WHITE DWARFS

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WHITE DWARFS

H. van Horn

To cite this version:

H. van Horn. WHITE DWARFS. Journal de Physique Colloques, 1980, 41 (C2), pp.C2-97-C2-104.

�10.1051/jphyscol:1980217�. �jpa-00219809�

WHITE DWARFS

H. M. Van Horn

Department of Physios and Astronomy £ §.£.Kenneth Mees Observatory, University of Rochester Rochester, NY 14627

Abstract. - The thermal properties and neutrino emissivity of matter in the dense, degenerate cores of white dwarfs, together with efficient heat transport through the high-density envelopes of these stars, affect the theoretical white dwarf lu- minosity function. The most recent observational data show departures from the results of elementary cooling theory at both high and low luminosities. Extreme UV and soft x-ray observations from space show the necessity of neutrino cooling for white dwarfs, have begun to provide some clues to the nature of their proge- nitors, and may be revealing evidence for white dwarf coronae. Investigations of very cool white dwarfs appear to show a luminosity cutoff due to the finite age of the galactic disk and have ifevealed very high density stellar atmospheres with quite remarkable physical properties. Element abundances in white dwarf atmosphe- res are beginning to be understood on the basis of accretion, convection, and diffusion theory, but the presence of C and the absence of H in some white dwarf spectra remain outstanding problems. Investigations of non-radial oscillations in white dwarfs may soon provide a sensitive probe of the chemical stratification and material properties in these stars. White dwarf stars are also essential com- ponents of cataclysmic binaries, and a few recent results concerning these sys- tems are briefly reviewed.

1. Introduction. - The basic proper- ties of white dwarf structure and evolution are by now well-known, and I shall not discuss them here. Reviews of these matters can be found in the literature ; cf. Schatzmann 1958, Weidemann 1968, Ostriker 1971, Van Horn 1971, Shaviv 1979. In, this talk, I shall instead concentrate on more recent developments, drawing heavely upon material presented at IAU Collo- quium No. 53 : White Dwarfs and Varia- ble Degenerate Stars, held in

Rochester, N. Y., on 31 July - 3 August 1979. I sahall be selective rather than inclusive in the topics I shall discuss, with emphasis placed on those points that appear to me to have special significance for our understanding of the physical pro- perties of these stars or on their impli- cations for somewhat broader questions of astrophysics.

To provide a framework for our discu- tion, I shall first review briefly, in §11, the classical theory of ::hite dv»ar£ cooling, due to Mestel (1952).

JOURNAL D E PHYSIQUE Colloque C2, supplément au n° 3, Tome 41, mars 1980, page C2-97

Résumé. - Les propriétés thermiques et l'émissivité neutrinique de la matière composant les régions centrales et dégénérées des naines blanches, ainsi que l'efficacité du transfert d'énergie &u travers des enveloppes à haute densités de ces étoiles, influencent la fonction de luminosité théorique des naines blan- ches. Les plus récentes Aservations jLndiquent la présence d'écarts aux prédic- tions de la théorie élémentaire du refroidissement aux grandes et aux faibles luminosités. Les observations dans l'ultraviolet extrême et les rayons X à partir de satellites ont démontré la nécessité de la présence de refroidissement par neutrinos dans les naines blanches, nous ont procuré quelques indices quant à la nature de leurs ascendants, et pourraient indiquer la présence de couronnes stel- laires. L'étude des naines blanches très froides semble indiquer la présence d'une coupure dans la luminosité due à l'âge fini du disque galactique, et a révélé la présence d'atmosphères stéllaires à très hautes densités avec de remar- quables propriétés physiques. On commence à comprendre les abondances observées dans les atmosphères des naines blanches en terme d'accrétion, de convection, de triage gravitationel et de diffusion. La présence de carbone et l'absence d'hy- drogène dans le spectre de certaines naines blanches sont cependant des problèmes non encore résolus . L'étude des oscillations nonradiales dans les naines blan- ches pourrait bientôt procurer une sonde sensible à la stratification chimique et aux propriétés des matériaux dans ces étoiles. Les naines blanches représen- tent également une composante essentielle des variables cataclysmiques, et nous discutons brièvement quelques résultats récents concernant ces systèmes.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980217

