum governs the coefficient very sensitively. You are going from 50 
to 1000 depending upon how you decay the energy in the high k, high 
CO, part of this diagnostic diagram we have heard so much about. This 
makes me afraid. When you have an answer that is so sensitive to what 
you do with the tail of the spectrum, how can we trust the energy 
estimates? How can we possibly understand the tail of the spectrum, if 
we don't know the physics of turbulence? 

Souffrin — You are quite correct. That theory is a dimensional analysis. It 
just tells us how much we will modify the output, if we modify the 
source in some way. That is not very useful for observations. 

Cayrel — At least has the flux been computed with exactly the same 
assuiription for a dwarf and a giant, for example? 



253 

Skumanich - The problem'with the dwarf and giant stars is that in the 
giants the flow is essentially supersonic. You get into the difficulty that 
the theory breaks down for Mach numbers close to 1 . 

Stein - About 4 years ago Strom and I computed the flux the Lighthill 
theory would predict for a series of main sequence stars and giants. We 
wanted to see the results of applying the same wave generation assump- 
tions to all the stars. I don't know how you measure the extent of a 
chromosphere, but we found exactly the opposite from what some of you 
seem to think is the case. Namely, the ratio of the mechanical energy 
input to the luminosity of the star goes down as you go down the main 
sequence to cooler stars, rather than going up. This is why we never 
pubUshed the paper. However, it does go up for the giants, but that is 
much more uncertain, because you get into much higher flow velocity. 

Skumanich — There is no theory for sonic turbulence. 

Jordan - I'd like to present the results of some calculations by de Loore. 
He used the Lighthill theory for generation of sound waves by turbulence 
in the convection zone of stars. To calculate convection zone models 
along the main sequence, from A5 to KO, he used the B5hm-Vitense 
mixing length theory. He found that the hottest, densest coronas could 
be expected for the late A and early F type stars, with coronal 
temperatures as high as four million degrees, and electron densities up 
around 10'° Figure III- 16 shows some of his results. The numbers in the 
left hand graph are effective temperatures; in the right hand graph, they 
are relative magnitudes for the mechanical energy flux. He normalized 
things with respect to the Sun, and got for the solar corona a 1.1x10* °K 
corona and Ng = 10'. In order to get that, he had to assume that the 
flux value was generated only over 10% of the solar surface. He did not 
include this normaUzation in his other calculations. His calculation in the 
convection zone for small t is inferior to a technique employed by Kyoji 
Noriai, and, therefore, de Loore tends to overestimate the convective flux, 
particularly for the earUer type stars where the convection occurs more in 
the surface regions. I mention this work without any comment, because, 
in view of all the assumptions and uncertainies in it, it is impossible to 
evaluate how relevant the calculation is. 

Skumanich — What are the observational impUcations? 

Jordan - One of the impUcations is that one should look at strong 
ultraviolet Unes in coronas of late A and early F type stars. If they do 
have such hot, dense coronas then you should see these lines. These 
atmospheres may even be optically thick in some of these Unes, due to 
higher predicted coronal densities, if de Loore is right. 



254 

Ulrich — Convection seems to exist in rather early stars, according to de 
Loore. 

Jordan — It is true that, even for stars earlier than A5 and for effective 
temperature up to 41,000° K, de Loore always found some convective 
instability. However, if you notice the vertical dashed line in Figure III-16 
for stars earlier than A5 , the region that carried the most convection had . 
a ratio of convective to total flux of less than 20%, and this dropped off 



RATIO OF CONVECTIVE TO TOTAL FLUX |DE LOORE| 



CURVES OF EQUAL MECHANICAL FLUX Fm 





M 


yC 


=f=- 

V5940 


0.8 


^-A 


\.l 


/V^^V 


0.6 


\ 


^^ 


/5350 


0.4 


- 




/ - 


0.2 


1 


J 


9510__^ 




3 
■ log i 



3.92 3.82 

— logTj,,- 



Figure III-16 Ratio of convective to total flux (de Loore) 
(left) curves of equal mechanical flux Fjjj (right). 

so sharply that he did not predict strong chromospheric activity for stars 
earlier than type A5. 

Mullan — The results of de Loore, and also the results of Castellani et al 
(Astrophys. & Space Sci. 10, 136, 1971), were computed using the 
formula F ~M5v3 for the mechanical energy flux. Here, v is the 
convective velocity and M is the. Mach number associated with this 
velocity. These authors have applied this formula even in cases where M is 
as large as unity. However this formula was derived theoretically in the 
limit of small M, say M < 0.1, and the accuracy of the formula is 
expected to become very low as M approached unity. And even if the 
formula turns out to be accurate, the uncertainties in v due to un- 
certainties in convection theory are enormously ampUfied in F. Further 



255 

uncertainties arise if magnetic fields are present, so theoretical estimates 
in mechanical energy fluxes computed in these papers can hardly be 
considered accurate, even to within an order of magnitude. 

Jordan — I agree. 

Skumanich — We have to go backwards from the observations to 
inferences about what is the mechanical flux, and further yet to 
inferences about what is the convective source. We need more from the 
theorists in terms of a simple physical picture. 

Leibacher - First, I have two comments on my own work. The heating 
calculation is being done for the Speigel mechanism right now. It may 
take a long time. Second, concerning the cause of the heating. Figure 
III-17 shows how we discriminate between various theories. This is a 
picture of velocity versus time at a number of different heights where the 
zero height is the Tj^q^^ = 1 point. There has been some argument 




1500 
TIME (sec.) 

Figure III-17 



about there being observational evidence for shock waves in the solar 
chromosphere. If you look at these profiles you will see that they are 
very symmetric up through 1000 km, up to the height where Ca K is 
formed. These are the highest Unes we can see from the surface of the 
earth. Right now it is very difficult for us, with the observed amplitudes 
here at the earth's surface, to expect to see shock waves in the 
chromosphere. In Figure III-17 we are looking at the velocity profile from 
a computer experiment. In some way we create an oscillation which has 
the correct amplitude here at the surface. This is a 0.2 km/sec oscillation. 
Now, the question is, as a result of this correspondence with observations, 
what would we expect to see in the chromosphere? Would we expect to 
see shock waves higher up? Can we decide on one of the various heating 
mechanisms? The answer is no; we would not from the surface of the 
earth. You have to go to the higher lines formed above 1500 km, where 



256 

you see the velocity profiles become asymmetric, and the pressure profiles 
become very narrow. The dotted lines are pressures and you can see here, 
nearer the base of the temperature rise to the corona, the pressure is very 
constant. It has a very narrow, in time, over-pressure. Again, those cannot 
be seen from the surface; we will have to wait for OSO I observations. 
Now I would like to report on a number of contributions from the 
informal meeting yesterday afternoon. 

Underbill - The temperatures, densities and pressures in the solar 
chromosphere vary somewhat like those in the atmospheres of early type 
stars. Only early type stars are much larger than the Sun, so we have a lot 
more material. It's very well known that you get sporadic emissions in 
some short period pulsating variables. You also get, as Fischel found, 
sporadic disappearance of the C IV resonance line. Pulsation like you 
show may occur in early type stars, and you might not need very much 
at all to tri^er them off. You might not even need a convection zone to 
start them. But the result of those shocks is superheating. I don't like the 
idea of saying chromospheres exist only for stars with convection zones. 

Leibacher — I would first like to consider two sets of observations by 
Musman and Beckers on the presence of exploding granules in the surface 
layers of the Sun. For a long time there has been a series of observations 
by Rosch of the appearance of very bright spots on the solar surface, 
which then expand into a ring and disappear. These are continuum 
observations. With the new Tower Telescope at Sacramento Peak, Musman 
has made movies of these appearances, and has made some hydrodynamic 
models of them which are very similar to cumulus clouds models. Beckers 
has been doing similar observations with his velocity filtergram system. It 
has velocity pictures and short velocity movies, and hopefully in the near 
future longer velocity movies of these exploding granules. To the extent 
to which oscillation and heating theories depend upon excitation by 
granulation, I think all of a sudden we are moving ahead very rapidly. 

However, it should be noted that recent work of Sheeley and Bhatnagai 
indicates that the granulation and oscillation horizontal scales differ by a 
factor of three. 

A second area of discussion was the observations of the 5 min. 
oscillations on the solar surface, and the reliabihty of these observations. 
Figure III-18 is for those who have been talking about the horizontal 
scales that are involved here. This is the famous diagnostic diagram. The 
isophotes here are iso-power lines and are the results of some obser- 
vational work by Frazier. A great deal of effort has been placed on trying 
to understand the double peak nature of the oscillatory motion. There are 
two distinct peaks. If you look at a power spectra, Fourier analyzing the 



257 



3r 



I ' 

Q 6 

° 7 

iij 8 

15 
30 



0.03 



0.02 



O 

UJ 

in 
- 3 



0.01 - 




Figure III-18 

velocities, compressing everything onto zero horizontal wave number, 
power as a function of frequency shows a number of very narrow peaks 
which correspond to very long coherence for oscillations. Figure III-19 is 
a very long record obtained at Mt. Wilson by Howard Which has been 
analyzed by Cha and White at HAO. You see here, for instance, what 



N 




A/VVW^/\M^ 



Figure IIM9 

appears to be an extremely long, in phase, series of oscillations. It is the 
length of that packet, then, that gives rise to the very narrow peaks in the 
power spectra. A lot of effort has gone into the interpretation of the 
multiple peaks and their positions. The result is now emerging from White 
and Cha, and separately from Deiibner, that the very peaked nature of 
the power spectrum is a result of statistical uncertainty in the records. 



258 

There aren't enough independent data points. More satisfying to White 
and Deiibner are single peaked envelopes, which are stable in time. There 
is bound to be some reluctance in accepting a change as drastic as this. 
One of the most convincing arguments in favor of it is White's ability to 
reproduce the observations in the statisitical sense, from introduction into 
a power spectrum such as this of purely random noise. In other words, he 
can take a filter and filter noise and get the observations back out. I have 
some of White's pictures. His work will be published shortly. In summary 
of their findings: the best representation they have for the observations of 
the 5 min. oscillations are that it is a narrow band random process with 
the emphasis placed upon the randomness. 

As a last point, there has always been some debate between the 
granulation excitation, as I have mentioned, and over-stability arguments 
such as Ulrich, and Stein and I have been proposing. If you look at the 
structure of the individual packets, you find you can get essentially 
whatever you want. If you look at frequency vs. time in a packet, some 
packets have their frequency increasing with time, until the packet 
disappears; others have the frequency decreasing with time. If you look at 
the ampUtude vs. time in a packet, in other words, and ask if the packet 
starts off very large and then dies out, you find just that. You also find 
the same result with time running in the opposite direction. So any 
theory you want to justify, you can find a section of the record that will 
reproduce it. If you take enough of the record a statistically , significant 
sample of the oscillation, all the determinism drops out. 

For the theory of the 5 min oscillation, there exist two primary schools 
of thought. One is currently represented by the people at the University 
of Rochester, Al Clark and John Thomas, who have been proposing that 
the oscillation consists of trapped internal gravity waves. Internal gravity 
waves are essentially bouyancy waves, to some extent similar to the waves 
one sees on the surface of the ocean. They are trapped by the 
temperature structure of the solar temperature minimum. The other 
school, represented by Ulrich, Stein and myself, sees the energy con- 
centration , of the 5 min oscillation as being sub-photospheric, and the 
model is more represented by an organ pipe, the upper surface of which 
is the top of the hydrogen convection zone. The lower surface is several 
mega -meters beneath the surface. The observations in fact, relate to 
evanescent waves, non-propagating waves that are tunneling through the 
temperature minimum. 

Skumanich — In view of its importance, I would like to reopen a 
discussion of the convection'zone. 

E. Bohm-Vitense — Umeasonable results are obtained by people who 
apply the mixing-length theory in cases where the convection zone is 



259 

thinner than the mixing length. It doesn't make sense to take a mixing 
length equal to the scale height, and obtain a convection zone which is 
only one half a scale height thick. Second, the mixing-length theory, as it 
stands, is certainly not the ideal theory. I think we can estimate the 
velocities without relying on the theory. If at some point, essentiaUy the 
whole energy is transported by convection then by putting the convective 
energy transport equal to the total energy transport you can derive the 
average velocity at this point without too much uncertainty. There is less 
than a factor of two uncertainty in the velocity which you get this way, 
as long as you are sure that at that point the total energy is transported 
by convection. 

Skumanich - Does this mean that the velocities become large. 

E. Bohm-Vitense — They do increase with lower densities, which means 
they increase with increasing temperature or increasing luminosity until 
the convection becomes ineffective. On the main sequence, that happens 
at about 8000 °K. 

Peytrenann - I have a question about the graph of de Loore which shows 
the ratio of convective flux to total flux: to what depth do they refer? 

Jordan — It varied. Certainly for the late A and early F stars, it was 
above mean optical depth unity. 

Stein — What we calculated, when Strom and I did it, was not the ratio 
of convective but of mechanical energy flux to luminosity deduced using 
the Lighthill theory. 

Peytremann — The mixing length theory you all use can be criticized, but 
whether it is wrong or not, it should lead to the same results when used 
by various people. The small ratio of convective to total flux in de 
Loore's graph (Figure 1 (Jordan) left hand graph) may result from the 
fact that this theory is certainly not valid when applied to layers thinner 
than the mixing length itself, as may have been the case for the hotter 
stars de Loore treated. 

Skumanich - I think that the idea of using a scale length the order of a 
scale height is not crazy at all. In fact, my own work in 1955 shows, this 
was for convection in a poly tropic atmosphere, and that as you change 
the horizontal length scale, the flow packs itself into that scale height 
which is like the horizontal size. You fix this size, as Bohm has found 
out, by damping effects. We are still investigating whether or not there is 
convection in the early type stars. 

Peytremann — In all the models I have calculated, I never had any 
convection in atmospheres earlier than spectral type A. 



260 

Kandel — The question is what are you using mixing-length theory for. If 
you are talking about energy transport, which is internal energy flux, then 
the mixing-length approach may be satisfactory; it may give reasonable 
results; and you get velocities out of that which are certain average 
velocities which work very well. For the purpose of computing a 
mechanical energy flux which will perhaps heat a chromosphere and 
corona, you have a very different type of average over the velocity. You 
are working with the tail of the distribution. I don't think the mixing- 
length people would say that they could tell you what the tail of the 
distribution will be, when it is involved with some average over velocity to 
the eighth power (as MuUan said). You have this enormous uncertainty 
which makes it very very hard to beheve any of these predictions. 

Skumanich — I agree. 

Mullan — Just how accurate are these models? The fact is that we do not 
know the run of Mach number with depth in any star. We do know that 
certain M dwarfs (the flare stars) have coronas, for they have been 
observed to have radio bursts somewhat similar to Type III solar bursts. 
Kahn and Gershberg have found that gas densities in the coronas and 
chromospheres of the flare stars are up to 100 times greater than in the 
Sun. However, the maximum convective velocity in an M dwarf is 
expected to be smaller than in the Sun according to current convection 
theories. If this is so, then a star with small convective velocity is 
somehow able to generate sufficient mechanical energy to support a 
corona 100 times denser than that in a star with a higher convective 
velocity. 

Scumanich — That's a good point. We certainly have avoided the variation 
of model and dynamical properties along the main sequence. I think part 
of that is that we don't have a full understanding of the observations. The 
observations exist, thanks to Wilson. 

Stein — It may be that turbulent noise generation by the Lighthill 
mechanism, while present and important for heating the chromosphere, is 
not the primary source of mechanical energy for heating the corona. The 
calculations of Leibacher and myself suggest that the 5 minute oscillations 
are heating the corona. Such long period waves will get their energy up to 
the corona more easily. We are in the process of calculating the 
generation of the 5 minute oscillations by thermal instabiUty in the 
superadiabatic convection zone. This process will presumably have a 
different dependence on stellar properties along the main sequence than 
the Lighthill mechanism. 

