Ever since Graham’s Strömgren photometry (1972) demonstrated the existence of a single well defined cooling sequence of DA white dwarfs the question of the mass dispersion (or the width of the number-mass distribution) has been in the foreground of my studies (Weidemann, 1970, 1977).

Indeed it turned out that the shape of the white dwarf mass distribution provides strong constraints on the theory of stellar evolution with mass loss, a fact which will be demonstrated again in the following lecture. It therefore seems worthwhile to dwell in some detail on the methods of its determination. For the benefit of the non-specialists I shall first present some of the historical results and then continue to discuss the present situation.

The luminosity function (LF) and total space density of white dwarfs in the solar neighborhood contain important information about the star formation history of the stellar population, and provide an independent method of measuring its age. The first empirical estimates of the LF for degenerate stars were those of Weidemann (1967), Kovetz and Shaviv (1976) and Sion and Liebert (1977). The follow-up investigations made possible by the huge Luyten Palomar proper motion surveys, however, added many more faint white dwarfs to the known sample. While the number of known cool white dwarfs grew to nearly one hundred, these did not include any that were much fainter intrinsically than the coolest degenerates found from the early Luyten, van Biesbroeck and Eggen-Greenstein lists.

Recent preliminary USNO CCD parallax solutions for over 100 fields have yielded relative parallaxes with formal errors less than 0″.0030 for approximately 60 faint (15.9 ≤ V ≤ 20.3) stars. The stars observed include a variety of late-type dwarfs, extreme subdwarfs, and degenerates. Among the latter are the well-known, spectroscopically confirmed degenerates LP543–32/33 (= LHS239/240), LP131–66 (= LHS342), LP754–16 (= LHS483), LP702–7 (= LHS542), LP374–4 (= LHS2364), and LP322–800 (= LHS2673), all of which have Mv ≥ 15.0. In addition, two “new” (in terms of previously lacking both spectroscopic confirmations and absolute luminosity estimates) late-type degenerates were identified — LP53–7 (= LHS1405) and LP550–178 (= LHS2288) — both with proper motions in the range

The main evolutionary phases having some interest for the formation of the remnant white dwarf are discussed, starting from the core helium burning phase, in the attempt of evaluating a theoretical relation between initial main sequence mass and final white dwarf mass. Several difficulties, mainly due (but not only) to uncertainties in the theory of mass loss, have been met, so that only a fiducial bona fide correlation can be drawn. The mass function of population I white dwarfs has probably a secondary maximum at M = 0.9 – 1 Me.

The ultimate aim in the study of White Dwarf (WD) evolution is to understand properly the observed Luminosity Function (LF) of WDs, that is the number of WDs observed per unit magnitude interval. The complicated route to the interpretation of this scarne quantity (12 fiducial points in the recent update of Liebert et al. 1988) is schematically summarized in figure 1. Clearly, the main input to the LF are the evolutionary (cooling) times, but it is necessary to consider their non trivial dependence on galactic evolutionary inputs, namely the initial mass function of disk stars, their age distribution with time (ultimately: the disk age), and their evolutionary properties. Stellar evolution enters in the problem of cooling by two main routes: first, by determining the mass of the WD as a function of the inital stellar mass and chemistry, second by fixing the internal constitution of the WD remnant for each given mass, and the initial physical conditions at the start of WD evolution (mainly the temperature distribution, which is important for the first phases of evolution). Of course, there is no need of good evolutionary inputs to study “theoretical” WDs. In fact, historically, the first approach in the study of “cooling” (Mestel 1952, Schwarzschild 1958)) has been directly related to the stimulating physical properties of these objects, in which neutrino losses at the beginning (Vila 1966, Savedoff et al. 1969) and, in late stages, liquification and crystallization of the plasma (Brush,Sahlin and Teller 1966, Hansen 1973) long recognized to be dominated by coulomb interactions, (Kirzhnits 1960, Abrikosov 1960, Salpeter 1961), are the main features to be investigated (Mestel and Ruderman 1967, Van Horn 1968, Kovetz and Shaviv 1970).