C2-98 JOURNAL DE PHYSIQUE

Next, in § 111, I shall summarize a few of the most recent results of spaceborne obser- vations in the EUV and soft X-ray regimes that are relevant to questions of the space density of hot white dwarfs, the nature of the white dwarf progenitors, and the ques- tion of white dwarf coronae. In § IV, I shall sketch some problems relating to very cool white dwarf : specifically, the white dwarf luminosity function at low Teff and properties of the atmospheres of very cool He-envelope white dwarfs. The problem of element abundances in whitedwarfs is taken up in 5 V, where I shall briefly outline re- cent results from diffusion theory and point up twooutstanding current problems : The lack of H in the atmospheres of some white dwarfs and the presence of traces of C in others. In S VI, I shall briefly review the status of our knowledge of white dwarf oscillations, emphasizing recent advances in both observations and theory. I shall conclude, in § VII, with a very brief men- tion of a few topics involving white dwarf stars in cataclysmic binary systems.

2. The Structure and Evolution of White Dwarfs.- It has been recognized for about half a century now that the mechanical structure of a white dwarf star is complete- ly dominated by the pressure of degenerate electrons. Indeed, the white dwarf mass- radius relation is given exactly, to within observational accuracy, by the mass-radius relation of zero-temperature, fully degene- rate stars composed of elements heavier than hydrogen. In addition, it has been known for somewhat more than 25 years that white dwarf stars evolve simply by gradual cooling

(Mestel 1952) as the primordial heat produ- ced in earlier stages of steller evolution leaks but through the insulating non-degene- rate surface layers surrounding the nearly isothermal, degeneratp core and is radiated away into space. This has led to the idea, accurate insofar as it goes, that white dwarfs are "the burned-out' stumps of dying stars", thus conveying the image of dead, and consequency rather uninteresting, objects. However, the thermal properties of

white dwarf matter have turned out both to have some potentially interesting observa- tional consequences and to be of considera- ble interest in themselves, involving ques- tions that are at once at the very fore- front of modern statistical physics and simultaneously of considerable practical importance in connection with current la- ser fusion research. To provide a back- ground for discussion of these matters, let us begin with a very brief review of the main points of classical white dwarf cooling theory.

Following Mestel (1952) and Schwarzschild (1958), we idealize a white dwarf as a star with M* % 0.7 M having a massive

0

degenerate core surrounded by a very thin, non-degenerate envelope. Because electron conduction is highly efficient, the degene- rate core is very nearly isothermal.

Furthermore, degeneracy greatly reduces the electronic heat capacity in compari- son with that of the ions. Insofar as the ion specific heat can be approximated as that of an ideal gas, the total thermal energy content Eth of the entire star is thus given by

where Tc is the temperature and A is the atomic mass of the ions in the white dwarf core. The luminosity L of the white dwarf is simply the rate of decrease of this thermal energy.

The luminositp is also proportional to the spatial gradient of temperature through the non-degenerate surface layers of the white dwarf. The simultaneous integration of the heat transfer equation of hydrosta- tic equilibrium through this thin region inward to the boundary of the degenerate isothermal core yields.

H e r e 5 is a constant that depends upon the details of the envelope model.

For a Kramers's law opacity, the exponent

ci = 7/2.

Equations (2) and (3) can be integrated to give the time-development of Tc and L for a white dwarf. With a few general assumptions, this history in turn predicts a luminosity function for the white dwarfs. In particular, if all white dwarfs have the same mass and composition and if the white dwarf birthrate has been constant in time indefinitely far in the past, the luminosity function Q, the number of white dwarfs per unit interval in absolute magnitude, is simply proportional to the time required to cool through that interval (cf. Weidemann 1968, D'Antona and Mazzitelli 1978) :

dlogL ciloge (4)

For a Kramers' law envelope opacity, (4) gives

This simple relation was consistent with the existing data a decade ago (ci.

