Physica X l I , no 9-10 |)ecember 1946

T H E I N T E R N A L C O N S T I T U T I O N O F G I A N T M S T A R S

by DONALD H. MENZEL

The conventional theories of stellar interiors are generally con- cerned with representing the following observational features: flux or total light intensity, radius, and mass. The only additional factor commonly taken into account is the relative abundance of hydrogen, as introduced by S t r 6 m g r e n. This abundance has a direct influence on the mean molecular weight, which in turn affects the stellar luminosity. Thus, in any a t tempt to fit the theoretical calculations to an actual star, we have a disposable constant.

These theories specify the internal distribution of temperature and density. There is one additional check on the correctness of these theories. According to B e t h e's theories of stellar energy genera- tion, certain critical temperatures must be reached in the deep interior, if the carbon cycle of energy production is to operate. For the sun and most of the stars of the main sequence, it appears that conditions are favorable to operation of the carbon cycle. But for giant stars in general and especially for the red giants, the calculated central temperatures are much too low. Accordingly, other processes of energy generation, such as the Lithium-Hydrogen reaction, have been reviewed. None of them, however, have proved satisfactory.

Theories of stellar constitution have proved to be disappointing in one particular respect. Many stars, including the sun, possess spectro- scopic anomalies entirely inconsistent with their photospheric sur- face temperatures. The intensities of lines of helium and ionized helium in the solar chromosphere require temperatures of the order of 25,000 °. The solar corona requires a temperature of 1,000,000 ° or higher to explain the presence of Fe XIV and other half-stripped atoms. These characteristics would not be recognizable in the spectra of distant stars. The chromosphere and corona are too faint. Never- theless, the F r a u n h o f e r spectrum does exhibit certain anoma-

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PHYSICA XlI Page 768

A photograph of the largest prominence ever recorded. This picture was taken at the High Altitude Observatory of Harvard University and University of Colo- rado at Climax, Colorado. It is one of the frames from the motion-picture Prof. Menzel showed at the Amsterdam Zeeman Conference.

THE INTERNAL CONSTITUTION OF GIANT M STARS ,769

lies, inconsistent with the photospheric temperature, and certainly associated with the chromospheric peculiarities. The B a 1 m e r lines of hydrogen and the infrared line of helium are far too intense to be reconciled with a temperature of 6000 °.

It was hoped that these spectral peculiarities might be attribut- able to local turbulence or to some other shallow excitation effect. The million-degree temperature required for the solar corona, how- ever, indicates that the source is probably very deep seated.

Many, if not most, stars exhibit spectral anomalies of similar character. In certain cases the high- and low-excitation features co- exist in a most puzzling fashion. The repeating nova, RS 0 p h i u- c h i, displays high intensities of Fe X (forbidden), long after out- burst, when the variable simultaneously shows an M-type spectrum, with characteristic Ti 0 bands. There are a number of related objects such as Z Andromedae and A X Persei, which possess both low and high excitation. R Aquarii is a long-period variable, which acts as the nucleus of a planetary nebulae. All of these objects are examples of the phenomenon that M e r r i 11 terms "symbiosis".

Many years ago I suggested that such objects were double stars, consisting of a cool red star and a hot companion. This proposal has been widely accepted, but I no longer subscribe to it. I regard these objects as a single star. There is a very hot, small, condensed nucleus, surrounded by a very extensive atmosphere that derives its support from a combination of radiation pressure, turbulence, and stellar rotation.

If the atmosphere is not sufficiently thick optically to form a photosphere near the external boundary, the star would exhibit the general characteristics of a W o 1 f-R a y e t spectrum. The very blue continuum would be crossed by emission bands, D o p p 1 e r- broadened because of the high velocities of ejection. The analysis by K o p a l and Mrs. S h a p l e y of the ec l ips ingW-s ta rV444 Cygni has shown that the atmospheric envelope is far from being absolutely transparent. If the total material in the envelope had been sufficient to make the photosphere, defined as the layer whose optical depth is unity, lie near the external boundary, much of the very blue radiation of the nucleus would have been transformed-into low-temperature radiation appropriate to a red giant.

I am arguing, primarily from observational considerations, that a giant star is built something like a planetary nebula. A kinetically

Physica XI I 49

770 DONALD H: MENZEL

supported atmosphere surrounds the small, hot core. The gaseous envelope has sufficient opacity to transform most of the high- temperature stellar radiation into low-temperature flux appropriate to the large radius.

The spectra of novae have clearly shown that distended shell of gas can radiate like a photosphere, as long as it is optically opaque. There are definite indications, for certain novae, of directional ejec- tion and even of partial photospheres. The material may be shot out in spurts, jets, and filaments, not dissimilar to those of the solar prominences. Planetary nebulae, which seem to be the remnants of old novae, still exhibit a filamentary structure. It would not be sur- prising to find similar structure in the atmospheres of ordinary stars.