White dwarfs (WD) are the final configurations of all stars up to initial masses between 5 and 9 M⊙. Two feeder channels for the creation of single WDs can be distinguished: Either evolution through the asymptotic giant branch (AGB) and the following planetary-nebula (PN) phase, or evolution from the horizontal branch through the hot subdwarf region. Prelimary estimates by Drilling and Schönberner (1985) and Heber (1986) indicate that the creation of WDs via the horizontal–branch channel is rather insignificant (few percent of the total WD birthrate) and can be neglected. Thus the evolution through the AGB determines the internal structure of single WDs, and the study of the PN stage serves to elucidate the inital conditions for the white-dwarf evolution.

Recent developments in the studies of the transport processes and the neutrino emission processes in the interior of white dwarfs are reviewed. Special emphasis is placed upon the accuracy of the calculations. Ionic correlation effects play an essential role in the transport processes and the neutrino bremsstrahlung process. The Weinberg-Salam theory is the basis for the calculation of the neutrino emission processes.

Detailed evolutionary calculations show that Coulomb interactions between the charged particles of a stellar plasma reduce the core mass at which a low mass red giant undergoes the helium flash (contrary to a recent claim). This has implications for the determination of the rate of mass loss from red giants.

The usual approach to the problem of the Equations Of State (EOS) for White Dwarfs and super giant Planets, under the conditions of high densities and low temperatures, faces two problems.

The first has to do with Pressure Ionization : the energy levels of the electrons in the case of extreme pressure ionization cannot be treated in the same way as the energy levels in a single isolated atom. The simple treatment of pressure ionization, in which the level of the continuum is reduced by an amount equal to the electrostatic energy, leads to problem because the number of energy levels, entering the Saha equation (partition functions), is not conserved, also the usual approach may lead to absurd results in which ions recombine as the density increases.

Massive star (M ≥ 10 M ) core collapse is the standard mechanism for neutron star formation (see Brown 1988 for a recent review). It has long been realized (see, for instance, van den Heuvel 1988, and references therein) that the neutron stars found in different types of binary systems cannot come from such a standard mechanism. Those systems include wide binary radio pulsars, millisecond pulsars (not in wide binaries), galactic bulge X–ray sources (including QPO’s), type I X–ray burst sources and X–ray transients, andγ–ray sources. Formation of those neutron stars is now widely attributed to the gravitational collapse of a white dwarf, growing above Chandrasekhar’s limit by mass accretion from the current neutron star’s companion in the binary system (Canal and Schatzman 1976; Canal and Isern 1979; Canal, Isern, and Labay 1980; Miyaji et al. 1980). Mass growth up to dynamical instability means that both explosive ejection of the accreted layers and explosive disruption of the whole star must be avoided. The former is associated with the nova phenomenon. The latter, with the occurrence of type I supernovae.

Through the use of accreting binary systems, it is possible to study the effects of the deposition of matter and energy on the surface of a white dwarf. The observed atmospheric properties of composition and temperature obtained from direct observation of the spectral lines and the continuum flux can be used to compare with those of single white dwarfs to understand the consequences of mass accretion on binary evolution.

Cataclysmic variables provide one of the best targets for this type of study because a) the primaries are all white dwarfs b) the level and the timescale of the accretion cover a large range from the high rate, relatively steady novalike accretors to the dwarf novae systems which are modulated on short timescales in a quasi-periodic manner. Unfortunately, due to the mass transfer process, an accretion disk builds up to the point where its radiation overwhelms the white dwarf light in most cases. Thus, to study the effects on the stellar primary, systems must be found which have low mass transfer rates (generally the short orbital period systems (Patterson 1984)) and/or high inclinations (since most of the disk flux emerges perpendicular to the plane of the disk). The best identification of the white dwarf emerges from IUE spectra which show a broad Lyman α absorption profile (in contrast to the normal emission lines from a disk at quiescence). The shape of this profile provides a sensitive indicator of the temperature and gravity. In some cases, broad absorption lines are also evident in the optical Balmer lines, although the broad emission lines from the disk usually make these difficult to detect. The steeply falling flux distribution of a white dwarf throughout the optical region, combined with a flat disk distribution usually means that the white dwarf contributes a minor amount to the optical flux. However, in the ultraviolet, the rising energy distribution of the white dwarf easily dominates the falling energy distribution of a low accretion rate disk (Mateo and Szkody 1984). White dwarfs are generally acknowledged to be prominent in the dwarf novae U Gem (Panek and Holm 1984), VW Hyi (Mateo and Szkody 1984) and Z Cha (Marsh, Horne and Shipman 1987) and suggested in EK TrA and WZ Sge (Verbunt 1987). In addition, the white dwarf has been seen in some novalike systems which sporadically turn off their mass transfer, (resulting in the disappearance of most of the disk and the resulting appearance of the white dwarf). This has been the case in TT Ari (Shafter et al. 1985) and some limits have been determined for MV Lyr (Szkody and Downes 1982) and V794 Aql (Szkody, Downes and Mateo 1988). Several magnetic white dwarfs have also been seen when the mass transfer ceases in the AM Her systems (summarized in Szkody, Downes and Mateo 1988).