Weidemann 1967). However, advances in theory have predicted departures from the elementary theory ; various spaceborne observations in the E W have provided new information about the white dwarfs at high luminosities ; and recent efforts to extend observations to the intrinsically coolest white dwarfs are beginning to provide new insights at the faint end of the luminosity function.

3. EUV Observations and Hot White Dwarfs.- The discovery of soft X-ray and EUV radia- tion from the white dwarf HZ43 (Hearn et' al.

1976, Lampton et al. 1976)imrnediately marked it as one of the hottest white dwarfs known.

A self-consistent, pure hydrogen model at- mosphere analysis by Auer and Shipman (1977) yielded Teff in the range from 55,000

-

70,000K. Subsequently, this star has been studied extensively with a variety of satel- lite experiments (cf Bowyer 1979).

0

Particulary noteworthy is the He11 A228A Lyman edge detected by Malina, Bowyer, and Paresce (1978). This implies a helium

abundance of 1 x N (He) /N(H)

z

^{3 x} (Heise and Huizenga 19791, which is consistent with limits on the helium abundance in the cooler DA white dwarfs.

Other hot white dwarfs that have been studied in the EUV spectral range include :

Feige 24 (Teff % 60,00OK, N(He)/N(H)

% cf. Bowyer 1979) ; Sirius B (Teff

s 27,00OK, DA : see below) ; HZ21 (Teff

s 50,00OK, DO : Koester, Liebert and Hege 1979) ; and perhaps the hottest white dwarf yet discovered, HD 149499B (Teff % 82,00OK, N (He) /N (H) % 10 : Parsons, Wray, and Henize 1979). These observations clearly show that, in contrast with the cooler white dwarfs which tend either to have pure H atmos- pheres or to have He-dominated atmospheres in which H is undetectable,

both

H and He tend to be present, in variable intermedia- te amounts, in hot white dwarfs(&. Green and Liebert 1979). These findings bear directly on the rapidly developing theory of spectral evolution in white dwarfs to be discussed below : it is possible to un- derstand how gravitational settling of He out of a mixed H/He atmosphere can produce DA (H-compositon) white dwarfs, but where .

are the progenitors of the DB (He-composi- tion) stars ? One answer has recently been suggested by Nather et al. (1979) and will be described in § VII.

Another result from EUV and soft X-ray observations is a limit on the density of very hot white dwarfs. Because of the high opacity of the interstellar medium at these wavelengths, the limits depend upon the assumed density of interstellar matter. The best current observational limits are from the E W data of Cash et al.

(1976)

,

and if NH

3

0.3 ~ m - ~ , these limits are below the level given by pre-white- dwarf evolution theory without v-loss (cf.

Wesemael 1978, Bowyer 1979). This clearly supports the operation of v-emission pro- cesses in these stars, and improvements in E W and soft X-ray instrumentation over

JOURNAL DE PHYSIQUE

t h e n e x t few y e a r s may prove t h i s .

EUV d a t a have a l s o begun t o be d i r e c t e d t o i n v e s t i g a t i o n s of t h e p o s s i b i l i t y of coronae around white dwarfs. A few white dwarfs have been found t o show emission l i n e s ( i n t h e v i s u a l band b u t t h e g r e a t e s t impetus has come from t h e r e p o r t e d s o f t X-ray d e t e c t i o n of S i r i u s B by Mewe

g

a l . (1975). This de- t e c t i o n has n o t been confirmed, however, p o s s i b l y because of t i m e - v a r i a b i l i t y of t h e source. I t has r e c e n t l y been argued theore- t i c a l l y both t h a t t h e convective f l u x i n S i r i u s B i s i n s u f f i c i b n t t o d r i v e a corona according t o conventi n a l t h e o r y (Fontaine 1977) and t h a t t h e s o

t

c a l l e d "minimum f l u x "

coronae a r e i r r e l e v a n k (Vaiana and Rosner 1978)

.