Underhill — There is a theory that suggests that stars with magnetic fields 
are rotating underneath. These magnetic fields will become wound up and 



261 

they can become very strong. This theory explained how to get a 
magnetic field in a white dwarf. At the same time, the star blew off its 
atmosphere, so you had the white dwarf left over. If the white dwarf has 
a fair amount of cool expanded atmosphere around it, it will give you a 
nebular spectrum. If those magnetic fields somehow accelerate the 
material, you will get x-rays. Perhaps some of the highly excited 
atmospheres are not heated by mechanical energy, but may be heated by 
soft x-rays which we caimot observe because of their attenuation between 
us and the object. It's not impossible. 

Skumanich — I think, by arguments of homology, that along the main 
sequence the fields can be ignored. The observations of the solar wind, 
which is driven by the energies deposited in the corona, seem to be 
independent of the magnetic cycle of the Sun. I am not sure that this 
argues that they are secularly independent. All we know is that they 
don't follow the actual oscillation. But they may follow the mean 
amplitude of the magnetic field. Whether the field can act as the energizer 
of the gas, as you suggest, I leave to the white dwarf men. However, 
whether flares represent, in some generalized sense, some heating mech- 
anism for the corona, I think that that would also be cycle dependent, 
which we don't observe. 

Mullan — Observers cannot depend on theoreticians for guidelines as to 
what should be observed, simply because uncertainties in the theory of 
mechanical energy generation are so great. In fact the problem must be 
inverted; and I would like to ask the observers to present theoreticians 
with a value for the solar mechanical energy flux deduced from observa- 
tions. Theoreticians might then profitably use this as a constraint on the 
various free parameters at their disposal. 

Skumanich — One problem is that some of the theoreticians give uS a 
model for the dissipation as a function of height in the atmosphem, while 
others give us temperature and density models, but the two don't spend 
enough time checking each other. One might say that the atmosphere is a 
filter and what we really want is the pass band of the filter. 

Souffrin - I would like to surest that people not look too closely at the 
observations. Many excellent theories in science would not have been 
developed had people had very detailed observations. A number of large 
scale effects on the Sun which have been discovered would not have come 
to Ught if people had been concerned only with more detailed observa- 
tions. This is not to say that I advocate no observations, but only that I 
think the theory should be better developed so that we at least 
understand the large scale phenomena. 



262 

Skumanlcli — So long as we always keep in mind that, in the absence of 
laboratory experiments, theory and observations must bootstrap each 
other in astronomy if we're to understand anything at all. 

Schwartz — Concerning observations, I would just like to emphasize that 
observations of velocity fields are not observations of the power which is 
propagating through the atmosphere. The only way to learn if there is 
energy propagating from velocity field measurements is to measure the 
phase relations between pressure and velocity. If these two quantities are 
in phase, then you know energy is propagating. If the pressure and 
velocity are 90 degrees out of phase, then it doesn't matter how large the 
velocity you have is, you aren't propagating any energy. So what we fluid 
dynamics people need is for the radiation transfer people to solve the 
transfer problem to give us information on the pressure from the intensity 
variations. I know this is a tall order, as it means doing the transfer 
problem many times (10 or 12) during the 300 sec period, rather than 
once; but it is what we need. 



PART IV 



VARIATION OF CHROMOSPHERIC 
PROPERTIES WITH STELLAR MASS AND AGE 



Chairman: Lawrence AUer 



263 



Page intentionally left blank 



CHROMOSPHERIC ACTIVITY AND STELLAR EVOLUTION 

Rudolf Kippenhahn 

Gottingen University Observatory 

STELLAR EVOLUTION AND MECHANICAL FLUX 

Stellar evolution carries a star through the Hertzsprung-Russell -Diagram. 
For a given mass, M. one obtains both luminosity, L, and radius, R, as 
functions of time, t. From these parameters we determine the surface 
gravity and the effective temperature as functions of t: 

g(t).T^ff(t)- 

It is these two parameters which determine the properties of the 
outermost layers of a star, the atmosphere and the top of the hydrogen 
convective zone. 

From the equations of mixing lengths theory (Bohm-Vitense, 1958) one 
can derive for the Mach number, M, that: 

8 n2 ^ 

where C = mixing length, Hp = pressure scale height and V= d fin T/d fin P, 
Vad = (d finT/dCn P)^^ . We thus see that the Mach number can approach 1 
only in regions where V- Vgd is large, that is in those regions where the 
stratification is highly superadiabatic — as it is at the top of the 
convective zone. Sound waves can be formed in these layers only; thus 
the mechanical flux also depends only on g(t) and Tgff(t). Therefore, for 
the determination of the mechanical flux a grid of models of stellar outer 
layers as functions of the two parameters g, T^jj is necessary. 

Recentiy de Loore (1970) has computed the flux for a set of model 
atmospheres. The mechanical flux Fniech which he derived is given in the 
log Tgff - log g - plane of Figure IV-1 . As has been said yesterday, de 
Loore's models exaggerate the mechanical flux for those models which 
have convective zones thinner than the mixing lengths. In the next three 
figures evolutionary tracks are plotted in the log Tgff - log g - plane 
together with de Loore's mechaiiical flux areas. In Figure IV-2 the pre- 
main sequence evolution as well as the post main sequence evolution up 
to helium flash are plotted for a star of one solar mass. One can see that 
the star is always in the region of strong mechanical flux. This holds also 

265 



266 



2' 




4 4 4.3 4.2 4.! 4 19 3,8 3.7 3,6 35 34 3 3 



log Tell 



Figure IV-1 The mechanical flux Fmech ^ ^ function of g and Tgff computed by de 
Looie (1970) with the Lighthill-Proudman theoiy. The numbers at the 
white lines give log F^iec), where Fn,e(.|i is in c-g-s units. The straight 
line in the lower left corner gives the slope of an evolutionary track 
which is horizontal in the HRD. 



for the post main sequence evolution of a 1 , 3 solar mass star (Figure IV-2). 
Stars of 1, 3 solar masses settle down on the main sequence near F5. This 
is the region where on the main sequence one observes the transition 
from stars with Ca emission to those without. One therefore is surprised 
that according to de Loore's computations such a star is right in the 
middle of the region of strong mechanical flux. One would expect the 
star to be on the left border of the area of strong mechanical flux 
instead. This is probably due to the enhanced mechanical flux in the thin 
convective zones in de Loore's computations. Figures IV-3 and IV-4 show 
that stars of higher masses start on the Hayashi track in the region of 
strong mechanical flux, move into the low flux region and then come 
back into the high flux region during central helium burning and further 
later evolution. While the more massive stars make loops they go several 
times from high flux to low flux regions and vice versa. 

It has been indicated during this conference that the mechanical flux 
computed according to the Lighthill-Proudman theory is not very reUable 
due to uncertainties in the theory of convection. We were confronted 
yesterday with at least two new and different possible mechanisms of 
heating. Certainly these mechanisms have to be worked out more 
thoroughly before one can decide whether we really have the correct 



267 




<4 43 42 41 40 33 38 37 36 35 34 3j 



• '^iV?-?."^'^^^#^«t»'^'^!Jfeiri"'-/ --^.'■- --*-,^JT'a^-!^^---">?;-,^".?;rex'' ■ •->^>'V-" " • ' ^i. 



in Tp„ 



Figure IV-2 Evolutionary tracks for 1 M® and for 1.3 M®in the log g-log Tgf^ plane. 
The 1 M® star starts in the lower right comer, moves into its pre-maln se- 
quence evolution towards the main sequence and goes back into the lower 
right comer in the post ms evolution. For the 1.3 M®staronly the post 
ms evolution is plotted. 

theory of mechanical heating. It is, for instance, not sufficient to show 
that a certain type of motion is unstable by making only a linear analysis. 

What one has to show is that such an instability, if it is fully developed, 
has sufficient energy to produce the mechanical flux necessary for 
chromospheric heating. In the case of convection we know that in many 
stars all the energy of the star is transported through such motion and it 
is therefore easy to get the required energy from convection. It should be 
kept in mind that in the HRD the observed transition from stars with 
observed calcium emission to those where calcium emission is not, or is 
only seldom, observed seems to agree fairly well with a line of constant 
mechanical flux generated by convection. 

In particular on the main sequence there is a sharp transition between 
calcium emission and no calcium emission (as it is observed by O. C. 
Wilson, 1964) which coincides with the well known transition from 
convection to no convection. Since the flux depends on the eighth power 
of the turbulent velocity one would expect a sharp cut-off in the 
mechanical flux at this transition. That this cut-off is not so pronounced 
in Figures IV-1 to IV-4 may be due to de Loore's treatment of thin 
convective zones. 



268 




43 4 2 4! 4 3.9 3B 37 3 6 



3i 3.3 



Figure IV-3 The evolutionary tracic for 5 M®fi:oni the pre-ms evolution to the ms. 
Central hydrogen burning starts at point A and is terminated at point B. 
Further evolutionary stages go from C to R , . 




log Te„ 



Figure IV-4 The evolutionary track for 9 M0from the pre-ms evolution to the ms. 
Central hydrogen burning: A-B/further evolutionary stages: C-H. 



269 

INFLUENCE ON STELLAR EVOLUTION 
OUTER BOUNDARY CONDITIONS 

I do not think that stellar models would be drastically different if the 
normal grey or nongrey atmospheric boundary conditions were replaced 
by a fit to an outer layer with a more complicated temperature profile. 
Only cool stars are sensitive to their outer boundary conditions — but 
only in the sense that their radii and therefore their position in the HRD 
is dependent on boundary conditions. 

But the evolution itself is steered by the very deep interior and the 
interior of an evolved star does not know about the envelope. 

MASS LOSS BY STELLAR WIND 

The mass per year blown into space by the solar wind is small. It is less 
than the decrease in mass of the Sun due to the mass equivalent of its 
radiated energy. From the point of view of stellar evolution this mass loss 
can therefore be neglected. According to Weyman (1962) a Ori has a 
mass loss of 

-^ = 4 X 10-6 M^yr. 

a Ori is a star of about 20 solar masses in its post main sequence 
evolution. In the most favorable case this mass loss might add up during 
central helium and carbon burning to a mass loss of a few percent for 
that star. 

The luminosity of a main sequence star is reduced by mass loss according 
to the mass-luminosity relationship. But a star with shell burning remains 
at the same luminosity even if 90% of its hydrogen rich envelope is 
removed. This is well known from computations of mass exchange in 
close binary systems. Therefore it is very difficult to decide from 
observations whether an evolved star has undergone mass loss. 

This is the reason why for years an argument has been going on between 
the non4inear cepheid pulsation theory people on the one side and the 
evolutionary and linear pulsation theory people on the other side. Christy 
(1968) claims that he can get agreement with observed light curves only if 
he assumes that cepheids have but half of the mass given by the normal 
evolution theory. On the other hand Lauterborn, et al., (1971), give an 
evolutionary track for a 5 M®star which has loops in the red giant region 
with several slow crossings of the cepheid strip. They found that if more 
than 5% of the mass of the star were taken off the envelope, the loops 
disappear. Therefore, they argue, if mass loss takes place there would be 



270 

no slow crossings of the cepheid strip, there would then be no cepheids 
and Christy would then have no observed light curves to compare his 
theoretical curves with. 

Since the mass of the cepheids is still undetermined (Fricke, Strittmatter, 
Stobie, 1972, Cox, King, Stellingwarf, 1972) if we wish to understand 
whether mass loss from coronas influences the evolution of stars we 
certainly have to look for the masses of the cepheids since this offers a 
chance to obtain information. 

LATE PRE-MAIN SEQUENCE AND MAIN-SEQUENCE-EVOLUTION 
AND CHROMOSPHERIC ACTIVITY 

When 0. C. Wilson (1963) found that field stars have less chromospheric 
activity than the same type of stars in galactic clusters a completely new 
point of view came into play. Imagine: stars" at the same place in the 
HRD and (since they are, therefore, also on the main sequence) stars of 
the same mass, differ in their Ca + emission! These stars should have the 
same atmospheres since g and Tgff are the same. They certainly have the 
same mechanical flux if it is computed in the same way as de Loore, but 
they differ in their chromospheric activity. The puzzle would remain even 
if one of the two new mechanisms mentioned yesterday were to replace 
the mechanical flux due to sound waves coming out from the convective 
zone. All those mechanisms would produce the same mechanical flux for 
the same values of g and Tg^j . 

Kraft (1967) found the correlation between chromospheric activity and 
rotational velocity. Now we know from the work of Skumanich (1972) 
that roughly 

, Ca"*" -emission ~ J2 ~ t"" 

where SI is the angular velocity of the surface. From the Sun we know 
the Ca"*" emission is correlated to the magnetic field. Beckers and Sheeley 
during this conference told me that for fields between and lOOF there 
is a positive correlation between Ca"*" emission and the magnetic field 
strength IB I although there is a large scatter around >this relationship. 
Finally,, we know that the solar magnetic field is related to the rotation 
of the Sun. We therefore come up with the following logical scheme, as 
shown in Figure IV-5. 

The outer five boxes, forming a pentagon, give the logical structure as it 
follows from the first two sections of this article. Stellar evolution 
changes effective temperature and surface gravity of the stars, and these 
two parameters determine the top of the convective layers in which the 



271 



coronal 
heating 



B from 
turbulent 
dynamo 




convective 
zone 



differen- 
tial 
rotation 




loss of 
angular 
momentum 



u> (t) 

of outer 
layers 



stellar 
evolution 




Figure IV-5 The logical structure which connects stellar evolution 
with nonthermal heating of chromospheres coronas. 

mechanical flux is generated which heats the outer layers. Heated outer 
layers may produce a stellar wind which may influence the stellar 
evolution. 

Due to the effects mentioned in this section one must also take into 
account the inner boxes. We know much less about these boxes inside the 
pentagon. What seems to go on inside the pentagon is more secret to us. 
As you see in the figure, almost all the arrows, that is all the 
information, goes into the interior of the pentagon and almost nothing 
comes out. But there is one leak. 

If rotation is taken into account we must keep in mind that during stellar 
evolution when the star is contracting or expanding the angular velocity 
distribution will change. The angular velocity fl, near the surface might 
therefore also be influenced by stellar evolution. For the Sun there is an 
indication that convective zones show differential rotation. Differential 



272 

rotation together with convection can produce magnetic fields which on 
the one hand can enhance the outcoming magnetic flux and especially 
can determine the region where the dissipation takes place. It therefore 
influences the heating of the outer layers. On the other hand the steUar 
wind together with magnetic fields can produce a strong loss of angular 
momentum which, together with stellar evolution, influences the angular 
velocity distribution of the star. In the following we will discuss in more 
detail the interior of the pentagon. 

EVOLUTION AND STELLAR ROTATION 

Even if we assume that the star does not lose angular momentum the 
problem is difficult. We do not know how effective mechanisms, such as 
large or small scale motions or magnetic fields, are at redistributing 
angular momentum in the stellar interior. We do know that only very 
restricted angular momentum distributions are stable, but we do not 
know what the time scales of some of the instabilities are and whether 
they are really important during the life time of a star. 

If we knew the true theory of the flow of angular momentum inside the 
star during evolution, the surface angular velocity would be known as a 
function of time: Q = Q, (t). From numerical calculations with different 
assupiptions about the redistribution of angular momentum during stellar 
evolution Kippenhahn, Meyer-Hofmeister, Thomas 1970) one can derive, 
as a very crude thumb rule, that 

i2(t) ~ ^(,) 

This relationship is valid in the case of local conservation of angular 
momentum. It turns out that this is a fairly good approximation in the 
physically more reaUstic case when one assumes that the hydrogen 
convective zone rotates as a solid body and that in the radiative regions 
angular momentum is locally conserved. 

For our purpose in this review it is not so important to know the 
numerical details but rather to understand the logical structure, that is to 
find out what determines what. For this purpose it is sufficient to know 
that, when stars from the main sequence evolve into the red giant region, 
the surface angular velocity goes down roughly as indicated by the above 
formula. Observed rotational velocities for red giants (Oke, Greenstein, 
1954) support the above formula. 



273 

DIFFERENTIAL ROTATION 

Winding and unwinding of magnetic fields seems to be important for the 
solar dynamo. Therefore differential rotation is essential. The turbulent 
viscosity of the hydrogen convective zone gives a time scale of only 100 
years for adjustment. The differential rotation therefore is certainly not a 
fossil relic from earlier phases of evolution. It must be maintained by 
some unknown mechanism. 

