Model atmosphere analyses of white dwarf spectra have contributed significantly to our understanding of the properties of degenerate stars.: In particular, the pioneering investigations of Bues (1970), Strittmatter and Wickramasinghe (1971) and Shipman (1972) have provided the first reliable determinations of the effective temperature and surface gravity of these objects (see Shipman 1979 and Weidemann 1978 for recent results). We now know with certainty that the hydrogen-rich white dwarf sequence extends at least over the range Te ∽ 6000 – 60.000K. In contrast, the hottest identified helium-rich white dwarfs seem to reach Te ~ 25.000K only, a puzzling result since the progenitors of DB white dwarfs should presumably also be helium-rich.

About eight years have elapsed since the publication of an extensive grid of model atmosphere calculations for DB white dwarfs by Wickramasinghe (1972), and some selected data on colours and line strengths by Bues (1970), Shipman (1971, 1972), Strittmatter and Wickramasinghe (1971), and Wickramasinghe and Strittmatter (1970). Since then only rather few theoretical results applicable to individual objects have been published by e.g. Wickramasinghe and Whelan (1977), Shipman, Greenstein, and Boksenberg (1977). On the other hand, a large amount of observational material on DB stars has accumulated, mainly through the work of Greenstein (1976), Wickramasinghe and Bessell (1977), Hintzen and Strittmatter (1974), Wickramasinghe et al. (1975), Wegner (1973, 1979), Schulz (1979), Bessell and Wickramasinghe (1978), Oke (1974), and Liebert (1977).

The production of hard X-rays in accretion onto degenerate dwarfs appears manifested by such sources as the magnetic variables AM Herculis and 3U0311-227 and the dwarf novae SS Cygni, EX Hydrae and U Geminorum. Upper limits on flux above 2 keV from Ariel 5 (Watson, Sherrington and Jameson 1978) and from the high energy detectors of the HEAO A2 experiment show that only a few others usually exhibit more than ~10-11 ergs cm-2s-1 or ~ 1031 ergs s-1. However, while there are only a few sources that these experiments could study, their behavior is complex (Swank et al. 1977a; Ricketts, King and Raine 1979; Swank et al. 1978; Mason, Cordova and Swank 1979). This paper is a brief summary of results for AM Her, EX Hya, SS Cyg and U Gem obtained with the high energy detectors of the HEAO A2 experiment from 2-60 keV and the Solid State Spectrometer Experiment (SSS) with the Monitor Proportional Counter (MPC) on the Einstein Observatory.

WZ Sge was observed spectroscopically during quiescence in August 1978 and July 1979, before and after the December 1978 outburst. The same instrumental set up was used, namely the Image Photon Counting System on the Anglo-Australian Telescope. Time resolved spectra were obtained in phase over several orbital periods, in wavelength ranges covering Hβ and Hγ and also separately Hα. These data are being used to study the “before and after” changes in the emission line profiles, in the radial velocities of the S-wave and of the emission lines, and in the broad absorption line profiles. Additionally these features are being studied as a function of orbital phase in order to improve the determination of system parameters. When completed, the results will be published elsewhere.

The energy liberated by nuclear burning of matter accreting onto degenerate dwarfs can be more than an order of magnitude greater than that available from the release of gravitational potential energy. Nuclear burning therefore significantly alters the characteristics of X radiation from such stars. Here we report the results of calculations in which steady burning occurs at the accretion rate, and compare them with our calculations (Kylafis and Lamb 1979, hereafter KL) which assumed no burning. These two studies illustrate the maximum and minimum effects of nuclear burning. Results for intermediate burning rates can be found by scaling from them.

We present spectrophotometric observations of three southern dwarf novae – BV Cen, EX Hya and VW Hyi - in the wavelength range 1250 – 7500Å. Because of the rapid variability of these objects, spectra were obtained simultaneously using the IUE satellite and the Anglo-Australian Telescope. BV Cen and EX Hya were observed in quiescence and VW Hyi on the decline from outburst.

In the review, I attempt to focus on what we have recently learned from the observations about three general topics of great theoretical interest:

1. 1. evidence for evolution of white dwarf surface abundances,

2. 2. the special problems of determining atmospheric parameters and abundances at the cool end of the sequence, and

3. 3. evidence for a peaking of the white dwarf luminosity function at Mbol = + 15 ± 1, with possible implications for cooling theory and the history of galactic star formation.