I n a d d i t i o n , B8hm-Vitense (1979) has f a i l e d t o f i n d u l t r a v i o l e t emission l i n e s i n d i c a t i v e of a corona i n S i r u i s B. The q u e s t i o n of w h i t e dwarf coronae may be i m - p o r t a n t i n r e g a r d t o mass l o s s (however, s e e Bbhm 1979) and i n connection w i t h white dwarf s p e c t r a l e v o l u t i o n . Continuing impro- vements i n t h e s e n s i t i v i t y of d e t e c t o r s a t EUV and s o f t X-ray wavelengths can e v i d e n t l y be expected t o add c o n s i d e r a b l y t o o u r knowledge i n t h e near f u t u r e .

4 . Very Cool White Dwarfs.- As a w h i t e dwad sols, a variety of physical e f k c t s not included i n the Mestel theory begin t0appear.W L ~ O - ~ L ~ , white dwarfenvelopes develop r e l a t i v e l y deep

surface convection zones, which u l t i m a t e l y reach i n t o t h e &generate o o r c ~ o r L ; ~ O - ~ t o 1 0 - ' ~ @ c r y s t a l l i z a t i o n b e g i n s a t t h e c e n t e r l a n d f o r s t i l l lower l u m i n o s i t i e s =bye coolingbecomes important. a e s e f a c t o r s s u b s t a n t i a l l y change t h e white dwarf cooling t i m e s c a l e s a t low L, and t h i s has prompted new t h e o r e t i c a l and chserva

-

t i o n a l w o r k o n t h e white dwarf luminosity func- t i o n T h e o r e t i c a l luminosity f u n c t i o n s have been computed by Lamb and Van Horn (1975) for l M g and by Shaviv and Kovetz (1976) f o r 0.8 and 0 . 6M0. A review of t h e s e and o t h e r t h e o r e t i c a l calculii- t i o n s h a s r e c e n t l y b e e n g i v e n b y s h a v i v ( 1 9 7 9 ) . Sion a d L i e b e r t (1979) a n d - L i e b e r t ( 1979) have compared t h e s e t h e o r e t i c a l r e s u l t s w i t h r e c e n t e x t e n s i o n s ~ o f t h e o b s e r v a . t i o n a 1 f u n c t i o n t o

<

~ . ~ 1 0 - ~ ~ ~ . O v e r m o s t o f t h e l u m i n o s i t y r a n g e , t h e o b s e r v a t i o n a l d a t a a r e i n d i s t i n g u i s h a b l e fr.om

t h e Mestel theory. A t t h e high-Luminosity end t h e r e a r e s u g g e s t i o n s of d e p a r t u r e s d u e t o n e u t r i n o cooling,whichwe have a l s o seen

( 5 111) i n connection w i t h t h e EUV observa- t i o n s . A t lower l u m i n o s i t i e s , t h e observa- t i o n s again i n d i c a t e a d e p a r t u r e from t h e Mestel t h e o r y , i n t h e d i r e c t i o n c o n s i s t e n t w i t h o u r understanding of t h e p h y s i c s , down t o L ^Q, I O - ' L ~

-

⁴

For L < 10 L@, however, t h e most r e c e n t

o b s e r v a t i o n s show s t r i k i n g evidence f o r a much g r e a t e r d e f i c i e n c y than p r e d i c t e d by c u r r e n t c o o l i n g theory. The most probable e x p l a n a t i o n f o r t h i s i s t h a t such low l u - m i n o s i t i e s r e q u i r e c o o l i n g times l o n g e r than t h e age of t h e g a l a c t i c d i s k , so t h a t t h e r e a r e no white dwarfs f a i n t e r than

~ o - ' L @ . From t h e c o o l i n g t h e o r y , t h e age of t h e d i s k i s t h u s % 5 x

l o 9

y e a r s .

The i n t r i n s i c a l l y f a i n t e s t w h i t e dwarfs a r e a l s o t h e c o o l e s t ones, and s e v e r a l de- g e n e r a t e s have now been found with Teff

<

-.