Many attempts have been made to explain the solar rotation law. I think 
everybody now agrees that it is a pure hydrodynamic phenomenon; that 
the magnetic fields there have to follow the gas in the hydrodynamic flow 
and do not influence the rotation. This is indicated by the fact that the 
differential rotation does not vary with the solar cycle during which the 
magnetic field changes sign. 

Among the hydrodynamic approaches there is that via non-isotropic 
viscosity proposed by L. Biermann (1951), Kippenhahn (1963) and 
Kohler (1970). This approach did not encounter much enthusiasm from 
the professional hydrodynamicists. On the other hand there are the 
attempts by Busse (1970) and recently by Oilman (1972). 

In the present we do not know if any of these approaches will really turn 
out to be true. But, for the moment, we can just assume that convective 
regions like to rotate differentially — whatever the reason is. 

TURBULENT DYNAMOS 

During the last years, theories for the solar cycle have been developed by 
Babcock (1960) and Leighton (1969) and also by Steenbeck and Krause 
(1966). Both approaches have in common that turbulence and rotation 
are considered in a statistical theory which yields equations for the mean 
velocities and for the mean magnetic field. These equations contain terms 
in addition to those of ordinary magnetohydrodynamics due to cor- 
relations in the turbulent quantities. In normal magnetichydrodynamics 
one has 



^ = -^ A B + cure [V B] 

7\i d ■n n ~ 



at 4 no 

where B, V, are the magnetic field, the velocity field and a the electric 
conductivity. The first term on the right hand describes the dissipation of 
magnetic energy due to ohmic losses while the second term alone would 
give the frozen-in condition. From Cowling's theorem there follows that 
in the axisymmetric case a given velocity field V can not maintain a 
magnetic field against the dissipation. But in the case of turbulent motion 



274 

one obtains an equation similar to that above for the mean field but this 
equation contains an additional term as indicated in the lower part of 
Figure IV -6. This additional term has been derived by Steenbeck and 
Krause, and it contains the fact that rising and falling turbiilent elements 



LEIGHTON'S NONLINEAR MODEL: 






Winding of Frozen-in Field 



5 ■ const I B^ I B^ 



Depletion Due to 
Eruption 



at 



Tq a cose 



2 ^"r 



dcose 



Diffusion 



3(B cosS) 

5 • const — zr^ — ^ — 
dcosS 

Creation of B^ by Tilt " 



B^from V- 1 = 



1B^I<|B. 

1 otherwise 



KRAUSESTEENBECK'S LINEAR THEORY: 



|£ = const. A B + curl. (5^x6) + 


curl (ag) 


■ > • 


Diffusion Winding of 


a -effect 


Frozen-in Field 




V. B = 





Figure IV-6 Formulae for the two types of models for turbulent dynamos. 

are forced to a helical motion by Coriolis forces. The magnetic field is 
tilted by these elements in such a way that the mean field behaves as if 
there is a mean electric current parallel to the mean magnetic field 
(a-effect). This effect was already indicated by Parker (1955). The papers 
by Krause, Radler and Steenbeck on the turbulent dynamo have recently 
been translated by Roberts and Stix (1971) (See also Deinzer, 1971). 

Similar additional terms have been introduced into the magnetohydro- 
dynamic equations by Leighton as one can see in Figure IV-6. In this 
theory similar to the a-effect of Steenbeck and Krause a "tilt" is assumed 
when a pair of sunspots appear when a magnetic "rope" comes to the 
surface. 



275 

The Babcock-Leighton theory is non4inear and one therefore obtains for 
any given angular velocity distribution, and for a given differential 
rotation, a magnetic field configuration. Recently Dumey and Stenflo 

(1971) have investigated the strength of the magnetic fields in Leighton's 
dynamo in dependence on the angular velocity assuming the differential 
rotation to be the same. They found that the magnetic field is approxi- 
mately proportional to the angular velocity. 

|B| ~ n 

New solutions of the Steenbeck-Krause equations have recently been 
found by Kohler (1972) who used a solar model with a realistic 
convective zone, and derived from the properties of the convective layer 
the factor in fjont of the AB term of the Steenbeck-Krause equation as 
well as their a as functions of depth. He indeed obtained periodic 
solutions. Certainly the Unear theory can not give amplitudes. But Stix 

(1972) investigated the case of non4inear limiting which would set in if 
the ampUtudes become sufficiently high. Then, as already suggested by 
Steenbeck and Krause, the magnetic fields would be so strong that they 
would react on turbulence and inhibit the helical motion. With such a 
cut-off he found that the amplitudes roughly go like 

IB I ~ 12 3/2 

The theory of the solar cycle is incomplete but one might already dare 
to make some predictions for other stars. If stars have a convective zone 
and are rotating, one would expect that they also have differential 
rotation. In this case the turbulent dynamo may work and one would 
expect the magnetic field to increase with rotational velocity if everything 
else including the degree of differential rotation is kept constant. 

LOSS OF ANGULAR MOMENTUM 

It had first been pointed out by Schatzman (1954) that mass loss from a 
rotating star with a magnetic field gives a high loss of angular momentum. 
This is due to the fact that the outstreaming material gains angular 
momentum from the magnetic field until it has reached a point where it 
is released into space. Following Weber and Davis (1967) one can write 

A (kM.R2«) = |.,2„M_ (1) 

kM R^ is the inertial momentum of the star. The factor k can be 
computed for any given stellar model. The radius r^ is the distance from 



276 
the star at which the Cowling number 

C2 = 



B2/47rp 



is one. Here v^ and B, are the radial components of velocity and magnetic 
field. If we follow recent work by Durney (1972) in a more generalized 
way one can show that 



'a 



Bo^JS (f )" 



where v^ is the value of v, at the point where C = 1 and B^ the field at 
the surface of the star. If we assume from the dynamo theory it follows 
thatBo~J2T we can then write 



'A~"''f(f)' 



From equation (1) it then follows that — as long as the radius of the star 
is not varying with time, as it is in the case for the main sequence stage 
to a high degree of approximation, one can write 

1 dS2 , n^T 

— -— = const. 

i2 dt ^A 

Therefore for any given rate of mass loss and for any assumption as to 
how the radial velocity, v^, varies with time, one can determine the 
angular velocity as a function of time. Probably v^,^ as well as dM/dt will 
vary with the angular velocity since the angular velocity will enhance the 
turbulent dynamo and therefor enhance the heating and therefor the mass 
loss. Generally one can assume 

v^ ~ nf 

with a free exponent f . Then equation (2) can be integrated and gives (as 
long as f+27) 



SI = const, (t - tp) f ■ 2t 

Durney has used this formula for the special case f = 0, y = 1 in order to 
obtain Skumanich's law r2~t"'^. Certainly one must know more about 
the mechanisms inside the pentagon of Figure lV-5 . The main purpose here 



277 

is to show that, in principle, the time dependence of the angular velocity 
distribution is determined. 

We have now discussed the boxes inside the pentagon and I must say I 
have the feeling that the whole logical structure indicates quite a closed 
picture although many details still have to be worked out. 

TURBULENT VELOCITIES IN THE ATMOSPHERES 
OF ROTATING STARS 

I would like to add a comment on the question of hot main sequence 
stars where convective theory gives practically no turbulent velocities. It 
has been shown by Baker and Kippenhahn (1959) that near the surfaces 
of rotating stars meridional circulation can reach fairly high velocities. I 
will give a different approach here. We consider very rapidly rotating 
stars where, near the equator, the centrifugal force almost balances 
gravity. Then it follows from von Zeipel's theorem that the effective 
temperature at each latitude is connected with the effective gravity: 

T ~ o^ 

It follows that pressure and temperature are constant on equipotential 
surfaces for hydrostatic equilibrium. But when we try to construct 
atmospheres in each latitude it turns out that the mean optical depth t is 
not constant on equipotential surfaces = const: 

dr = -K dT = -K d0/g, K = k(P,T) = /c(0), 

T = -JKi(t))d<j>l g 

Therefore t varies on equipotential surfaces like g"' . Solution of the 
transfer equations yields the temperature which is not constant on 
equipotential surfaces. This can be most easily seen in the case of a grey 
atmosphere where radiative equilibrium in the simplest approximation is 
given by 



T = const. X T.„ It + —j 



'eff 



Tgff* varies on equipotential surfaces like g and t like g* . Therefore T is 
not constant on equipotential surfaces. This is in contradiction to the 
condition of hydrostatic equilibrium. The equilibrum condition with the 
longer time scale will not be fulfilled. This is the equation of hydrostatic 
equilibrium. We therefore must assume. that there are strong horizontal 
motions with velocities hi^ enough that the inertia terms are of the same 



278 

order as the pressure gradient. This means the velocities are near the 
velodty of sound. 

The theory of atmospheres of rotating stars has recently been worked out 
by C. Smith (1970) and indeed he found that there are velocities which 
come near the velocity of sound. Therefore if chromospheric activity is 
found in rapidly rotating hot stars where convection cannot account for 
it, turbulent atmospheric motions in the atmospheres caused by rotation 
may be responsible. 

ACKNOWLEDGEMENT 

This work was carried out with financial assistance of the "Schwerpunkts- 
programm Stellarastronomie" of the Deutsche Forschungsgemeinschaft. 

REFERENCES 

Babcock, B. W., I960, Astrophys. J., 133, 572. 

Baker, N., "The Depth of the Outer Convection Zone in Main-Sequence- 
Stars," preprint. 

Baker, N., Kippenhahn, R., 1959, Z. f. Astrophys., 48, 140. 

fiiermann, L., 1951 , Zeitschr. f. Astrophys., 28, 404. 

Bohm-Vitense, E., 1958, Z. / Astrophys., 46, 108. 

Busse, F., 1970, Astrophys. J. 629. 

Cox, J. P., King, D. S., StelUngwarf, R. F., 1972, Ap. J. 171 , 93. 

Christy, R. F. 1968 Quart. J. Roy. Astron. Sac, 9, 13. 

Deinzer, ^.,Mitt. Astron. Ges.,30 67, 1971. 

Durney, B.R., Stenflo, J. O., 1971, On Stellar Activity Cycles, preprint. 

Durney, B. R., 1972 in C. P. Sonnet (ed.) Proc. of the Asilomar Solar 
Wind Conference, in press. 

Fricke, K., Stobie, R. S., Strittmatter, P. A. 1972 ApJ. 171, 593. 

Oilman, P. A., 1972, Boussinesq Convective Model for Large Scale Solar 
Circulations, preprint.. 

Kippenhahn, R., 1963 Astrophys J., 137 664. 

Kippenhahn, R., Meyer-Hofmeister, E., Thomas, H. C, 1970, Astron. + 
Astrophys., 5 155. 

Kohler, H., 1970, Solar Physics, 13, 3. 

Kohler,~H., 1972 priv. comm. 

Kraft, R. P., 1967 , Astroph. J., 150 551. 

Lauterborn, D., Refsdal, S., Weigert, A., 1971, Astron. + Astrophys. 10, 
97. 

Leighton, R. B., 1969 , Astrophys. J., 156 1. 

de Loore, C, 1970, Astrophys and Space Sc, 6, 60. 

Oke, J. B., Greenstein, J. L., 1954, Astrophys. J. 120 384. 

Parker, E. N., 1950, Astrophys. J. 122, 293. 



279 

DISCUSSION FOLLOWING THE INTRODUCTORY TALK 
BY KIPPENHAHN 

Skumanich — This may be quibbling with numbers, but if you use the 
revised age of the Hyades that Conti and von de Heuvel suggest then, in 
fact, I get that the rotation and calcium emission curve decay with an 
inverse cube root. But then the rotation, the lithium, and the calcium 
emission very rapidly decay past the Hyades point. Maybe that's due to 
the appearance of the Goldreich-Schubert strong mixing but in any 
respect there is this uncertainty about the ages. 

Shatten — With regard to the mass loss term. I presume what you mean is 
the particle mass loss term which mostly affects the angular momentum, 
to distinguish that, as we said before, from the mass loss term of the star 
itself, mostly due to the loss of photons. 

Kippenhahn — It takes 10' ' years to get a loss of mass from the Sun due 
to the mass equivalent of the radiated energy. Correspondingly, the loss 
of angular momentum is negligible . 

Jennings - I'd like to point out that on the pentagon diagram you had 
the coronal heating directly connected to mass loss. I think Weymann has 
shown that for late type giants and supergiants, there seem to be rather 
serious observational problems with that particular mechanism. 

Kippenhahn — The arrows in my diagram just indicate possible influences 
they do not necessarily indicate important effects. The arrow in my 
diagram which indicates the influence of mass loss.from coronae on stellar 
evolution presumably does not indicate an important effect, either. 

Jennings - There is one other point I'd like to make. It seems possible 
that grains may drive mass loss. If that is indeed the case, and one has a 
grain field around some stars it would act as a strong sink for heating. 
One would have inelastic gas-grain collisions and the grains would radiate 
away a lot of the energy that might normally be deposited in a 
chromosphere -corona . 

Skumanich — This again doesn't change your results. But I might say that 
Durney's argument follows even without assuming the mass loss, M, to be 
a constant. In fact one can show that the product of the mass loss times 
the Alfvenic "gyration" radius squared goes as B^. So maybe we should 
look for that other little square root in the moment of inertia; maybe the 
revision of the Hyades age is correct. 

Kippenhahn — One can repeat Dr. Durney's computations with different 
assumptions. But one always gets something similar to the Skumanich 
law. 



280 

Underbill — I'm concerned about the remark you made, that towards 
their later stages of evolution stars, on their outside, don't really know 
what their age is inside. This rather worries me, because we stellar 
spectroscopists look at the outside of stars and say that's part of the star, 
therefore the star must have such an age. 

Kippenhahn — If a star of a given mass comes twice during its lifetime to 
the same point of the HRD its spectrum should be the same unless 
chemically more evolved material has been brought from the deep interior 
to the surface. This is not in controversy with the usual age criteria, 
which either compare stars with different original metal content or 
different positions on the HRD. If a star, in its later evolution, happens 
to cross the main sequence, it normaUy will have a slightly higher 
luminosity than it had during its first main sequence stage. But, in 
principle, it would be difficult to distinguish whether the star is a real 
main sequence star or just an occasional visitor. 

Underhill — That's what worries me , because every time we see a star of a 
certain type, we go to the first possibility and ignore the second. 

Kippenhahn — What I said only holds for simple stellar models, corre- 
sponding to the outer ring of my pentagon diagram. But this is 
insufftcient. The boxes of the inner ring are important too. They involve 
rotation and magnetic fields. The star coming to the main sequence for a 
second time would differ in its rotational properties. Therefore the 
Skumanich law should help you to distinguish between a young star and 
an old star at the same point on the HRD. There is another point which I 
would like to comment on. In the picture I sketched in my talk, a star 
like the Sun would slow down its rotation on the main sequence and, 
after a while, the dynamo would be rather weak and the enhancement of 
mechanical flux by magnetic fields would be small; the Ca emission would 
be weak. When the star leaves the main sequence and moves into the red 
giant area of the HRD, its angular velocity is getting even smaller, due to 
conservation of angular momentum. But at the same time convection 
becomes more violent. So we have two effects acting against each other: 
Rotation which goes down and convection which goes up. Which will 
win? But it would be possible, also, that even with slow rotation the 
dynamo becomes more active, since it has not yet been investigated how 
the effectiveness of the dynamo changes, when convection becomes 
stronger while rotation becomes slower. We also do not know how the 
enhancement of convection will affect the differential rotation. We 
therefore are unable to predict whether the Ca emission of the Sun will 
come back when the Sun will become a giant star. 