In this theoretical review about cool white dwarfs, I will restrict myself to the problem of the metallic content in white dwarf outer layers. The first section will be a short review of what we know about the metal abundances. The hottest presently known white dwarf showing metal in its spectrum is the DB GD 40 (Te = 15 000 K). This temperature will be considered here as the hot boundary of the “cool” white dwarfs. Many efforts have been recently devoted to the understanding of these metal abundances. Section 2 will be a summary of recent calculations of diffusion time scales in both hydrogen and helium white dwarfs. It will be seen that diffusion is so efficient in white dwarf conditions that the convection zone which develops in the envelope as the effective temperature decreases along the cooling sequence is never deep enough to bring back to the surface the metals which had previously diffused downwards. A discussion of the carbon white dwarfs, also called λ 4670 stars, will be presented in section 3. Recent calculations show that the convective mixing between a helium envelope and a carbon core would produce λ 4670 composition for only very special conditions and for this reason we believe that this is an improbable explanation for this type of white dwarfs. We clearly need another physical mechanism to compete with diffusion and to maintain an observable amount of metals in some cool white dwarf atmospheres. We discuss in section 4 the competition between diffusion and accretion. This seems a very promising mechanism in spite of the fact that considerable improvements are still needed in the theory of accretion. Substantial progress has to be made in this direction. A few problems related to this model are invoked in the conclusion.

White dwarfs fall in two main categories (1) the group with H-rich atmospheres (DA) the most numerous, and (2) the group with He-rich atmospheres (DB, DC, DF, DG, λ4670). Calculations of element separation (via gravitational settling) and convective mixing in white dwarf models have been made by Koester (1976) and Vauclair and Reisse (1977) in order to understand the existence and maintenance of these distinct groups and to predict at what stage during the cooling of the white dwarf some connection may occur between the two groups. Over the last few years, Wickramasinghe, Bessell and Cottrell (Wickramasinghe et al., 1977; Cottrell et al., 1977; Bessell and Wickramasinghe, 1979; Bessell, 1978 and Wickramasinghe and Bessell, 1979) have investigated the properties of cool (T < 6000K white dwarfs observationally and theoretically. We have attempted to establish at what temperature mixing does occur in DA white dwarfs, whether cool white dwarfs could be confused with G, K and M dwarfs, and if one can discriminate spectroscopically cool He and H-rich white dwarfs. In this paper we will discuss the spectra and colors of the coolest (Te < 5000K white dwarfs and compare them with model atmosphere calculations.

The cool white dwarf stars G 128-7 and G 165-7 have a quite different character: While the line spectrum of G 165-7 is the richest of all white dwarfs known, G 128-7 shows only a strong Hα line (Wλ ≈ 5.5 Å) and a much weaker Hβ line (Wλ ≈ 1 Å).

8 white dwarfs of spectral type λ4670, LP 93-21, EG182, BPM 27606, EG82, G257-38, EG148, G99-37 and L97-3, with more or less well observed carbon bands in their spectra, have been analyzed by detailed model atmosphere techniques. For the very strong band stars the blanketing effect of the molecular band systems of the Swan band and the Deslandres-d’Azambuja band had to be included in the computation of the models. The best fit of the fluxes with scanner observations and spectra is obtained for abundance ratios of 103 ≤ He/H ≤ 105, 800 ≤ He/C ≤ 5000, with LP 93-21 being the most carbon-rich object. The results are summarized in Table 1.

Current theory of stellar evolution predicts that stars of initial masses up to 4-6 M⊙ evolve into Carbon-Oxygen White Dwarfs surrounded by a Helium envelope and, possibly, by a Hydrogen envelope. It also predicts that the mass of the Helium envelope which remains on the star at the end of its double shell burning evolution is a function of the Carbon-Oxygen core mass (Paczynski 1975). It can be shown that this mass can be reduced – but only slightly – during the following evolution of the star towards the White Dwarf region, either by nuclear burning or by mass loss (D’Antona and Mazzitelli 1979). During the White Dwarf stage, Helium convection grows into White Dwarfs having Helium atmospheres. The maximum extension of Helium convective mass is a function of the mass of the star (Fontaine and Van Horn 1976; D’Antona and Mazzitelli 1975,1979). It turns out that the Helium envelope remnant mass is always at least three orders of magnitude larger than the maximum Helium convective mass, whatever the mass of the star may be. This statement is unlikely to be changed by refinements either in the theory of double shell burning or in the theory of White Dwarf envelope convection.

It has been known for some time (Schatzman 1958) that diffusion could play an important role in the spectral evolution of white dwarfs. However, it is only recently that quantitative estimates have become available, making use of detailed envelope models (Fontaine and Michaud 1979, hereafter referred to as FM; Vauclair, Vauclair, and Greenstein 1979; Alcock and Illarionov 1979). These studies suggest that the observed monoelemental character of white dwarf spectra can qualitatively be explained in terms of the diffusion model. Moreover, it appears that the diffusion time scales are so short compared to evolutionary times that competing mechanisms, such as accretion, must be invoked to explain the small but measurable abundances of heavy elements in the spectra of cooler white dwarfs.