^{5000K. A t} such low temperatures n e i t h e r He nor H a b s o r p t i o n l i n e s a r e d e t e c t a b l e i n t h e s t e l l a r atmospheres, and one of t h e key q u e s t i o n s t o be answered i s whether H o r He i s t h e dominant atmospheric s p e c i e s . For t h e h o t t e r white dwarfs (Teff

-

10,000

-

30,000K)

,

H (DA) s p e c t r a predomi- n a t e by a r a t i o

-

^{2 : l .} Preliminary evidence s u g g e s t s t h a t t h e o p p o s i t e may be t r u e a t low Teff ! I f t h i s i s c o r r e c t , it w i l l p r e s e n t a formidable problem f o r t h e o r i e s of t h e s p e c t r a l e v o l u t i o n of white dwarfs

( c f . § V)

.

There a r e a l s o c o n s i d e r a b l e problems i n understanding t h e atmospheric s t r u c t u r e of t h e very c o o l e s t w h i t e dwarfs ( c f . Bbhm a l . 1977 ; Bbhm 1979). I n t h o s e s t a r s w i t h

-

He envelopes and Teff

2

4 0 0 0 ~ ~ degeneracy b e g i n s t o p l a y a r o l e

even

i n t h e atmos- pheres ! This has t h e immediate consequen- c e t h a t e l e c t r o n conduction must be consi- dered along w i t h convection and r a d i a t i v e t r a n s f e r i n computing models of t h e s e atmospheres, with t h e f u r t h e r consequence t h a t t h e atmospheric temperature p r o f i l e i s e x c e p t i o n a l l y f l a t . Because of t h i s , t h e spectrum i s n e a r l y f e a t u r e l e s s and

closely resembles a black body. In pure He atmospheres, the opacity is also extremely low at these low temperatures ; one thus sees very deep into the atmosphere, so that the pressure at the photosphere is very lar- ge and any lines present are very broad.

5. Element Abundances and Spectral Evolu- tion.- It has been clear from the very first

-

spectroscopic observations of white dwarfs that the element abundances in these stars are peculiar. It is now known that about 2/3 of all white dwarfs show nothing but H

(spectral type DA). A fraction of the rest shows only He (type DB) ; some have purely continuous spectra (type DC) and appear to be cooled-down DB's no longer hot enough to produce He absorption lines ; a few show only molecular carbon (type A4670) ; and the remainder show various metals (Ca, Fe, Mg), but with very low abundances. It was poin- ted out 20 years ago by Schatzman (1958) that the large gravitational fields of the white dwarfs should make gravitational settling very efficient, and it is general- ly Believed that this accounts for the very high purity of H in the DA white dwarf at-

< ^-4

mospheres (e. g., He/H

-

^{10 ) :} everything else has sunk below the photospheres of these stars. Similar arguments explain the high purity of He in DB atmospheres. The DB stars present two outstanding problems, however : 1) How was the H lost from the progenitors of these stars ? 2) Why does accretion from the interstellar medium not contaminate the DB spectra ? The first question I again defer to § VII. The second can perhaps be answered by dilution of a very thin H surface layer in a very deep He convection zone, if the white dwarf has

<

M

-

0.4 Mg (cf. Wesemael 1979)

.

^{This low}

mass is required because the convection zone mass is greatest in the least massive white dwarfs, and the convection zone must be deep enough to dilute

-.

^{10'' years of}

accretion from the interstellar niedium, at

-.

1 0 - l ' ~ ~ yr.-l, to a fractional abundance

<

XH

-

There is some weak evidence that DB white dwarfs may indeed have such low masses (Trimble 1979), but this is still very uncertain. Another mechanism has re-

cently been suggested by Michaud and Fontaine (1979), who argue that strong electric fields may be set up in the sur- face layers 05 white dwarfs, perferentidly expelling the H.

The abundances of the metals observed in cool white dwarfs, however, have stimula- ted most of the recent activity on the question of, gravitational settling. (cf.

Vauclair 1979 for a recent review). It was originally thought that the observed metaLs might have been dredged up from below as the convection zone deepens.

However, recent calculations by Fontaine and Michaud (1979a) and by Vauclair, Vauclair, and Greenstein (1979) have shown that the convection zone cannot catch up with the settling. The most plausible al- ternative appears to be a competition between quasi-steady accretion and settling.