Pecker — My comment is related to the question by Anne Underhill. Of 
course, the question she asked is: Are we right to use a 2 dimensional 



281 

diagram to represent steUar spectra. And the reply is of course "no, we 
aren't right." To come back to the specific question: "Does the K line 
emission enable us to distinguish between the pre-main sequence or the 
post -main sequence stage?", I would like to refer to a computation which 
has been made in Nice by Nicole Berruyer. She shows (using Larson- 
Starrfield kind of techniques), that, when you reach the main sequence 
for stars of high mass (~20 solar masses), then the time of contraction of 
the envelope is long compared to the time during which the star is staying 
on the main sequence before leaving the main sequence. Therefore, near 
the main sequence, you cannot distinquish easily between pre and post 
main sequence stages; both stars still have very large envelopes. At the 
opposite, for a lot of stars in the H-R diagram (in the pre-M dwarfs for 
example, where you have the T, Tauri stars) it is exceptional to find an 
example which is still in contraction, because the lifetime on the main 
sequence is lO'" yrs. vs 10^-10* yrs. for contraction of the envelope. 1 
think we should certainly look at things in the spectrum that are oriberia 
of the age of the stars, and others that are oriberia of the age of the 
envelope. 

Aller — We can look at the problem of solar and stellar chromospheres 
from several different points of view. One point of view, which was 
emphasized yesterday, is understanding the manner in which chromo- 
spheres are created and heated in the neighborhoods of stars. At the 
outset we assume that chromospheres exist. Furthermore, we have some 
biased view of what they ought to be like from observations of the solar 
chromosphere. Now, how can we make use of this information in 
investigating the radiation of other stars? Here, of course, we are severely 
limited by the nature of our observational material. Whereas we can make 
detailed observations of the structure of spicules and other fine points of 
the solar chromosphere, observations of stars involve only their integrated 
Ught. It is true that one can make time resolved studies. These have, 
shown, for example, rapid spectral changes in the emission lines of some 
stellar envelopes. Whether you call them chromospheres or not depends 
on your point of view. My favorite star in this respect is HD 45166 
whose rapid variations were discovered. many years ago by Carol Anger 
Rieke at Harvard Observatory. This is perhaps an extreme example. The 
question before the house is to what extent can we make use of 
chromospheres to evaluate the status of a star with respect to its evolu- 
tionary development. This was the point which was raised by Anne 
Underbill, and it is a matter which concerns many observers. For the 
most part, we are limited now to a narrow spectral range. Part of the 
material we urgently need falls in the "vacuum" ultraviolet and, until we 
get a proper space telescope, we are going to be frustrated in our efforts 
to get even a rough picture. In the meantime, we have to get by with 



282 

what we have. In addition to conventional spectroscopic observations, we 
also have some radio data for a few interesting binary systems, though we 
have not yet begun to understand the physical significance of what we are 
observing. The rapid rise in the efficiency and sophistication of infrared 
techniques will undoubtedly give us a great deal of information about this 
important spectral region. This infrared radiation may not all come from 
dust clouds, as is the favorite hypothesis today, but some of it may come 
from bona fide chromospheric activity. Therefore, from the observational 
point of view, there are only a very small number of handles that we can 
grasp, a very small number of things that we can do. Those of us who are 
observers would like to have the help of theoreticians who may point out 
what are the specific observable phenomena that we should seek in 
different stars in different parts of the Hertzsprung-Russell diagram in 
order to get clues as to evolutionary development. 

Durney — I would like to discuss some work 1 have done recently with 
John Leibacher of JILA on the location in the HRD of different types of 
stellar winds. In a recent paper, Roberts and Soward (1972) have 
determined in the Nq, Tq plane (the density and temperature at the base 
of the corona) the regions where the stellar winds are A) supersonic for 
distances larger than the critical point located outside the surface of the 
star (usual stellar winds), B) always subsonic (stellar breezes), and C) 
supersonic for all distances larger than the surface of the star. With the 
help of Kuperus' (1965) calculations of Nq and Tq for a variety of stars, 
we locate the stellar winds of type A), B), and G) in the Hertzsprung- 
Russell diagram.. The relevance of static envelope models for stars with 
winds of type C) is discussed. 

Figure IV-7 is taken from Roberts and Soward 's paper (1972). In the 
following, we designate by "subsonic" the "Chamberlain" region of 
Roberts and Soward. This is not quite proper, and we refer to the above 
paper for a more detailed discussion of this region. If Nq and Tq are 
located to the right of the dashed curve, then the stellar wind is 
supersonic from the surface of the star outwards. Since Tq is given in 
units of ^-^ (where G is the gravitational constant, m half the hydrogen 
mass, M and Rq the mass and radius of the star and k the Boltzmann 
constant), it is clear that if Rg is large and the star has a corona with a 
typical coronal temperature and density, then the stellar wind, according 
to > Figure IV-1, will be supersonic for all distances larger than Rq. As an 
example, if we assume Tq = 2 x 10*°K and M = Mq the critical radius of 
the star for which the stellar wind is supersonic from the surface 
outwards is ~ 13 Rq for No > 2 X 10^ cm"^. 

We discuss now the physical meaning of stellar winds which are super- 
sonic at the surface of the star. It is well known that the stellar wind 



283 



N, 



10' 



10^ 



10^- 



10 - 



10-'- 



10 



-2 



I HI I — I — I — I — r 
Chamberlain 



2/7 



Whang 

and 
Chang 




0.1 0.2 0.3 0.4 0.5 0.6 0.7 



Figure IV-7 The types of acceptable solutions of the stellar wind equations as a 
function of the temperature, T^ and density, Nq at the base of the 
corona (T- is measured in units of GMm/kRQ and Nq in units of 2kq 
(GMRQ)-l/2/k where « = Kq (T/To)^/^ is the electron conductivity). In 
the regions denoted by 2/7 and 4/3 the asymptotic behavior of the 
temperature is T ~ r'^P and T ~ r"^/3 respectively whereas T ~ r^/S 
for the Whang and Chang line (c.f. Dumey and Roberts 1971). To the 
right of the dotted line the flow is supersonic at the surface of the 
star. (From Roberts and Soward 1972). 

equations allow for two degree of freedom: it is possible to give 
arbitrarily N^ and T^ or alternatively the mass flux, C, and the residual 
energy per particle at infinity, Coo. The mass flux, C, is introduced in the 
momentum equation by the use of the continuity equation, and eoo is the 
arbitrary constant appearing in the integral of the energy equation. These 
two equations are of first order and the two boundary conditions which 
determine the flow speed and temperature are (a) T -* as r -> «> and 
(b) p ->■ as r ->■ oo, i.e. the solution should cross the critical point. This 
last boundary condition disappears when the stellar wind is supersonic 
from the surface of the star and the problem becomes undetermined. The 
mass flux, for example, could be given, between limits, arbitrarily. In such 
a star the solution of the stellar wind equations is not as simple as it is 
for the Sun. The heating of the corona by acoustic waves must be 
included explicitly and the equations must be started from the chromo- 
sphere where the velocities are subsonic. Static envelope models for these 



284 

stars are probably not meaningful. Ulmschneider (1967) has calculated the 
structure of the outer atmosphere of cool stars. By virtue of the above, 
however, we consider that his determination of the initial flow Mach 
number, M^, is very approximate; Mq should be determined by requiring 
only that T -* as r ^ 0. The supersonic of subsonic character of the 
flow carmot be prescribed as a boundary condition. 
With the help of Figure IV-7, and values of Nq, T^ and R^ as evaluated 
by Kuperus for a variety of stars, it is possible to give the approximate 
location of stellar winds of type A), B), and C) in the Hertzsprung-Russell 
diagram. This has been done in Figures IV-8 and IV -9. There is no doubt 



-5 



0- 



Mk 



5 - 



1 1 
0. 


III 1 

logg=2s^ 

N 
\ 

N. 

\ 

3^ 




~ 






^Main Sequence ^v 


c 


c 


■N 




\ 






\ 


'^^^^— ^^W 


^^^^^^ 


3^ 


1— 


B 


— ^ 


^^ 






^1 ^^' 1 


"^ 














~ 


N. ^^^ 


- 


5-. 


N^ ^v^ 




1 1 


III 1 


•^ 



10 9 8 



Tg„(xlO-») 



Figure rV-8 The mass of the star follows the mass luminouslty relation. Regions 
A), B), and C) have been determined from Figure IV-1 and from the 
values of Ng T^ and R,, as evaluated by Kaperus (c.f. Figure 22 of 
Kaperus (1965). Region: A) usual stellar winds; B) stellar breezes; C) 
the flow is supersonic: at the surface of the star. 



that Kaperus calculations are very approximate. However, since in classi- 
fying stellar winds according to type A), B), and C) the values of N^ and 
Tq are not too critical we can have some faith in the general location of 
regions A), B) and C) in the Hertzsprung-Russell diagram. We stated above 
that the validity of static envelope models of stars in region C) had to be 
carefully examined. It is tempting to speculate that stars with very large 



285 



radii can suffer appreciable mass loss by this process of "coronal 
evaporation" (c.f., Weymann (1960), for the cage of red giants ). The 
importance of radiation pressure in the mass loss of hot stars and stars 
with circumstellar dust shells has been considered by Lucy and Solomon 
(1969), and Gehrz and Woolf (1971). Further work on this subject is in 
progress. 



M 



-b 


1 1 r 1 1 1 

b 




'°9 9=2^^..^^ Giants. 



b 


^C Sequence "--^^ / /^- 


5 


■^^^ 




1 1 1 .1 1 1 \ 



10 9 8 



7 6 5 

Tg^fCxio-') 



Figure IV-9 The mass of the star is equal to the mass of the Sun. 
Regions A), B), and C) as in Figure IV-2a). 



REFERENCES 

Durney, B. R., and P. H. Roberts, {1911), Ap. J., 170, 319. 
Gehrz, R. D., and N. J. Woolf, (1971), Ap. /., 165, 285. 
Kuperus, M., Rech. Astron. Observatory. Utrech., (1965), 17, 1. 
Lucy, L. B., and P. M. Solomon, (1970), ^p. /., 159, 879. 
Roberts, P. H., and A. M. Soward, Proc. Roy. Soc. London (in press). 
Ulmschneider, P., (1967), A Astrophys., 67, 195. 
Weymann, P., (1960),^p. /. , 132, 380. 



286 

DISCUSSION FOLLOWING TALKS 
BY PRADERIE AND DOHERTY 

_ Heap — We can see where the velocities are perhaps supersonic at the 
surface of the star. What do you mean by the surface? Is it the stellar 
evolutionists' surface or the photosphere? 

Dumey - Tq is measured in units of GmM/kKg and N^ in units of 2 
Ko(GMRo)"'^Vk; Ro '^ ^^^ surface, In general Rg would be the distance at 
which energy deposition takes place. 

Heap — My next comment is on the stars populating your Region C. A 
regular star is in Region C, and a planetary nucleus would also be in 
Region C. Observations of these stars tend to support your suggestion 
that Region C objects have some sort of chromosphere. As I mentioned 
earlier, both types of stars show a velocity-broadening that is 75 km/sec 
or greater. In the case of some Of stars, both young stars and the very 
old planetary nuclei, the Hell X.4686 Une is very broad, indicating 
velocities up to ±1000 km/sec, so these stars have a mechanical flux 
which could possibly be dissipated in forming a chromosphere. There is 
one young Of star, Zeta Puppis, showing broad Hell X4686 emission 
whose chromosphere in fact has been seen. The UV spectrum of this star 
has been observed from rockets by Morton and Smith, and it shows 
several high-excitation emission lines. These UV lines would be an 
indication of a chromosphere, because the excitation of, say the VI 
emission line, certainly is greater than that of the photosphere. No 
planetary nucleus has been observed in the rocket-UV, but there is 
possible evidence for chromospheric enhancement of radiation in the 
far-UV, below the Hell limit at 228A. The evidence lies in the dis- 
crepancy between the Hell Zanstra temperature and the temperature 
derived from the visible spectrum of the star. For example, ihe nucleus of 
NGC 2392 has a Hell Zanstra temperature of 94,000°, while the visible 
stellar spectrum indicates a spectral type of 06 or 07. Perhaps the nebula 
is "seeing" chromospheric radiation from the resonance Unes of high- 
ionization states of C, N, and rather than photopheric radiation. 

Durney — You are right, the temperature range is too large. This is 
because the figures shown are identical to Figure 22 of Kuperus. The 
division of the Hertzsprung-Russell diagram into regions A), B), and C) 
applies only to those stars for which Kuperus did evaluate Nq and Tq . In 
particular he did not calculate N^, and Tq in the high temperature region 
of the figures. 

Jemiings — When you say that this type of flow might affect stellar 
structure, is that to mean that the quasistatic approximations for calculat- 
ing models would not be valid? 



287 

Durney — For calculating envelopes they probably break down. 

Jennings — I would argue by continuity that the interior would not know 
anything about this mass loss. 

Durney - In general, I think it would not. 

Cassinelli — I think it should be pointed out that radiation pressure 
effects become important in region C. At the higher luminosities the- 
outward acceleration due to the radiation pressure gradient may be 
greater than, or equal to, the inward acceleration of gravity. 

Durney — Right. In this calculation the radiation pressure was not 
included. 

Ulrich — How sensitive is the location of the boundaries on the H-R 
diagram to the mechanism you used to derive those values. You don't 
know what the coronal temperatures are. 

Durney — We have accepted Kaperus results. From Figure lV-7 and the 
units in which Tq is measured (GmM/kRQ) we expect regions A) and C) 
not to change much for values of Tq not drastically different from typical 
coronal temperatures. This is because the range of variations in mass is 
smaller than variations in radius. Region B) demands a more sensitive 
balance of N^, Tq, and R^, and could, for example, disappear if 
Kaperus calculations are seriously in error. 

Alia: — So evidently in these hotter stars the wind starts blowing very 
close to the stellar surface so that you do not have a conventional 
chromosphere. I mean you don't have a semi-steady one like the solar 
chromosphere; the wind is blowing all the time; the material is always 
flowing outward. Is that your conclusion? 

Durney — Yes. 

Underhill — But that doesn't mean it's not a chromosphere. We didn't 
define a chromosphere as having to stay still. 

Afler — The physicist's problem is that one must consider differently a 
mass of gas which is moving violently 'outward from one which is 
quasisteady. The velocities are already large at the surface of the star. 

Thomas — If I were to paraphrase what Delache said yesterday, what you 
just said is not true. All that happens is, when I look at a sequence of 
stars, maybe I have to worry more and more about the outward 
component of the mass flux as I change the spectral type. Sure, I agree in 
detail it's different, but, in terms of the broad physical picture, it is 
not. 



288 

Aller — Precisely these details may be very important in an interpretation 
of the data and analyzing the obtainable observations which may admit 
several, equally plausible, but different pictures. 

Thomas — The details are always important, but unless I know the 
structure first, I become a number juggler. You must first have a 
structure; then of course, if all you have is a structure, you're going to 
miss the details. I must have the detailed computation of the numbers to 
be able to convert the observations. But if I just compare the numbers 
without having the structure, then it looks as though each different star is 
a problem by itself; and that is a viewpoint I disagree with. 

Aller — I would disagree with that too. 

Kippenhahn — Am I to understand that you want to redo the work and 
replace the normal static by kinetic boundary conditions? One would 
then expect that this would remove the difficulty that near the surface 
you get supersonic velocities. Then everything would look rather decent. 
The difficulty that you encounter is that you use stellar models with 
static atmospheres and fit to these dynamic atmospheres. 

Dumey — This proves that one cannot construct static models. One needs 
to construct consistent kinetic models. 

Pasachoff - Again here we have to be careful that the definition that we 
get for a chromosphere does not exclude the solar chromosphere, which is 
not at all static. The solar chromosphere is probably composed entirely of 
spicules, which have velocities of approximately 20 km/ sec. 

Dumey — But the outward flow velocity is small in the solar chromo- 
sphere. It is only randomly non-static. 

Underbill — I think we're just hung up on the fact that an observation of 
a Une profile gives you an average over the stellar surface. It can 
frequently be a net general outward velocity. What you're saying about 
spicules in the Sun is that you're looking at individual features and you 
can see there are large changes. It is a question of statistical averages. 

Aller — That is correct. The fine structure doesn't change things very 
greatly. I think there is a rather important quahtative difference between 
a chromosphere like that of the Sun and the atmosphere of a P Cygni 
star. Aside from the greatly different temperatures involved, the inherent 
differences in the velocity fields give them a very different character. I'm 
not saying they shouldn't be called chromospheres, but I think we have 
to be aware that the definition may embrace envelopes that are almost, 
but not quite, in hydrostatic equilibrium, on the one hand, and also 
evanescent structures, where you have a violent wind blowing, on the 
other. 