Two decades ago it was realized (Schatzman, 1958) that metals should be rapidly removed from the atmospheres of white dwarfs by diffusion through the steep pressure gradients present. Yet metals are observed. Their presence thus prompts us to consider the diffusion process in greater detail and to seek mechanisms which might deposit metals in WD atmospheres.

Heavy ions rapidly sink out of the base of a white,, dwarf convective zone, and a balance is set up between accreting interstellar material and this sedimentation flux. The heavy element abundances are lower than they would be in the absence of convection. The accretion process is responsible for any gross departures from the cosmic abundance ratios among the heavy ions. A chemically pure white dwarf must have mass greater than 0.2 M⊙. The DB stars have masses lower than 0.4 M⊙.

Today there is no doubt that white dwarfs represent the most common final stage of stellar evolution. Considerable progress has been made during the last decade in our understanding of their origin and distributions. This is reflected by the fact that it is now possible to predict – from basic theory of stellar evolution and stellar atmospheres – the existence of cooling degenerate stars with nearly the observed properties, i.e. a sequence of white dwarfs which fill in their majority a narrow strip in both two-color and color-magnitude diagrams. With other words: the empirically determined surface gravity and radius distributions – which correspond via the mass-radius relation to mass distributions – can now be basically understood within the currently adopted general scheme of stellar evolution with mass loss.

We present a brief review of the basic properties of white dwarf atmospheres) convection zones and corona models emphasizing qualitative and intuitive aspects.

1. Atmospheres: We restrict our discussion essentially to very hot and very cool atmospheres since these are especially interesting. With regard to the first type of objects we study the fundamental differences between DA and non-DA models and between their surface fluxes. We discuss the important role of electron scattering in determining the EUV spectra of these objects. The differences between DAs and non-DAs with regard to backwarming effect and surface cooling are summarized.

In our discussion of very cool non-DA atmospheres we emphasize the importance of the additional energy transport mechanisms convection and conduction which should both be very effective for Teff < 4000K and which lead to a very flat temperature gradient. This small gradient must lead to a rather featureless surface flux.

2. Convection Zones. After a survey of the basic numerical results in this field we investigate the question whether convection in white dwarfs has the same basic properties as convection in other stars. We find that contrary to intuitive expectations the Rayleigh number in very cool non-DAs is higher than in the sun (indicating very turbulent convection). The Prandtl number in these objects is 6 to 7 orders of magnitude higher than in the sun.

3. Coronae. The basic methods of the calculation of coronae for white dwarfs are very briefly discussed. We present some results for DA and non-DA stars from unpublished work by D.O. Muchmore and the author. It uses revised values for the emissivities. Only non-DA coronae are of practical interest. DA coronae have much lower densities and temperatures. White dwarf coronae do not generate a stellar wind.

In the nine years since Symposium No. 42 at St. Andrews, Scotland, the number of spectroscopically identified white dwarfs has grown from 285 then to over 750 spectroscopic degenerates now. Significant increases in the number and quality of faint star parallaxes and the multichannel spectrophotometry at the 5.1m Hale reflector by Jesse Greenstein has made possible a major breakthrough in the color-luminosity relation for white dwarfs. Of the present sample only ninety-one stars lack measured colors. Over 300 white dwarfs have multichannel colors while over 200 have Strömgren photometry due primarily to Graham (1972), Eggen and Bessell (1978), Wegner (1979), and Green (1977, 1979). Green’s north galactic pole survey of hot white dwarfs will present Strömgren colors for each of several hundred stars in his sample. At the time of this writing it is anticipated that Green’s blue survey will add 500 – 700 new white dwarfs with spectra and measured colors. Thus by the first half of 1980 the spectroscopic white dwarf sample will number between 1300 and 1500 stars.

Observations of 22 DB stars using the uvby photometric system are discussed. In the [(b–y),(u–b)] diagram, these objects define a relatively tight sequence, but the interpretation is hampered by the lack of a precise knowledge of atmospheric element abundances in these stars. The recent models of Koester (1979) show a larger gravity separation for the DB’s using Strömgren photometry and appear to fit the observations better than earlier theoretical results. Due to the tightness of the DB sequence at the hot and cool ends, respectively, there appears to be evidence for restricted ranges in log g and the atmospheric hydrogen abundance.

The extremely blue foreground LMC star LB3459 (= HDE 269696) was reported by Kilkenny, Hilditch and Penfold (1978) to be an eclipsing binary system with a period of 6h17m. Preliminary analysis of uvby photometry and data obtained with the University of Cape Town highspeed photometer (Nather 1973) indicated that the system was composed of two degenerate stars, probably 0-type subdwarfs.