Alcock (1979) has shown that this leads to the following expression for the abundance X of the diffusing species :

where F is the accretion flux of that spe- cies, and n o , w,, and r o

=

Po/(wopog) are the number density in the plasma, the se- dimentation speed of the diffusing species, and the time for settling through one pressure scale height, all evaluated at thebase of the convection zone. Ex-

plicit numerical calculations show 1) that diffusion timescales are very much shorter than the cooling times and 2) that the abundances predicted by the accretion plus settling hypothesis are in rather good accord with observation (cf. Vauclair 19791, even for the longer diffusion timescales resulting from the more accurate recent evaluation of the diffusion coefficients by Fontaine and Michaud (1979b)

There remains the problem of C in the 14670 white dwarfs. Analysis of the obser- vations (cf. Bues 1973, 1979) shows C

JOURNAL DE PHYSIQUE

still to be only a trace element : C/He

-

³

10

.

This presents a severe problem for theories relying on convective dredging-up of C ; calculations by Vauclair and Fontaine

(1979) show that, except under very special circumstances, the inward growth of the convection zone in a cooling, He-atmosphere star either fails to reach the C core or else dredges up so much C that the atmos- pheric abundance of C becomes orders of ma- gnitude too large. An alternative is to suppose that the C is primordial, left over from an earlier stage of evolution, and that gravitational settling of the C is somehow inhibited (cf. D'Antona 1979).

However, no physical mechanism has yet been suggested for this inhibition, and one must conclude that the presence of C at the abundance levels seen in the A4670 stars is one of the current outstanding problems.

6. Non-Radial 0spillations.- Rapid oscilla- tions were first detected in white dwarfs in the early 1970's (cf. Warner and Robinson 1972). However, the periods of these oscillations were found to be

-

^lo2

-

lo3 sec., much too long for radial pulsa- tions, for which the periodsare 5

-

^10s.

Another class of modes of stellar oscilla- tion, the so called non-radial "g-modes", do have periods as long as a few hundred seconds for cool white dwarfs, and it was natural to suggest that these were the modes being observed. This explanation seems to work very well for some white

- ^---

(l)~n addition to the oscillation in the Z Z

Ceti stars, rapid oscillations have also been observeid in several of the cataclysmic binary systems. I do not have time to dis- cuss them here and must be content to refer to Robinson (1976) and Patterson (1979) for details. I must, however, call attention to a wholly new type of white dwarf variable discovered in late April by McGraw et al.

(1979). This star, PG1159-035, from Green's (1979) recent list of hot white dwarfs, has oscillation periods of about 539s and 460s, is probably H-Deficient, and has Teff >

50,000K. It is thus totally unlike the DA

dwarfs (such as R548 Z Z Ceti, the proto- type of the class), but

not

for all of them ! Subsequent observations have shown that these Z Z Ceti stars(l) have the follo- wing characteristics (cf. the recent review by Mc Graw 1977 and Robinson 1979) : 1) They are without exception DA white dwarfs. 2) They have 10,000K 5 ^Teff 5 14,000K. 3) They all appear to be multiply-periodics only a few periodicities appearing in the low-am- plitude variables, but a very large number in the large-amplitude cases.

The existence of oscillations in the Z Z

Ceti white dwarfs immediately raises two questions. 1) What are the actual modes of oscillation ? 2) How are these modes exci- ted ? Theorists have tried very hard to find models of white dwarfs which have

-

lo3 second periods, but as yet with no success. The good agreement found between the observed periods in R548 (a,

-

^213s,

a,

-

273s) and the !L = 2 g-mode periods computed for

-

^{~o'K, 0.} 6M0 white dwarf models:

strongly suggests that these general types of oscillations are the correct ones. As yet however, the right modes have not all been found. The second question is even more difficult. The location of the ZZ Ceti stars in very close proximity to a naive ex- tension of the Cepheid instability strip

suggests that the same process of excita- tion that is at work in the Cepheids also drives the oscillations in white dwarfs ;

however, Cox and Hansen (1979) have recen- tly pointed out that this cannot be correct in detail for the g-modes. Within the past year, three independent calculations have discovered pulsational instability, driven

by the Cepheid mechanism, in the so-called p-modes of white dwarfs (of which radial oscillations are a special case). Such ins- tabilities were first reported by

Dziembowski (1977) for the non-radial p-modes. The first radial mode instabili- ties were found by Cox et

&.