289 

Stein — In looking at your first figure, one might turn that around and 
say that the boundary of the region where the flow is supersonic from 
the surface, gives an indication of the maximum temperature which is 
possible in a corona, since, for higher temperatures, such a large mass loss 
(and therefore energy loss) occurs, that the temperature is reduced to 
approximately the critical value. This might provide a Umit to coronal 
temperatures. 

Durney — Yes, but there is some arbitrariness in this. We think that one 
needs to solve the problem consistently. 

Stein — It's true that it's arbitrary, but because the thermal velocity is 
approaching the escape velocity, the maximum possible corona tempera- 
ture must be of the order of your Tq . 

Dumey — I agree. 

Skumanich — I'm disappointed that Dean Petersen hasn't said anything. I 
received recently a preprint from him about the problem of a radiation 
driven flow in which the sonic point is inside the envelope. He uses a 
plane parallel approximation to the flow, because he's dealing with a 
fairly large radius, but I think the physics is really the same. You only get 
aC^/rterm difference in the driving forces what he finds is that the flow 
is decelerating after it goes through the sonic point. It reaches a 
maximum and then becomes a decelerating flow. But what bothers me 
about the work is that there is a finite pressure, a wall as Delache said the 
other day. I don't know where it comes from and what its consequences 
are on the actual detailed dynamical flow. Is this wall the back pressure 
of the outward traveling shock that the wind has ultimately produced in 
the interaction with the interstellar medium? There must be some time 
dependent phenomenon at the leading edge of this wind and at the tail 
where the rarefaction is eating into the envelope of the star. So these 
steady flows are quasisteady flows in the sense that they settle down to a 
constant form in space, but they have time dependent leading edges. I 
don't know what that does to this whole problem, the time variations and 
so on. 

Pasachoff — Though we haven't agreed on what a chromosphere is in the 
general case, I thought that we should at least show the meeting a picture 
of one, so that we know what it really tooks like. Figure IV- 10 is a 
photograph taken of the solar chromosphere in Ha at the Big Bear Solar 
Observatory on May 22, 1970. It represents the current state of the 
observer's art. Resolution is better than 1 second of arc. 

Underbill — I'm not at all sure about the revisions of T^^j vs B-V around 
type AO V. The revision you were talking about brought Vega down 
from 10,000 to 9750°K. 



290 




Figaie IV-10 



291 

Conti - No. It was 10800 to 9750''K. 

Underbill - So it brought T^ff down 1000°K.' Consider the problem of 
the large ultraviolet blanketing which I discussed a couple of days ago. If 
you enter that into our standard model calculations, you get the usual 
effect of backwarning. The net result is, as Deane Peterson mentioned, 
you can probably make a fully line blanketed model for Vega that fits all 
of the visible region with an effective temperature of the order of 
9300°K. This is one of the difficult things that you have to remember 
about model atmospheres: they are only models, and every time we put 
some more factors in them, this parameter, T^f^, which is essential for 
stellar interiors comes out a bit different. The real problem is that this 
parameter is not at all essential for stellar atmospheres. We're trying to tie 
this B-V to a non-essential parameter. In fact stars can have exactly the 
same spectrum and be of entirely different ages. You have to realize that 
this pillar of stellar structure is no pillar whatsoever for the stellar 
atmosphere. You have to look for another pillar. 

Conti — There was some discussion by Andy Skumanich on the revised age 
of the Hyades from a paper by van den Heuvel and the applicability of his 
number. I should say you better believe it. If you look at his paper, which is 
in the P.A.S.P. of about 2 years ago, you'll see that when you draw a theo- 
retical H-R diagram with the turn-off age between 8 and 9x10' years, for 
the Hyades, it matches extremely well all of the members of the cluster. 
That's where the age determination comes from. The reason that the age 
was revised by about a factor of 2 was that when you go from a 
theoretical H-R diagram to an observed H-R diagram, you've got to make 
some connection between a B-V color and an effective temperature. What 
had happened was that the T^j^ vs. B-V relationship for A type stars had 
been altered, primarily because of the continually changing temperature 
calibration of Vega. It has now pretty much settled down, and what van 
den Heuvel realized was that this would effect the turn-off diagrams and, 
therefore, the evolutionary times of clusters that have turn-off points 
somewhere in the A stars. For example, this does not affect the Pleiades 
nor M67 but it does affect the Hyades. This somewhat more elderly age 
for the Hyades does now have implications for the solar system, the 
lithium depletion, and the H and K emission, and so on, as Andy 
mentioned. That's the first comment. My other comment has to do with 
massive stars. We've heard that the star forms and that the star starts 
burning nuclear fuel, and that the envelope still doesn't have enough time 
to fully contract. This is the work of Larsen and-Starrfield. I think this 
has direct appUcation to the star I discussed on Tuesday, 6' Orionis C, 
where we see material accreting. I just wanted to make that connection. 



292 

Pecker — I want to reply to Peter Conti. Consider the H-R diagram. Now 
we've just discussed the caUbration of Tgff. I want to draw attention to 
one thing which is extremely relevant to the problem. In those stars with 
strong emission lines, very often infrared excesses are strong, but not 
always known. Then bolometric corrections are absolutely wrong. For 
example HD 45677, a Be star, has a bolometric correction a little bit 
more than one magnitude in error, compared to the value given by the 
classical B models. That is my first comment. 

The second comment is linked with what Peter Conti said about the 
reversed P Cygni profile observed in a Trapzium star. Such P Cygni 
profiles are associated with contracting (or pre-main sequence) objects. 
There is another case which no one has mentioned yet at this meeting, 
and that is FU Ononis. I would like to draw your attention to a series of 
papers which has been pubUshed in Russian by Ambartsumian (and so far 
translated for me by an Armenian astronomer). This comment is quite 
relevant to the origin of the heating. Ambartsumian is regarding the 
Hayashi like theories for contraction before pre-main sequence stars as 
unsuitable for objects such as FU Orionis. He is assuming that there is a 
new class of objects that he calls "FUORs", the first one of them being P" 
Cygni itself. I might recall the fact that P Cygni is now of a magnitude 
which is visible, while at the time of Tycho Brahe it wasn't. This is the 
reason which makes Ambartsumian think it is a star of this type. P. Cygni 
is number 1, FU Ori is number 2, in this series of objects. Number 3 is 
Lick Ha 190. According to Ambartsumian, a FUOR is a superdense star, 
a member of a binary, and from time to time the super dense star is 
throwing away high energy particles, which are heating the outer part of 
the other star. This is what creates the chromosphere and its abnormal 
heating. I just wanted to draw this to your attention because I don't 
think we've been exploring all the possibilities of heating. We have so far 
been trying to concentrate only on the heating from inside. My question 
is, are there any possibilities of heating from outside? 

Then I come to my third point, which is a question for Di. Kappenhahn. 
(Now let's forget about this reference to Ambartsumian; I don't know 
whether or not I can believe it. I think I am myself more in favor of the 
classical contraction theory of Larson, or Penston, especially for the 
interpretation of FU Orionis.) My question is: when you have a pre-main 
sequence star, in pre-main sequence evolution, then you have something 
which contracts. To avoid confusion, let's not take a hot star where there 
is the extension of the HII region which mixes up the problem. Let's take 
a cold star. There is some energy which is released by contraction of the 
mass. Now where is this energy Uberated, what is the quantity of energy 
which is liberated, and can it contribute to the formation of a chromo- 



293 

spheric heating and of a chromosphere? I ask this question specifically for 
the T tauri stars. 

Kippenhahn — Do you have in mind that the star is contracting and 
probably there are some outer layers which follow more slowly? We come 
back to the old problem of meteorites faUing on top of a star and heating 
the outer layers." I would say this is still possible for the T Tauri stars, 
although what we observe is that there is mass loss from these stars and 
no infalling material. But, on the other hand, if you look at the Larsen 
solutions of the problem of star formation, you find dust clouds raining 
on top of stars for long periods. Material is falling on stars -which have 
just been formed. They might already be close to the main sequence. 
What will happen with the kinetic energy of the infalling material? 
Certainly this is a problem which should be looked into. 

Kuhi — I think bringing these stars into the discussion is going to throw 
the field wide open for drastic speculation. It is interesting to me that the 
calculations by Larsen and others for contracting stars always show 
material falling in during the contraction phase, and also a large amount 
of dust surrounding the star which presumably then reradiates in the 
infrared. Aside from about six or seven stars in Orion, there is no 
evidence for any infalling material in any contracting star that I am aware 
of. It is ironic indeed that Peter Conti should mention a star which is a 
very high temperature object, with which we normally associate a large 
HII region, a large radiation pressure, and from which we would normally 
think material is being driven off the surface. On the other hand, he finds 
material falling in. It seems to me that somewhere our theory is in drastic 
error. The point about the dust clouds surrounding these young stars is a 
very good one. I should mention the observations of Gary Grasdalen (a 
graduate student at Berkeley) of stars like Lk Ha 190, which is also 
known as V1057 Cygni. This object was an extreme case of a T Tauri star 
before it blew up (or whatever else it did), having a very rich emission 
line spectrum which some of us would call a chromosphere. Anyway, if 
we accept Larsen's picture, then we must also accept a large infrared 
contribution to the flux for this object in its pre-outburst phase. After its 
outburst it was indeed a bright infrared object, so we might say 
everything is fine. However, Grasdalen has looked at a number of T Tauri 
stars in the same part of the sky which have virtually identical spectra to 
the pre-outburst Lk Ha 190 spectrum, and- he finds no infrared excess 
whatsoever. So I think that our theoreticians have much further to go 
than they would be willing to admit. 

There is one other point that I woiUd like to add about bolometric 
corrections. The infrared observations have cast considerable doubt on our 
old ideas concerning even the hot stars. Many of the hot stars, especially 



294 

Ae and Be stars, have shown large infrared excesses, and when one adds 
these to the total fluxes emitted by the stars to get the total bolometric 
luminosity, I think we find again serious discrepancies with previously 
held ideas. The same thing applies to the pre-main sequence contracting 
stars. You often find that the luminosities in the infrared are many times 
that in the visual and coming back to the T Tauri stars, you find that you 
need masses much larger than the previously assumed one or two solar 
masses to explain the total luminosity. Just to make one concluding 
remark. Lick Ha 190, a typical T Tauri which we all thought was one 
solar mass popped up and is now an A supergiant. Explain that. 

Aller — You're giving the theoreticians a pretty rough boundary 
condition. 

Bohm — I would like to ask Peterson : how can you calculate mass loss in 
a plane parallel approximation? Isn't it true that in a plane parallel 
approximation you have to do an infinite amount of work to push matter 
to infinity? I don't see how one can ever get mass loss, but maybe I 
misunderstood something. 

Peterson — That's right. Because it is an artificial geometry, you have to 
impose a sink at the top of the atmosphere. Basically, it shows up in the 
equations as a finite boundary pressure. Fortunately the equations do not 
leave that boundary pressure a free parameter. 

Bohn — So this pressure which was mentioned is somewhat artificial. 

Peterson — . It's artificial, yes, and it goes away in the spherical case. 

Lesh — I'd just like to add something to Anne's comment that stars can 
have the same spectrum and still have widely or slightly different ages. We 
have been looking at a class of B type variable stars, the /? Cephei stars. 
As a star evolves away from the main sequence it turns around at a 
certain point and describes a loop in the H-R diagram, as you well know. 
Near the turnaround point, a star can actually be doing quite a number of 
things. It can be evolving away from the main sequence; it can be 
contracting back; it can be burning hydrogen in a shell source; and, in 
addition of course, it might be contracting towards the main sequence. In 
a particular small region of the HRD, there are a large number of normal 
non-variable B stars, but there are also about 20 of these odd creatures 
called ^ Cephei variables. It seems very likely that they (variable and 
non -variable stars) occupy the same region of the H-R diagram, because 
they are in different stages of evolution, in other words, because they 
have slightly different ages. However, the work I have done on these stars 
with Morris Aizenman at Montreal has shown that there doesn't seem to 
be any spectroscopic distinction between the variable stars and the 



295 

non-variable stars. So it would appear that here we have a case of stars 
which do, in fact, have slightly different ages, if we assume that 
contraction towards the main sequence is ruled out, but which do not 
differ in any observable spectroscopic fashion. 

Aller — This would appear to be another incidence where the surface of 
the star doesn't pay any attention to what the interior is doing. 

Boesgaard — I'd like to discuss a Centauri in cormection with differences 
in the chromosphere with stellar age. a Centauri is a triple system. The 
first component A is exactly the Sun observed at steUar distances; it's a 
G2 V star. Component B is a Kl dwarf, and component C, Proxima, is a 
dMe flare star. The fact that component C is a flare star would indicate 
that it, at least, and presumably all three stars, are probably young. 
However, the intensity of the chromospheric calcium emission in a Cen A 
and B, gives, as far as I can see, no indication that those two stars are 
young, a Centauri A has very weak calcium emission. It looks similar to 
the Sun. At 3.3 A/mm on a long exposure one can just see weak K2 
features. I have two long exposures of this taken at Mauna Kea. (We can 
get down to , declinations of -60.) The two spectrograms look slightly 
different in the K2 structure. In one case it looks like the red peak is 
stronger than the blue; in the other case it looks like the 2 peaks are of 
equal intensity, but I'm not willing to say that this represents a solar 
cycle type of variation, or the kind of local variation you see in the Sun, 
because the emission is so weak. 

The Kl star shows a calcium intensity of 2 on the Wilson scale. This was 
also observed by Warner. That's about the relative intensity you'd expect, 
for the relative temperatures of the two main-sequence stars. 

Aller — Do we really know enough about emission processes in dMe stars 
to apply this rule? I was under the impression that a Centauri C was a 
fairly "late" M dwarf, that is to say, advanced in the sense of spectral 
type, in other words, a very cool object. I wonder how well the 
calibration works down in that spectral region. 

Mullan — There is unfortunately no simple relationship between the age 
of a flare star and its level of flare activity. Haro and Chavira (Vistas in 
Astronomy 8, 89, 1965) observed flare stars' in seven clusters ranging in 
age from the Orion group to the Hyades. They found that, as a flare star 
evolves towards the main sequence, it flares more frequently. This was 
direcfly opposite to a prediction of Poveda who believed that the 
youngest flare stars high above the main sequence should have retained 
fossil magnetic fields, and should be more active than older flare stars 
near the main sequence. However, observational selection could account 
for the effect discovered by Haro and Chavira if the absolute luminosity 
fimction of flares is the same in stars of different type. 



296 

On the subject of fossil magnetic fields, I would like to supplement what 
Professor Kippenhahn said about dynamo fields by pointing out that 
fossU fields may also be important in understanding stellar chromospheres. 
Unsold showed that the decay of emission in the H and K lines of Ca II 
can be understood in terms of the decay of fossil fields by Joule 
dissipation. This is not to say that dynamo fields are never important. For 
example, although flare stars, in all hkelihood, require strong surface 
magnetic fields, it may not be important whether the fields are fossils or 
have been generated by dynamo action. A flare star might conceivably go 
through two phases of flare activity, one in which its field is fossil, the 
second in which the field is dynamo generated. This would help to 
interpret the lack of a unique relationship between the age of a flare star 
and its level of activity. 

Boesgaard — Isn't there information on the statistics of the galactic orbits, 
to get an age indicator for the flare stars? 

Mullan — Galactic orbits provide information about ages of field stars. 
The results of Haro and Chavira are confined strictly to cluster stars. In 
the case of the field stars, the most significant feature of the galactic 
orbits of M stars is Delhaye's discovery that the dispersion of peculiar- 
velocities of dMe stars is significantly smaller than that of dM stars 
without emission. As a subgroup of the dMe stars, flare stars are then 
expected to be, on the whole, a young group. But within a group so 
young, age discriminators are not really avaOable. 

Boesgaard - Any connection between that and the amount of flare 
activity? 

Mullan — I don't know. 