The opacity of a series of interlacing filaments would be apprecia- bly less than that produced by an equal amount of matter spread uniformly through a volume. Pressures and densities in stellar atmos- pheres may be somewhat greater than those calculated on the basis of uniform stratification. These effects may possibly account for the fact that the damping factor for spectral lines of giant stars appears to be no less than that for the dwarfs. At the same time, t he fore- going model provides the turbulence necessary to explain the inter- mediate portions of the curves of growth in the spectra of giants. The required velocities are usually far in excess of those prescribed by the boundary temperature.

Stars like Z Andromedae and R Aquarii appear to be transitional objects between novae and ordinary long-period variables. For such stars the envelope is extraordinarily thin. In the spectrum of Z An- dromedae, as S t r u v e has shown, we see clear evidence for the formation and dissipation of successive shells.

Mrs. G a p o s c h k i n ' has just completed a photometric s tudy of a number of such stars in red and blue light. Basing an analysis on the tentat ive assumptions that two stars are involved, whose color indices remain constant, Mrs. G a p o s c h k i n has determined the independent light curves of the blue and red components. I am deeply indebted to her for placirig the details of the analysis at my disposal. One of the most significant results is the apparent syn- chronous variations of the blue and red components . Such activity would be difficult to reconcile with two separate objects. It is entirely consistent with the view here proposed of a white star surrounded wholly or in part by a red envelope.

THE INTERNAL CONSTITUTION OF GIANT M STARS 771

Kinetic envelopes are closely related to stellar variability. The sudden release of energy in a nova or one of the lesser repeating novae may blast a shell completely away from the star. Nova-like variables of the SS Cygni or U Geminorum classes eject photo- spheric shells at cyclic intervals. Joy has shown that displaced absorption lines occasionally show up in the spectra and has sug- gested a binary constitution for these stars. As an alternative I suggest that these absorption hnes may arise in the partial photo- sphere of some eruptive jet.

I have already discussed Z Andromedae, which forms the next link in the chain of variables. This star has much in common with R Aquarii, although the latter behaves more like a normal longperiod variable. The shell-like eruptions are more distinct in the former. But both stars tend to exhibit a blue coloration at minimum, as if the red shell has completely vanished.

\Ve note that a conventional red giant, with a surface temperature of 3000 ° or less could not possibly excite the nebulosity of the pla- netary nebula that surrounds R Aquarii. It is this difficulty that led me to postulate tile existence of a blue component. But a hot nucleus with partial envelopes over the poles or around the equator, would serve to produce the M-type spectrum and at the same time expel enough ultra-violet radiation toward the unobscured regions to illuminate the more distant nebula.

There is one additional possibility that we must consider. \Vhipl~le has suggested that planetary nebulae are the product of a slow nova process. I ask, can we not consider long-period variables themselves as slow novae ? The association of the variable and planetary in the case of R Aquarii is altogether anomalous unless we regard them as truly symbiotic, in the biological sense of the word, a combined organism, each part dependent on the other. M e r r i 11, who in- troduced this descriptive terminology, did so because he sensed this interdependence.

If the viewpoint put forth in the preceding paragraph is accept- able, the evolutionary trend of the long-period variables is clear. The pulsing activity that tends to create successive shells gradually decays. Eventually the ejected shells are so feeble that they are no longer opaque. The hot, dwarfish core then Serves to excite the nebulous envelope, the residue of the earlier activity.

But, one immediately objects, why then do we not see more long-

772 DONALD H. MENZEL

period variables in the transitional stages ? The answer to this legi- t imate query is that we do. There are a number of red variables, most of them in the longest-period range, that display spectroscopic anomalies suggestive of nebulous tendencies. R Leonis, Chi Cygni, and U Orionis show forbidden iron lines in their spectra. I regard these as transitional between the symbiotic objects just mentioned and the general run of Mira variables.

in addition to R Aquarii and Z Andromedae, I name AX Persei, R X Puppis, T Coronae Borealis, RS Ophiuchi, RW Hydrae, C I Cygni, and AG Pegasi as stars with estar~lished nebular character- istics. Thi~ list includes at least two repeating novae. These stars display forbidden iron lines, from [Fe Il l to [Fe V] and, in certain cases, [Fe VIII and [Fe X], (red coronal line). Some of them also show various forbidden lines of ionized oxygen and neon, characteri- istic of nebulae. And yet many of them possess the definitive features of an M-type star, with the characteristic Ti O bands.

A question of particular interest relates to possible variation of the nebulosity as the star changes its brightness. Whether the variation of exciting radiation will produce a corresponding fluctuation in nebular brilliance will depend largely upon the density of the latter. Normal planetaries have a relaxation time of at least several months. The denser layers and filaments close to the exciting star may respond more rapidly.