(1979) and Starrfield

et g .

⁽¹⁹⁷⁹⁾

,

whose results were confirmed by Keeley (1979). The problem is that pu&sations are not ^obser- ved at such short periods, and they variables

probably should have been. Dziembowski (1977, 1979) has suggested that non-linear interactions couple the energy in the short-period modes to the long-period ones.

This has some very attractive features, but it is difficult to understand why only a few long-period modes should be excited this way rather than a broad spectrum of oscillations. Quite recently, Dziembowski

(1979) has begun to explore the consequen- ces of a stratified composition in the white dwarf envelope for the non-radial oscillations. For certain models he finds very large changes in the periods of the oscillations. Because we expect gravita- tional separation to produce such layered structures, this appears to be a very worth- while direction of investigation. Further, stratification can significantly modify the structure of the ionization zones in these stars, perhaps permitting a "correct" model not only to yield the correct oscillation periods but also to predict excitation of just those modes that are observed in the ZZ Ceti stars.

If this optimistic appraisal can be reali- zed, future calculations will provide information about the compositional strati- fication in white dwarfs. In addition, cal- culations of the excitation of white dwarf oscillations are rather sensitive to the physical parameters of matter in the regime just now beginning to be explored by laser fusion experiments. For this reason, one may expect the interaction between such experiments, theories of material proper- ties, and observations of white dwarf oscillations to be mutually rewarding.

7. White Dwarfs in Cataclysmic Binaries.- The cataclysmic binary stars contain white dwarfs in close orbit about a companion

star that transfers matter back onto the dwarf. I shall not describe these systems in detail, but shall refer to reviews in the literature (Warner 1976 ; Robinson 1976;

Warner 1979 ; Webbink 1979). In general these systems contain an accretion disk with a hot spot, and accretion onto the white dwarf star itself occurs either via

a boundary layer or through an accretion

column onto the poles of a magnetic white dwarf. Studies of such systems can teach us much about the nature of different accre- tion mechanisms and indeed about the white dwarfs themselves.

As one example, albeit an especially inte- resting one, I would like to summarize the very recent discussion of G 61-29 by Nather, Robinson, and Stover (1979). This system, originally found by Burbidge and Strittmat- ter (1971) to have a spectrum consisting entirely of He emission lines, has now been found by Nather et al. to be a close binary with an ohbital period of 46.52 min. With assumptions discussed by Faulkner

g . &.

(1972) in the context of the similar system HZ 29 (= AM CVn), the companion star in G61-29 appears to be a degenerate star of mass 0.02M0 (for HZ 29 the companion mass is 0.04MO)

ass

^transfer

from

such low mass companions onto a white dwarf leads to in- creasing separation of the system, but sin- ce the radius of a low mass degenerate star also increases as the mass declines, it is possible for the mass transfer to continue until the mass of the companion star has been peeled down to planetary size. For HZ 29 the timescale for this to occur is only

-

lo5 years, based on the current rate of period change. Because the low mass compa- nion is virtually per He, the end-product of this evolution will be a hot white dwarf with a pure He surface layer, indistingui- shable from a DB star, and Nather et al.

Suggest that this "cosmic canibalism" may produce many, and perhaps all, of the DB white dwarfs.

8. Conclusion.- I have barely touched on the multitude of problems in the physics of dense matter that are encountered in the context of white dwarf stars. For example, I have not even mentioned the magnetic white dwarfs (cf. Angel 1978 ; Landstreet

19791, which are of great interest in themselves. I have tried to indicate some of the currently most active areas of in- vestigation concerning white dwarfs in or- der to provide some of the "flavor" of this field. Our understanding of these stars has made tremendous progress. Some

c2-104 JOURNAL DE PHYSIQUE

of the most challenging problems remain, but there are already hints of impending breakthroughs in a few areas.

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