0. Wilson — About a year ago, Woolley and I had a paper in the Monthly 
Notices in which we compared the results that I got on about 400 
(Vissotsky) stars, on which I made very careful eye estimates of the 
intensity, with the predictions of galactic dynamics, which are that the 
older the group of stars, the greater should be the eccentricities of the 
galactic orbits and the greater the incUnations. This correlation was 
extremely good. There were no flare stars in the group, or there were so 
few that they didn't matter. But just looking at the spectra, I would say 
that the flare stars form a continuation at the end of the sequence where 
the calcium emission is very strong and where you see Balmer emission; 
they lie just a little bit farther along. But of course they're relatively rare. 

AUer — And you would conclude that these are relatively young stars. 

0. Wilson - I think there's no question about it. 



297 

Underbill — But the question is: does young mean a fraction of the total 
evolution track, or does it mean Uterally counted off in seconds as 
determined by atoms on the earth? 

Aller — I presume that it means young in the sense that a Centauri A and 
a Centauri B would not be as old as the Sun, according to this reckoning. 

Boesgaard — That's my impression, because C is a flare star. But I don't 
have any estimate in years. 

Kippenhahn - I would like to comment on the question about the fossil 
fields. In that area of stars where we deal with calcium emission, we have 
no evidence of fossil magnetic fields. In the case of the Sun we have a 
dynamo generated field. With the dynamo fields you can expect an age 
dependence of the chromospheric activity, as it is observed, while for the 
fossil fields you would have a time independent chromosphere . 

Jennings — I have a clarification question. At what dispersion were those 
observed? 

Boesgaards- 3.3 A/mm. 

Jennings — Have you actually traced them to see what the emission 
percentage is, and is it about 4% of the continuum Uke the sun? 

Boesgaard — Approximately. 1 don't have an exact number. 

Kandel — 1 must say that the pictures occasionally have been puzzling. 
Several years ago I looked at 61 Cygni B at lOA/mm. 61 Cygni is 
generally said to be old, associated with a group which has an H-R 
diagram like M67. Yet, it has awfully big H and K emissions. 1 couldn't 
resolve whether there was a central reversal there, but the emissions 
themselves were rather big. I think Dr. Wilson has observed variations 
there. Perhaps he would comment on that. 

O. Wilson - 1 will talk a little bit about this subject this afternoon and, 
while 61 Cyg B has certainly a well marked emission, 1 can find you 
other stars of similar type that have 2 or 3 times as much. So it's a 
relative matter. 

Aller — I would like to ask some of the stellar evolution people if they 
have tried to determine an age for the a Centauri system by seeing how 
well it fits the general main sequence. My impression is that it has not 
evolved off the main sequence by any distance sufficient to allow us to 
draw any conclusions. That's why it will be difficult to get its age by 
evolutionary arguments, even though it is certainly a star whose mass, 
luminosity, and perhaps even radius, are very well known. 



298 

Kippenhahn — I would guess that it is not possible to do this. Just the 
uncertainties we have in the opacities may spoil the whole picture. 

Steinitz — It has been mentioned a few times that there is a connection 
between the age and the characteristics of the spectrum in the atmo- 
sphere. One thing that has been mentioned is the chromospheric activity. 
It has been claimed that the atmosphere doesn't know about the age of 
the star below it; as an example, the B Cephei stars have been taken. I 
would like to mention the mere fact that we have classified them; that 
they look like other stars in the same region; yet, they oscillate while the 
others don't. So obviously the atmosphere knows that something else is 
going on. 

Lesh — The fact that some of the stars oscillate while the others do not 
does not mean that the atmosphere of the stars knows how old they are; 
the interior does. It is very likely that the oscillation arises in the interior 
and not in the atmosphere. 

Steinitz — It is an age effect. 

Lesh — Yes, it is an age effect in the interior and not an age effect in the 
atmosphere. 

Aller — I don't know to what extent we want to discuss the spectra' of 
oscillating stars. That is a fascinating field in itself, but perhaps we'd 
better settle this question first. 

Hack — The hne contours are rather different in the spectra of normal B 
type stars and in the spectra of j3 Conis Majoris, which sometimes show 
one, two, or three components variable with time and having different 
radial velocities. So 1 don't agree that they are equal to the normal main 
sequence stars. 

Aller — Well, certainly with high dispersion, the spectrum of a Scorpii, 
for example, doesn't look just like that of a normal B star. There are 
important differences. Please tell us what dispension you are using. We are 
talking about utterly different problems here in the sense that the K line 
effects mentioned by Mrs. Boesgaard can be detected only by going to 
very high dispersions, of the order of 3A/mm. They are very small effects, 
whilst the effects that you see in some of these oscillatiiig stars like a 
Scorpi, which belongs to the ^ Cephei class, are fairly obvious at relatively 
low dispersion. The changes are probably photospheric effects rather than 
chromospheric effects or strictly upper atmospheric effects of some kind. 

Conti — I'd like to return again to these and Of stars, and point out 
that what we think is the mechanism for the emission forming region and 
the extended envelope has something to do with the radiation pressure. I 
think Cassenelli has already, mentioned this. Another thing which has been 



299 

mentioned a little in the literature, but vMch is now receiving more 
attention, is the variation in the emission lines that you see in these stars. 
For example let's say you observe that emission lines vary on time scales 
somewhere between time scales of several minutes to several hours, I 
mean they're really drastically varying. So in addition to the extended 
envelope which we certainly do have, we have very good evidence of 
changes going on in this envelope which are very reminiscent of other 
kinds of stars. In fact, if I may return to my Zeta Puppians looking at the 
atmosphere of their star in the light of X4686, they might not be too 
surprised to see something looking a little like a solar spectroheliogram in 
Ha. 

Aller — It would probably look even more striking than that. 

Lesh — If I may just answer the comments of Dr. Hack. I'm talking about 
mean properties of these stars which are, in fact, observed at rather low 
dispersion, on the order of 60 to 100 A/mm. It is true that the line 
profiles in the P Cephei stars vary, but the mean profile — unless I'm very 
much mistaken — is not distinct from the mean profile in a non-variable 
star. Likewise the colors of the Cephei stars vary. But if you take the 
mean color, which is actually what you use to locate stars in the H-R 
diagram, it is not statistically different among the variable stars than 
among the non-variable stars. 

Aller — That's an interesting point. I don't think it's a statement that can 
be made for Cepheids. Maybe Mrs. Gaposhkin could answer that. Does 
the mean spectrum of a Cepheid look Uke any other star, or can you tell 
it immediately from the appearance of the spectrum. 

C. Payne-Gaposhkin — You certainly can tell. 

Heap - What happens to the Call emission of say, a G star and a B star 
when they enter the red-giant branch? What are the time-scales involved 
in the development of their chromospheres? If the magnetic field and 
calcium emission of G stars decrease with time, why do red-giants of one 
solar mass have strong chromospheres? 

Kandel — Nobody knows, but, in principle, the calcium emission should 
be detectable. 

Kippenhahn — The effect of rotation on the Ca lines, via magnetic fields, 
during the evolution, will become less and less important while convection 
will become more effective when the star becomes a red giant. 

Thomas — We're presumably worrying about chromospheres, and I read 
this very ambitious statement: "what properties of stellar chromospheres 
vary with stellar mass and age". So long as one talks about chromospheres 



300 

associated only with the convection zone, then you're hmiting your sights 
very much. I agree, from the standpoint of rotation, that in the example 
which you have given, you've tried very hard to tie in with something 
else, which one knows can produce a mechanical flux. Still, from my own 
standpoint, as one who beUeves that all stars have chromospheres, so long 
as you restrict yourself to only those two viewpoints, then you're still 
restricting your sights very much. I prefer Len Kuhi's comment of just a 
Uttle while ago, that maybe the theoreticians should be more ambitious 
than they are. He's trying very hard to understand what is meant by a 
chromosphere from the standpoint of understanding. Is it indeed some- 
thing which is a property of all the stars? So I think one of the things we 
have overlooked badly in this conference is to ask all those kinds of 
physical processes which can produce, in any way, any kind of mechan- 
ical flux of energy. That's why I personally like to associate the 
definition of a chromosphere with a mechanical flux of energy. But let's 
not argue. Let's take whatever definition we want, but realize that we are 
talking about ^e«era/ structures of stellar atmospheres. 

Cayrel — I have a question related to Dr. Kippenhahn's talk. Dr. 
Kippenhahn pointed out that rotation, age, and magnetic fields are three 
related things. I remember that at the time it was said that micro- 
turbulence could be also correlated with these three things. The problem 
is that I don't really see the mechanism by which microturbulence could 
be related to these things. Would you comment? 

Kippenhahn — I am not prepared to say anything at the moment to your 
question, but since I am already standing I would like to make a 
comment. I agree with what Dr. Thomas said. I think we should ask what 
are the observational facts, or how can we find out whether, the 
chromospheres are related to convection or not. Before the meeting, when 
I still was very naive, I thought that the calcium emission we see in G 
stars indicated chromospheres. Now, I learn that if we do not see Ca 
emission, this does not tell us anything. We have to determine whether 
the Unes are collision dominated or photoelectrically dominated, and — as 
far as I have understood the complicated story — we then still do not 
know whether there is a chromosphere or not. On the other hand, we 
learned from Dr. Praderie that the border line in the HRD between stars 
with Ca emission and those without is a straight line which coincides 
roughly with the Cepheid strip and its extention to the lower left. It 
happens that this line is close and parallel to the Une which separates the 
stars with pronounced outer convective zones from those without. Is this 
accidental? Can we learn from the experts of Une formation whether, 
from this fact, we can conclude that chromospheric activity is driven by 
convection? Or must we say Praderie 's border line of Ca emission is just a 



301 

border line for the significance of the Ca emission as an indicator for 
chromospheric activity? 

Thomas — My comment was not that calcium erhission may not be a 
strong indicator of chromospheres, where it occurs, but that there are also 
many other kinds of indicators of chromospheres in regions where we 
don't find convection zones. I don't disagree with what you say. 1 say 
only: please expand it. 

Bohm-Vitense — I would like to ask a question. Is the magnetic field 
proportional to the velocity Omega independently of the efficiency of 
convection? The convection is important isn't it? 

Dumey — Yes. We used Leighton's model for the solar cycle. This model 
has some arbitrary parameters which are chosen so as to reproduce the 
Sun's magnetic cycle. For stars with different convection zones these 
parameters would be different. There is every reason to believe that again 
B anand fi would be proportional. 

Bohm-Vitense — This means that the proportionality constant depends on 
the spectral type, doesn't it? 

Durney — Yes. The proportionality factor between B and Q, may depend 
on spectral type. 

Ulrich - I'd like to make a connection between today's and yesterday's 
discussions. I think the connection of the magnetic field to these motions 
is really a most intriguing aspect of the heating problem. I think in order 
to properly understand the heating problem, we must put in the magnetic 
fields. This is a real challenge to the people trying to solve the heating 
problem. You must be able to reproduce the hot plages over a mag- 
netically active area. Another comment iriefers to the fossil magnetic fields. 
In some solar models which I've calculated, the decay time for the 
fundamental mode is 25 billion years, so the field is quite constant. 
However, this doesn't rule out the higher modes which have decay times 
of some three to five billion years, so these could give time variations in 
times comparable to main sequence Ufetimes; however, you would have a 
constant term in addition. You'd have to add a variable to the constant, 
so it might not give you the correct behavior. 

Kippenhahn — If the star is rotating rapidly, we must really include the 
effect of turbulence and use the total pressure. liF it is only slowly rotating 
you can use hydrostatic equilibrium as a good approximation. 

Bdhm — May I just add one minor point to Kippenhahn's talk. When we 
talk about the Lighthill output of the convection zone we must re- 
member that this depends strongly on the helium abundance. For 



302 

example, the numbers mentioned for white dwarfs sounded a little 
surprising. These white dwarfs are surely helium white dwarfs. The point 
is that the helium convection zone persists to very high temperatures and, 
if you have a very dense star, a large fraction of the energy must be 
carried by convection. For these high temperature objects with highly 
developed convection zones, you get high convective velocities, which 
means, in turn, a high acoustic output. 

Aller - Would you say that some of the non-white dwarf helium stars 
might have such strong convection zones that they would be good places 
to look for chromospheric activity? 

Bohm — It certaihly is true that we expect higher acoustic outputs from 
helium stars than from stars of normal composition. 

Bohm-Vitense — I think that for a gravity of g = 10*[Cgs] the convection 
extends to about 13000 degrees for heUum stars rather than to about 
8000 degrees as for hydrogen stars. 

Evans - The decline of the RGB star, RY Sgr, in 1967 and its return to 
maximum in 1968-70 was studied spectroscopically by a group at the 
Radcliffe Observatory, Pretoria. A strong emission line spectrum (origi- 
nally studied by Cecilia Payne — Gaposchkin in R Cr B and attributed by 
her to a chromosphere), comprising mainly lines of singly ionized metals 
having upper excitation potential less than 6 eV, was present early on the 
decline. This decayed on a time scale of ~22 days, compared to a time 
scale of ~5 days for the initial rate of decline in photospheric radiation. 
The level of excitation and the effects of self-absorption declined with 
time. A strong continuum short of X4000 was attributed to CN". At 
minimum Hght only emission Unes of very low upper EP., mainly of Ti 
II, were present. The' lines H and K of Ca II appeared broader than the 
rest. Broad emission with a central absorption appeared in H and K of Ca 
II at times during the rise and near maximum Ught. These observations 
indicate strong chromospheric activity in a heUum star. 

Aller - That's somewhat cruder than the solar-model theory, but the level 
of excitation you describe is comparable with that observed in the Sun. 
So in giants and even supergiants you see that we can have densities and 
so-called excitation temperatures not significantly different from what we 
have in the Sun. This brings out a point Thomas mentioned earUer about 
using spectra for diagnostic purposes. 

Kippenhahn — I must repeat my question: Can I conclude that when 
there is no calcium emission there is no chromosphere either? Or would 
the stellar atmospheres people say that at some point in the HR-diagram 
the calcium emission goes away even though the star still has a chromo- 
sphere? 



303 

Pecker — Isn't it just a matter of the pressure sensitivity of the calcium 
emission? 

Thomas — In a Wolf-Rayet star, I certainly don't observe calcium 
emission. However, that doesn't mean the Wolf-Rayet star can't have a 
chromosphere. 

Kippenhahn — I am not deaUng with special objects like Wolf-Rayet stars. 
I am interested here in normal main sequence stars earlier than F. What is 
the significance of no calcium emission in these objects? 

Linsky — One can do a very simple experiment to answer this question. 
Take a simple model to represent the quiet Sun. This model will show a 
slight emission core for calcium. If you decrease the opacity by a factor 
of two or three, the emission is gone. Youll never see it. The emission is 
very sensitive to the optical depth in the line. As you go up the main 
sequence, the chromospheric temperatures are most likely hotter, because 
the temperature minima will be hotter, and the calcium will be more 
nearly completely ionized, thus decreasing the chromospheric optical 
thickness in the calcium Une. Youll very soon reach a point on the main 
sequence where the emission will not be seen at all, even though you may 
have a very pronounced chromosphere. 

0. Wilson — I'll say something about this in my talk, but it is noteworthy 
that the cutoff for calcium emission is amazingly sharp. The corre- 
sponding variation in mass, radius and effective temperature across this 
boundary is negligible. I don't know what causes this cutoff, but I think 
it must be something very fundamental. This whole transition takes place 
in a range of b-y of a couple of hundredths. It's just like you'd cut it 
with a knife. 