Nebular variation calls to mind objects like R Coronae Austrinae, T Tauri, and RY Tauri. The first is classified as G, peculiar, with bright lines. The second has apparently desplayed the following striking range of spectral characteristics : F 5e (Miss C a n n o n), F p e ( P e a s e ) , Gpe ( H u b b l e and M e r r i l l ) , Me ( A d a m s ) , W ( V o r o n t s o v - V e l y a m i n o v ) . S a n f o r d has noted the resemblance to eta Carinae. RY Tauri has received spectral classifi- cations within the range F8-G 5.

The behavior of T "Iauri is understandable in terms of the pro- posed variatfle envelope. The \~, spectrum predominates when the shell is nearly gone; the other spectra appear as shell or partial-shell forms. All of the above stars are irregular variables and.the first two are associated respectively with H u b b 1 e's and H i n d's well- known variable nebulae. R u s s e 1 1 has described the changes in the nebula as "suggesting lights and shadows (as from an intermit- tent ly obscured source)". The varying "umbrella" provides a "sun

THE INTERNAL CONSTITUTION OF GIANT M STARS 773

shade" for such obscuration and places it in the most effective posi- tion : near the variable star.

The foregoing analysis is an a t tempt to link together a wide varie- ty of variables, from novae to long-period variables. It is significant, I think, that the argument thus far has tied in objects usually con- sidered to lie at opposite extremes of the giant sequence, viz., the Me variables and the W-type stars. It suggests that the latter objects should be set at the extreme end (after the M's) of th.e giant sequence. The association also suggests that some of the W-stars may also be intrinsic variables. One star, V Sagittae, does show such variation. Examination of the continuous spectra of others may disclose small fluctuations. A variation of less than one quarter of a magnitude could produce ranges of many magnitudes in a star surrounded by an expanded envelope.

An alternative to be considered, however, is that all giant stars may consist of W o 1 f-R a y e t cores surrounded by turbulent shells. That many super-giants possess extended atmospheres is well known. We have Zeta Aurigae and a number of other late-type eclipsing stars, whose atmospheres are so tenuous that they show no sharp photosphere. There is further evidence, in the case of Zeta Aurigae, for irregularities in the atmosphere, suggestive of promi- nences or fi lamentary structure.

S t r u v e , G e r a s i m o v i ~ , and others have discussed the evidence for the presence of gaseous shells surrounding early-type stars. A number of these objects, such as Pleione, Gamma Cassio- peia, and others, show peculiarities, either of emission or absorption, which S t r u v e ascribes to the presence of shells. The argument for such shell formations is convincing.

Between the early-type shell stars and the Mira-type variables lies the important group of Cepheids. May we not also ascribe their action to the successive formation of shells and extended envelopes.

Acceptance of this viewpoint,which 1 regard as a logical extension of the evidence presented earlier, may require some modification of the conventional pulsation theories.W_Nevertheless, the shell ejection hypothesis is a type of pulsation; the new and old viewpoints may be easily reconciled.

The concept of a turbulent, distended atmosphere, whose effective density gradient is appreciably less than that for a star in gravita- tional, hydrostatic equilibrium, removes certain difficulties that

774 THE I N T E R N A L CONSTITUTION OF GIANT M STARS

have existed in the interpretation of stellar spectra. The numbers of atoms above the photosphere, derived from observation, are con- siderably greater than the numbers evaluated theoretically. In other words, the absorption lines are stronger than simple theory indicates The turbulence is also demanded by the curves of growth.

The general conclusion of this paper is that all giant stars may be considered as having a hot W o 1 I-R a y e t core, small compared with the radius of the surrounding envelope. The shell around the nucleus possesses but a minute fraction of the mass usually ascribed to this volume. Thes t ruc tu re of the material is filamentary and kinetic activity replaces the hydrostatic support required by the conventional model. The new picture leads to a nucleus whose cen- tral density and temperature are very much greater than those of the older theory, and B e t h e's carbon cycle may be called on to sup- ply the energy genel ation.

There are many complex problems still to be answered. The origin of the kinetic support has been only vaguely indicated as a combination of radiation pressure, turbulent convection, and stellar rotation. A detailed analysis of these problems falls outside the scope of the present paper. The observational evidence from many inde- pendent sources converges toward the conclusions herein drawn.

Despite the fact that the complications of a kinetic atmosphere preclude the further development of theories of atmospheric struc- ture along conventional lines, there is no reason why these theories will not still be applicable to portions of the nucleus. The flux and mass of the star remain the same as before. Only the radius is greatly changed. And it may be significant that most theories leave the radius indeterminate.

The foregoing synthesis applies mainly to stars of the giant sequence. In particular it has drawn together variable stars of widely different characteristics. It has indicated shell formation as the primary activity in stellar variation, though the fundamental cause is still unknown. It has been disappointing to me in one respect that the conclusions appear, superficially at least, to be inapplicable to stars of the main sequence.Thus the source of excita- tion of the solar corona is still unexplained. Whether or no~ some of the difficulties can be overcome is a question for the future.