Jefferies — I think the answer to Kippenhahn's question is that we 
have really not explored the matter enough yet. Along the lines of 
Linsky's comments, let me draw a line on the board and say that the gas 
below it represents the photosphere where the continuum is formed, and 
then say that the chromosphere is up here above the Une with the 
temperature increasing outwards. Now I have a certain optical thickness in 
the K line as I look down through this chromosphere. If I have a 
temperature increase and the optical thickness is greater than about three, 
then I should see some K line reversal. The^ size of the reversal depends 
on the size of the temperature increase outwards, and the value of the 
optical thickness. If for some reason, the base of the chromosphere moves 
in the Sun's atmosphere, we ultimately reach a situation where we have 
no optical tliickness left — we have run out of chromosphere, and no 
reversal will be seen. This is a possible situation as we go from the Sun to 
earlier stars on the H-R diagram. It is important to search for other 



304 

sensitive diagnostic tools for chromospheres there. One such indicator 
would be the very strong resonance doublet of Mg II, which shows such 
strong emission probably just because of the greater abundance of 
magnesium. You get some idea of their greater strength just by comparing 
them in solar spectra with the weak solar K line. The emission cores of 
the Mg II lines are enormous by comparison. So thatjs one additional 
chromospheric indicator, which has a certairi disadvantage in that it must 
be observed from above the earth's atmosphere. We should also search for 
other indicators, and among those, I have suggested that emission lines 
might be very valuable . In order to determine whether an emission Une is 
intrinsic, and so a good indicator of a chromosphere, we have first to 
solve the problem of what an emission line means. In particular, is it 
intrinsic or geometric in origin? Does this offer a partial answer to your 
question? 

Kippenhahn — 1 think so. Would you suggest, then, that when we move 
up the main sequence, we better get observations of the Mg II lines from 
a balloon in order to check for chromospheres. 

Underbill — Don't forget satellite observations here. 

Jefferies — Yes, and if the magnesium doesn't show us an effect similar to 
the calcium, then I think that we've run out of chromospheres. 

Underhill — You have run out of magnesium emission after the middle 
B's. 

Thomas — Of course it's all a question of how we define chromospheres 
too. 

Heap — Hasn't Kippenhahn 's question already been answered by some of 
the observations discussed here earlier? For example, Kondo's observa- 
tions of Mg II emission, suggests that chromospheres may be found in 
stars having spectral types much earlier than F4. 

Kendo — I just want to mention that our balloon program was initiated 
in the philosophy, similar to that articulated by John Jefferies, of 
searching for evidence of chroino spheres and of enhancing our under- 
standing of chromospheres through investigation of the magnesium res- 
onance doublet. I also want to add that, in future flights, we hope to 
address ourselves to the point raised by Anne Underhill regarding where 
in spectral type the magnesium emission is unobservable. 



305 
SUMMARY 

0. C. WUson 

Hale Observatories 

Carnegie Institution of Washington, California Institute of Technology 

I was asked to summarize this Conference. However I think that I can be 
more effective if I stay with those matters where I have some personal 
experience. Accordingly, I propose to restrict my talk to what I shall call 
solar -type chromospheres. I hope to review some of the things that are 
known, to point out what seem to me to be unsolved, or incompletely 
solved, problems, to comment on some issues raised during the meetings, 
and to bring you up-to-date on some of the current investigations. In this 
way, I hope to make some points of interest to the observers as well as to 
the theoreticians. 

By solar-type chromospheres I mean two things: First that the H-K 
reversals satisfy the well-known width-luminosity relation; second that the 
morphology of the reversals is essentially of the common double peaked 
form which is familiar from the Sun. The cross-hatched region in the 
schematic H-R diagram shows where such chromospheres are found; on 
the main sequence from F5 down, and in the giants from GO to later 
types. 

It is important to realize that a chromosphere is a completely negligible 
part of a star. Neither its mass nor its own radiation makes a significant 
contribution to those quantities for the star as a whole. Moreover, I know 
of no essential role that a chromosphere fills in the life of a star. For 
example, there are places on the main sequence where stars can be found 
which must have identical masses and energy productions, but whose 
chromospheres are very powerful in some, and absent, or almost com- 
pletely so, in others. The stars in question function equally well with or 
without chromospheres. Hence an outsider might be pardoned for asking 
why this many people have spent four days here studying something 
which seems as nonessential and insignificant as chromospheres. 

ActuaUy, of course, the motivations for people to engage in this particular 
type of research are as varied as their own interests and specialties. In my 
own case, I have been attracted to chromospheres in the first place by 
pure curiosity and secondly by the fact that they turn out to be packed 
with information. By proper study of stellar chromospheres and, indeed, 
thus far involving only the H-K reversals, it is possible to derive very 
valuable knowledge about the absolute luminosities of late-type stars, 
about the ages of stars on the main sequence, and, more recently, about 
the occurrence of stellar analogs of the solar cycle. I have hoped that the 



306 



theoreticians would be sufficiently intrigued by all this to provide 
believable explanations for the physical processes which underUe this 
wealth of information. 

I shall return to some of the foregoing matters later. -But first let us look 
at the schematic H-R diagram in Figure IV- 1 1 and consider the bound- 
aries contained therein. These are two in number: first, the one on the 



Mv 




BV 



Figure IV-11 Schematic HR Diagram. Cross hatching shows regions of 
occurrence of solai-type chromospheres. 

main sequence at spectral type approximately F5, and the other, which 
probably is essentially a vertical line through the giant and supergiant 
region, corresponding closely to spectral type GO. In the present context 
-these boundaries separate those regions in which H-K emission can be 
seen readily at a dispersion of 10 A mm"' from those in which H-K 
emission is invisible at this scale. Boundaries of this sort are Ukely to 
mark a place where some important physical change takes place and are 
therefore worthy of intensive study. 

The main sequence boundary has been investigated much more 
thoroughly than the one in the giant region ; The result is that the point 
on the main sequence where strong chromospheric emission terminates 
coincides, with great precision, with the point where the larger rotational 
velocities cease, as one proceeds down the main sequence from earlier 
spectral types. In fact, the mass range within which these two transitions 
occur can be only a very few percent at most. Since the deep hydrogen 



307 

convection may also set in at approximately this same point, according to 
theoretical studies, it seems to me likely that both transitions, from 
weak to strong chromospheric activity, and from large to smaU rotational 
velocities, are due to the onset of deep convection. The one remaining 
necessary link in this argument, that braking of rotational Velocity is due 
to ejection of charged particles by chromospheric activity, and interaction 
of these particles with the magnetic field lines of the rotating star, has 
been suppUed by Schatzman some years £^o. Of course, even though this 
picture of what occurs at the transition zone on the main sequence 
appears to be both reasonable and consistent, it may not be correct, and 
one must be prepared to consider other interpretations. 

The other boundary, in the giant region, requires further study. I have 
taken a few spectrograms of luminous stars of typeis F7-F9 and 1 have the 
distinct impression that, for these stars, the H and K lines become 
suddenly very much deeper than at GO, and the only emission, if present 
at all, appears merely as slight shoulders well down in the Unes. This 
boundary should be investigated more completely than it has been to find 
the real nature of the chromospheric transition. 

I should like now to comment on some recent developments, mostly 
unpublished as yet. The width-luminosity relationship was derived origi- 
nally by making use of the MK standards of appropriate spectral types 
and the line widths were determined in the simplest fashion by setting the 
cross hair of an ordinary measuring engine first on one edge and then on 
the other edge of the emission lines. The result is a linear correlation 
between log H^o (^•^o. is the width in km s"' after correction for 
instrumental width by subtraction of a constant) and the absolute visual 
magnitude, M^; and this extends from stars of absolute magnitude -5 or 
more down to the faintest stars on the M.S. for which the dispersion of 
10 A nun"' is adequate, i.e., to +6 or +7. A recalibration using the Sun 
(high dispersion solar spectrograms in integrated light) and the yellow 
giants of the Hyades agreed very closely with the original one based on 
the MK standards. There is an admitted weakness in this calibration for 
"the more luminous stars, since only f Aurigae and some of the bright 
M-type supergiants in h and x Persei could be used as checks, although 
they too showed good agreement. 

There have been various criticisms of this method of deriving absolute 
magnitudes, the most serious ones raising the question of a dependence 
upon the abimdance ratio [Fe/H] . I have recently been trying to shed 
some light on this matter, in collaboration with two colleagues at the 
Copenhagen Observatory, by observing certain physical pairs of stars. In 
these pairs, the primary is a G-K type giant and the secondary is a main 



308 

sequence star of type A-F. Spectrograms of the primary yield its absolute 
magnitude on the basis of the Sun-Hyades calibration. The Copenhagen 
observers use the uvby system of Stromgren to derive the absolute 
magnitude of the secondary and the apparent magnitudes of both stars. 
Their photometry also yields values of [Fe/H] for both stars and the 
average difference in this quantity between the members of 18 of the 
pairs is only 0.09, which is very good agreement. Reduction of incom- 
plete data for these 18 pairs shows that the Sun-Hyades calibration agrees 
with the Stromgren absolute magnitudes to an average difference of only 
G.l mag. The range of [Fe/H] encompassed is about 0.7, and over this 
range there is no definite evidence of dependence upon [Fe/H], but final 
completion of the project must be awaited before drawing more definite 
conclusions. 

I refer now, briefly, to the question of ages of stars on the main 
sequence. All the evidence, and there is by now an impressive amount, 
indicates that the degree of chromospheric activity, as measured by the 
strength of the Ca II emission in a main sequence star, is indeed a 
decreasing function of its age. Thus, at the present time, it is quite 
possible to observe, say, aU the K^ stars in the solar neighborhood in the 
proper'way, and put them in the right order of age. This is, in itself, a 
valuable tool. But even more important is the work being done by 
Skumanich to calibrate the rate of chromospheric decay in absolute 
terms. I think it is possible now to look forward to the time when the 
actual ages of all main sequence stars from F5 down, within reach of the 
appropriate equipment, can be specified in years. The value of such data 
in, for example, the study of galactic stellar orbits as a function of age is 
obvious. 

Calcium spectroheliograms have made it evident for a long time that the 
radiation in the chromospheric Ca II lines in the sunspot zones waxes and 
wanes in synchronism with the other indices of the solar cycle. If the 
stars behave in similar fashion, then, by monitoring the emission in these 
lines against the adjacent continuum, one should in principle be able to 
find and study stellar analogs of the solar cycle, and to determine the 
shapes, amplitudes, and periods of any cycles which occur. Since all 
theories of the solar cycle have, of necessity, been restricted to repro- 
ducing the features of the solar cycle itself, it may well be that they lack 
sufficient generality, and an extension to other stars should greatly 
improve this situation. To make this kind of observation it is essential to 
be able to isolate accurately narrow bands at the centers of the stellar 
H-K lines and to nfieasure the flux in these bands with respect to the 
nearby continuum with precision. 



309 

The coude scanner at the 100-inch telescope is an ideal instrument for 
this type of work, and, since 1966, 1 have been measuring the H-K fluxes 
in a number of main sequence stars from spectral type F5 to M^,. It is 
not feasible here to go into either the instrumental details or the results 
thus far obtained. Very briefly, it turns out that the earlier type main 
sequence stars, F5 to G5, have not so far shown variations that appear to 
be cyclical. Either they do not have them or their periods are too long 
compared to the time of observation. However, beginning at about type 
G8 there are perhaps a dozen stars whose variations could very well be 
cyclical in nature, though none have yet been followed through a 
complete period. Noteworthy also is the fact that not all stars of the 
same types show the same kind of behavior. A few more years of 
observation should settle some of these questions definitely. 

One item which has not been mentioned in this Conference, but which I 
think may well be of importance and which deserves further study, is the 
occurrence of He in emission in a number of stellar spectra. I first noticed 
this Une in the spectrum of Arcturus in 1938, on a high dispersion plate. 
In this example, the He Une has about the same width as the H-K 
emissions, but unlike them it has a smooth rounded top with no evidence 
for a central dip. It has seemed to me that these facts must contain 
important clues to chromospheric conditions, especially, perhaps, the 
approximate equivalence of line width for a ratio of atomic weights of 
40:1. 

Another topic which has been mentioned several times at this meeting is 
the well-known enhancement of chromospheric activity in the members of 
close binaries, a point which has been noted in the literature by several 
individuals. Here again is a field in which more systematic observation 
might succeed in shedding light on chromospheric mechanisms. I wish 
merely to call attention to what I consider a rather spectacular case which 
I came upon while looking for Li Unes in binaries, and which I believe 
might repay further study. This is the bright member of the visual pair 
ADS 2644, and I published a brief note about it in P.A.S.P. 1964. This 
star is a spectroscopic binary, of spectral type G9 V. The H-K emissions 
are very strong and much wider, about 1 A, than is normal for a star of 
this type and luminosity. But at Ha the situation is eyen more abnormal; 
here the usual Ha absorption line is completely masked by a strong, 
broad emission band of width 5 to 10 A. Evidently the presence of the 
companion has induced very large velocities in the chromosphere of this 
star, and the velocity spread in the region of Ha formation appears to be 
several times larger than that where the Ca 11 lines are formed. It is not 
impossible that further study of this and similar systems might yield 
information useful in the understanding of normal, undisturbed chromo- 
spheres. In any case, the relationship of hydrogen and calcium line widths 



310 

in this star is strikingly different than their relative widths in the 
presumably undisturbed chromosphere of Arcturus. 

There has been mention of surface magnetic fields during this meeting, 
and of their role in chromospheric excitation. I think there is general 
agreement on the part of theoreticians that such fields are necessary in 
the transfer of mechanical energy from the hydrogen convection zone and 
in its deposition in the chromosphere and corona. However, there seems 
to be some disagreement as to the source of the fields. If we appeal to 
the observations, we have seen that on the M.S., below the boundary at 
spectral type F5, a star begins its main sequence Ufe with strong 
chromospheric activity, but this activity gradually diminishes and may, in 
time, cease altogether. This can hardly be due to any change in the 
hydrogen convection zone whose existence depends only on the general 
parameters of the star, the great abundance of hydrogen, and the latter's 
high ionization potential. I cannot see what remains to explain the 
decrease in chromospheric activity except to suppose that the surface 
magnetic fields decrease with time, presumably because the magnetic 
energy is used up by transformation to energy of other kinds. This could 
happen if the magnetic energy in question is a residual left over from the 
star's extreme youth and not replenishable. But if it is produced by a 
dynamo within the star, then the dynamo must run down and effectively 
cease to operate. It is up to the theoreticians to decide which, if either, 
of these two views is the more acceptable. 

There is, however, one more clue to be obtained from the observations. 
We see that when stars which have been sitting on the M.S. for a time 
long enough to reduce their chromospheric activities to very low values 
begin to evolve up the lower boundary of the giant region in the H-R 
plane, they need to go only a httle way before their chromospheres 
reappear. Is this because some internal magnetic field has been allowed 
now to reach the surface, or has the internal dynamo been reactivated? I 
do not pretend to know the answer, but I feel that there are some 
fundamental and fascinating questions awaiting investigation. 

The study of stellar chromospheres, either for themselves or to abstract 
the information they contain, is essentially a question of high, or at least 
medium, dispersion spectroscopy. I wish to call the attention of the 
observers to some recent instrumental developments which I beUeve 
portend gains in this field fully equivalent to those which resulted from 
the introduction of photography into astronomy a century ago. These 
developments, insofar as I am aware of them, are two in number. The 
first involves a silicon diode device which has not yet been appUed to 
spectroscopy, but which appears very promising. The other has already 
produced very spectacular spectroscopic results. I refer you to a recent 



311 

paper in the Astrophysical Journal (J. L. Lowrance et al, 171, 233, 
1972). These authors succeeded in obtaining, in six hours, a spectrogram 
of dispersion of 9 A mm"' of a QSO of magnitude 16.5. 

The imphcations of this work for stellar spectroscopy are very impressive, 
especially since it is reasonable to anticipate improvements in the 
apparatus in the course of time . Let us consider only the appUcation of 
the widthJuminosity relationship to the determination of absolute mag- 
nitude as an example. It thus appears probable that in the relatively near 
future this method will become applicable to the red giants in a number 
of globular clusters, to the similar stars in many open clusters, and to vast 
numbers of non-cluster stars of special interest. Moreover, for stars which 
are now very difficult to handle at 10 A mm"' , higher dispersion and 
increased accuracy should become easy. I cannot help feeling that coude 
stellar spectroscopy, including of course the study of chromospheres, is 
on the verge of a new era of accomplishment and vastly increased 
capability . 

Finally I wish to address myself to the theoreticians. They have done 
much work, involving what might be called the standard theory, in 
attempting to explain the chromospheric emission lines. Their tools are 
non-L.T.E. theory, the equation of transfer, and source functions. I must 
confess that I have some misgivings about the appUcability of their results 
to the real world. As an example, and I have seen others at various 
meetings, I refer to Dr. Avrett's worthy efforts to account for the 
width -luminosity relationship. By scaling up the quantities applicable to 
the Sun, he derives emission Unes for a giant star, and they are indeed 
wider than the solar lines. But, unfortunately, they are quite different in 
shape from the lines one sees in nature. They have rather extensive wings, 
whereas the real lines have very well-defined edges which msut be very 
steep. Indeed, as a rough first approximation, the real lines must have 
edges which are nearly vertical; if this were not so the simple measure- 
ments which are employed in applying the width-luminosity relationship 
would not work, as they do, whether the lines are weak or strong. 
Incidentally, Avrett wishes to attribute the width-luminosity relationship 
to the effect of surface gravity, g and this carries the implication that p 
must be constant across horizontal lines in the H-R diagram, which is not 
the case. 

I have the feeUng therefore that the theoretical explanation of the 
chromospheric lines is presently incomplete. Perhaps some of the param- 
eters involved can be modified so as to arrive at good agreement and 
still remain within the believable range. But I suspect that an essential 
ingredient may have been left out and that this ingredient may be the 
velocity distribution of the radiating elements. The problem may be one 



312 

of hydrodynamics as well as of transfer theory. In any case further work 
is urgently required. First, high dispersion stellar spectrograms should be 
processed with care in order to define accurately and quantitatively what 
the properties of the chromospheric lines really are. Then the theo- 
reticians will have to reproduce these lines as best they can, even if it 
requires the introduction of additional parameters. 

I have tried to give here a brief but fairly complete view of the current 
status of the study of stellar chromospheres. We have learned a few 
things, but I think the subject is still in its very early stages and is 
deserving of much more effort on the part of observers and of theo- 
reticians. To me, one of its most attractive features is the curiously large 
number of contacts with other astronomical fields to which it is able to 
make contributions. 

CONCLUDING REMARKS FOLLOWING THE SUMMARY 

Thomas — Dr. Wilson was asked to summarize the conference, as it is 
customary to have someone with wide experience and breadth of 
knowledge in the field close such a symposium as this on a note of 
perspective. It is not necessary that he be an expert on all the matters 
covered; one hopes only to hear some sort of encompassing "impressions" 
of what we, the participants, have been exposed to, and how well it 
"registered" to one having a broad background. I, personally, regret that 
Dr. Wilson chose not to do this, because I think that we would all have 
benefited greatly to hear his impressions. But I think that someone should 
try to do it, both for the sake of those who have tried to present a digest 
of ideas and for those of us who have just listened and commented. 
Otherwise, one may be left with what I consider the mistaken impression 
that there is only one type of chromosphere really worth much attention, 
the solar type, and only one set of indicators of the universality of the 
chromosphere phenomenon, those relating to the H and K lines. So, let 
me attempt a rather general summary. 

First, I can say in an overall way that I disagree strongly with Dr. \Wlson 
on his assessment of the general importance of chromospheres. If I follow 
the logic of Dr. Praderie, in her presentation, that the properties of a 
stellar atmosphere may be discussed in terms of two kinds of fluxes — 
electromagnetic radiation and mass — then conceptually the chromosphere 
is that part of the atmosphere directly dependent upon a non-zero mass 
flux generating a mechanical energy flux. 

Also, in a wholly observational way, the chromosphere determines the 
properties of the cores of most strong lines in the solar (and most of the 
stellar) Fraunhofer spectrum: not what I would call an irrelevant thing. 



313 

Indeed, I well remember a discussion in the 1950's as to whether the 
solar chromosphere had any observational consequences on the 
Fraunhofer spectrum. And it was a major milestone in solar research 
when it was shown, unambiguously, from eclipse studies, just how many 
solar lines observed on the disk were influenced by the properties of the 
chromosphere. As an indicator of the existence of a mass-flux, and as a 
determiner of the properties of the cores of both strong and intermediate 
Unes — I hardly consider the chromosphere as a "negligible" part of the 
structure of a star. If I venture to comment on the direction from which 
K. Gebbie, Pecker, Praderie, and I have been working — which has 
evolved into viewing the atmosphere as a transition region between stellar 
interior and interstellar medium — the chromosphere is again a most 
important region in this transition, from the direction Dr. Praderie 
emphasized. So, having tried to restore the role of the chromosphere into 
focus, let me try to survey what the invited speakers summarized for us. 

Beginning at Day 1, which, in essence, was theory, Jefferies made two 
major points: 

• How can one find the temperature structure of the chromosphere? 
He noted that there are two kinds of lines: ones which have 
collision-dominated source-sink terms, Uke the Ca"^ and Mg"*" H and 
K lines, and ones which have photoionization dominated source-sink 
terms like the Balmer series of hydrogen. In the case of the former, 
you can tell something of the T^ structure; this is true particularly 
in the case of an atmosphere with a temperature reversal. Such a 
reversal may produce a central emission core, and the central 
emission core may be, in turn, reversed wholly by radiative transfer 
effects. This is in contrast with the old L.T.E. interpretation which 
required a second temperature reversal to produce the self-absorbed 
core. In the literature, there are a lot of predictions of these kinds 
of effects, ranging from lines with no self-reversal to lines with 
self -reversals. You can make the self -reversals as strong as you want 
to, as wide as you want to, and the emission core as steep as you 
want to' by "choosing" arbitrary distributions of T^. For example, 
see Lemaire's thesis on the Mg II H and K lines. Now Wilson is 
interested in square profiles, i.e., profiles with steep sides to the 
emission peaks. Strictly speaking, there is no such thing as a "square 
profile"; it is "square" only to some accuracy. Very steep sides on 
profiles have been computed, however, for particular atmospheric 
configurations, and they are in the Uterature. Furthermore such 
variations in steepness and behavior of the central core are found 
observationally in the Sun. Again, refer to the Lemaire thesis as an 
excellent compendium of observation and theory. 



314 

• Jefferies second point concerned the observed emission lines and 
how their existence may relate to the existence of a chromosphere, 
emphasizing the distinction between intrinsic emission lines and 
geometrical emission lines. If we consider spectral regions where the 
continuum is depressed, we can have either kind of emission line. In 
the visual regions, where the continuum is not depressed, we obtain 
emission cores in absorption lines as a reflection of an intrinsic 
emission line. We can have any combination of these, depending on 
circumstances. The. following approach by Avrett permits a demon- 
stration of these points. 

The summary by Avrett showed what one could and could not do with 
various models, i.e., various assumed distributions of Tg. It was numerical 
experimentation. Its approach is one that Wilson could call upon to ask, 
"Can I, under any circumstances, get theoretically such-and-such a 
profile ," and "How many kinds of circumstances can produce it?" 

Now, as a comment on the bearing of these H and K profiles on our ideas 
about chromospheres, and as a bridge to Dr. Praderie's summary, let me 
quickly summarize the evolution of the past 25 years in our outlook. 

In phase 1, the only star which had a chromosphere was the Sun. And 
the textbooks of that time (1950's) said that the chromosphere had 
absolutely no influence on the observed disk spectrum of the Sun. There 
were observations of line profiles which apparently showed (under LTE 
diagnostics) that the Umb temperature was as low as 2700° K, in 
conformity with the LTE line blanketing calculations. That was the end 
of phase 1 , essentially wiped out by the body of non-LTE theory applied 
to interpreting solar eclipse observations, which among other things 
showed such temperatures to be erroneous. 

In phase 2, which Wilson's talk summarized masterfully, there were 
admitted other stars, besides the Sun, with chromospheres, and it was 
thought that these were essentially measured by H and K self-reversed 
emission cores. Recognition of these other chromospheres was an 
enormous step forward. Such stars occupy some part of the HR diagram, 
and about this part we have considerable "suggestive" information coming 
from those empirical relations which Wilson discussed. These tell us that 
there is some profound relation between the energy production by the 
star and that fraction of it which goes toward providing a chromosphere. 

In phase 3, we advance to the rest of the HR diagram, so long as one 
makes synonymous the concept of a stellar chromosphere and the 
existence of Ca'''H and K line. No stars here were supposed to have 
chromospheres; cf. the 1955 lAU Symposium and comments by Biermann 
and Schwarzschild. 



315 

In phase 4 we admit a chromosphere may exist in stars which do not 
have H and K as the major chromospheric indicators; and we begin an 
open-minded search for what these other indicators are. So, we broaden 
our sights, and we are here at this conference. 

On Day 2, Dr. Praderie emphasized two conceptual points. First, a 
necessary condition for a chromosphere is a mass flux, taken in the broad 
sense of mass motion somewhere in the star. Second, a sufficient 
condition for a chromosphere is mechanical dissipation. She then de- 
scribed the direct observational evidences for chromospheres, only one 
kind of which is provided by the H and K lines. These H and K lines 
stand out in the minds of all of us because the Unes are so well observed 
and because there is some kind of theory to interpret them. As you go to 
more complex atoms, there are comphcations, i.e., multilevel atoms, etc. 
One cannot predict theoretically all the features Dr. Praderie talked 
about, but she divided them into two aspects: excitation phenomena and 
ionization phenomena. For example , just the existence of helium Unes on 
the solar disk and in the solar chromosphere tells us right away that there 
is some kind of anomaly. These are all direct observations. Praderie then 
went on to the indirect evidences for chromospheres — the existence of 
velocity fields of one form or another. This aspect might have been 
discussed by John Jefferies in his review of diagnostic techniques, but one 
must have a great deal of sympathy for why he did not cover these 
things, since our explanations and our analysis of the existence of velocity 
fields are extremely rudimentary so far. We take the direct diagnostics as 
giving some evidence for a temperature rise, and the indirect diagnostics 
as giving some evidence for the possibility of mechanical dissipation, 
which may then produce a temperature rise. While Wilson stated that 
there is general agreement among theoreticians on the necessity for 
magnetic fields for the transfer of this mechanical energy, I think this is a 
misleading statement. All the original work on chromospheric heating by 
mechanical dissipation ignored magnetic fields. One currently invokes 
magnetic fields to understand differential heating over the solar surface. I 
believe the question of the relation between mass flux and mechanical 
dissipation and magnetic fields is most important but badly understood at 
present. While simple correlations between the presence of magnetic fields 
and Ca* emission are excellent guides, a theoretician cannot afford to 
depend wholly on them. Agreed, one needs empirical relations to start 
and to be stimulated, but one needs to go far beyond that. Also, this 
coupling between the velocity fields and the H and K lines is a very 
strong point right now. The problem of interpreting the half-widths of 
these lines, and the Ha Unes, and aU the other lines Dr. Praderie 
discussed, is a very real one. It all comes down to indirect indications of 
chromospheres: the indications of potential chromospheric heating in the 
presence of velocity fields. 



316 

Doherty's summary put very well those aspects which have been exciting 
to all of us who had to live so long on the observations in the visual 
spectrum; viz, the enhancement in the "space" ultraviolet of all these 
things that one could only guess at from the cores of the H and K lines. 
The balloon observations of the enhanced Mg""" emission cores provide a 
direct extension of the Ca^ material. Then, we have in great profusion P 
Cygni-like lines showing evidence of outflow of mass, which links strongly 
to the theoretical work by Parker and subsequent work on the solar wind. 
When we find evidence for many lines showing P Cygni characteristics, 
plus many emission lines in stars which cannot be interpreted wholly in 
terms of geometrical effects, then we have enormously powerful chromo- 
spheric indicators. 

I think that if the theoreticians are to be criticized, it should be in a 
tough but realistic way. And the tough way is that the theoreticians have 
not provided simple, straightforward models, both of the physical con- 
cepts underlying all this non-LTE diagnostics and of the physical concepts 
underlying mechanical heating and really non-equilibrium thermo- 
dynamics, in such a way that the observer can both see it clearly, and can 
sit down and make simple-minded approximations in order to interpret 
these space observations. Non-LTE theory is not conceptually that 
complex. That is my summary of the first two days. 

In some sense, the third day was the real meat of the conference to those 
of us who are concerned with the definition of a chromosphere in terms 
of mechanical heating. The preponderence of thinking in this symposium 
has been to define a chromosphere in terms of a T^-rise, because we 
know what that predicts. 

This is the real focus of the conference so far as many of us are 
concerned. But, we are staggering. We have some kind of diagnostics 
developed; we have enormous numbers of observations; we have from 
Wilson and his co-workers enormous stimulation so far as one kind of 
chromosphere is concerned, that kind centered on the H and K lines as a 
diagnostic tool, suggesting, in the Wilson -Bappu relationship, that there is 
some correlation between the intrinsic luminosity of the star and that 
part of the mass flux which provides a mechanical energy dissipation to 
heat the chromosphere. How do we explain it? If you go back to the 
early days, when these very first suggestions on mechanical heating were 
made by Biermann, Schatzmann, and Schwarzschild , then we have very 
naive ideas, to which reference has been made today. One goes on from 
there to ask: how do I produce, first, the flux from a given internal 
convective structure; how much flux do I produce; how do I get up into 
the regions of hearing; and where do I heat the atmosphere? There were 
strongly technical discussions on day 3, and certainly, those presenting 



317 

the discussions did not bring us all up to their level. But there were two 
interesting summaries: One was by Jordan who summarized the applica- 
bility of various approximations on when a sound wave becomes not just 
a sound wave but something strong enough to produce heating in the 
atmosphere. That is the sort of investigation we need to explain the 
Wilson-Bappu relationship. Jordan summarized the current thinking on 
that kind of approach. The emphasis lay on the basic physics. The second 
summary by Delache was an attempt to go back from that standpoint and 
to ask, what do I do when I talk about those phenomena which produce 
a chromosphere or a corona? And you start from the very basic thesis by 
Parker that you can't have quiescent stars, so long as you do not have a 
constraining boundary in some sense. He went on from there to develop 
what possible kinds of structures one could have, recognizing that the 
Parker stellar wind means that all the way down into the star some kind 
of a mass flux must exist, no matter how small in the deepest layers. This 
is the kind of approach one needs to begin to make some kind of 
theoretical structure. If I only try to say that all I have is a variety of 
motions of unknown origin in the solar atmosphere, and it is their 
resultant that produces the observations, introduced in an ad hoc way, I 
go to a situation similar to terrestrial meteorology. It is like saying there 
is no point in making a first-approximation model of the terrestrial 
atmosphere because I can not reproduce all the local phenomena that you 
see when looking out the window of an airplane — lightning discharges, 
beautiful clouds with periodic structure, enormous plumes, etc. The 
answer to that viewpoint is that it is siihply defeatist. One has to do the 
best he can to start. What do we do? First we make a spherically 
symmetrical model of the stellar interior, and then a spherically sym- 
metrical model of the stellar atmosphere, not because we believe that is 
the last word; but each time we made a model, we should say, "That 
model is good to some degree of accuracy." We make models to be 
compatible with the observations, good enough to achieve internal 
physical consistency; and then we try to reproduce our observations. All 
Day 3 was trying to tell us was the accuracy to which we know the basic 
physics; namely, how much mechanical flux is put in the atmosphere, 
how much is stored, how much is propagated, how much is dissipated to 
the accuracy that we know initial boundary conditions; all in the hope 
that, with this knowledge, we can use those results on two things — 
mechanical dissipation of energy and velocity fields. 

On Day 4, Kippenhahn gave what I consider to be a fine complimentary 
summary of the work that Wilson has presented here. Kippenhahn gave 
essentially a theory behind this particular kind of chromosphere, based on 
the internal structure of particular stars. He presented for us a very 
beautiful, complex, "flow diagram" of the linkage paths between mass 



318 

loss, angular momentum loss, magnetic field from the turbulent dynamo 
and its relation to differential rotation and the convection zone, and 
stellar evolution. Somehow, he suggested these axe measured by g and 
Tgff — myself, I have a hard time seeing how these two, parameters 
suffice — but this probably just reflects my own ignorance, which is a 
good admission for a summarizer to make. 

That is what we have had in the conference: some diagnostic techniques; 
a summary of observations of different kinds of chromospheres that 
appear to exist; a summary of the theory for some very particular effects, 
namely the aero-dynamics as we know it today; and a supimary of the 
observations of some particular stars, following a summary:;,of the relation 
of the interior structure of certaiii types of stars to chromospheres. 






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