The variable white dwarfs repeatedly force theory to conform to their observed properties so that further progress can be made in understanding the structure and evolution of all white dwarfs. We use the term “understanding” in a loose sense here because, as we will show, both observational constraints and interpretation of the observations vis-à-vis theory contribute to uncertainties in our understanding at this time. In any case, recent progress in this field (sometimes called white dwarf seismology) has provided some fascinating insights into the evolutionary and structural properties of white dwarfs and their progenitors. This short review is our attempt to describe recent progress made in the interaction of theory with observations.

The history of our galaxy and the detailed history of star formation in the early universe is written in the white dwarf stars. Recently we have learned how to reach beneath their exposed surfaces by observing white dwarfs that are intrinsic variables. We use the stellar equivalent of seismology to probe their interiors, and thus to unravel the history they hold inside. We have designed and placed into operation an observational technique that uses the whole earth as a telescope platform, defeating the effects of daylight which, until now, had seriously limited the length of a single light curve, and therefore the amount of information we could hope to extract from it. This paper describes our new telescope and presents preliminary results from our first observing run in March, 1988.

We have investigated the effects of relaxing the normal assumption of frozen in convection on studies of radial instabilities in 0.6M⊙ carbon-oxygen white dwarfs with either pure hydrogen layers overlying pure helium layers or 0.6M⊙ carbon-oxygen white dwarfs with pure helium surface layers. In this paper we assume that convection can adjust to the pulsation at a rate determined by the time scale of a convective eddy. Using this assumption in our analysis stabilizes most of the modes in both the DA and DB radial instability strips. We also find that the blue edge of the DA radial instability strip, assuming frozen in convection, is between 12,0O0K and 13,000K. The blue edge for the DB radial instability strip (frozen in convection) is between 32,000K and 33,000K.

PG 1707+427 was identified in the Palomar-Green survey (Green Schmidt and Liebert, 1986) as an object with a significant ultraviolet excess. Observations by Bond and Grauer in 1982 showed it to be a pulsating variable (Bond, Grauer, Green and Liebert, 1984). Fourier transforms of the discovery time-series photometric runs revealed power in PG 1707+427’s light curves in two bands with periods near 450-s and 333-s. The longer period peak was observed to have a variable amplitude while the other one appeared relatively constant in strength. Wesemael, Green and Liebert (1985) placed PG 1707+427 in the spectroscopic class of PG 1159–035 (DOV) pulsating variables.

Spectrophotometry, BVRI CCD photometry and CCD trigonometric parallaxes of the southern DC stars vB3, ER8 and ESO 439-26 are presented. These stars should be considered among the lowest luminosity degenerates known, with absolute visual magnitudes of 15.4, 16.2 and 17.2 respectively.

Spectrophotometry of the common proper motion pairs ES0439-162/163 and ESO440-55a/55b shows that the first is formed by an mv =18.8 magnetic DQ white dwarf and an mv = 19.8 DC9 white dwarf separated by 23”. ESO440-55a/55b has an mv = 20.2 red dwarf (ST=M5.1) component and a DZ7 white dwarf with mv = 19.3, their angular separation being The proper motion of the pairs is μ=0.38±0.03”/year and μ=0.22±0.04”/year respectively.

The Palomar Green survey (Green et al., 1986) of faint blue, high galactic-latitude objects, turned up several interesting new classes of objects, such as gravitational lenses (Weyman et al., 1980), the ultra hot star H1504+65 (Nousek et al., 1986), and the PG 1159-035 variables (McGraw et al., 1979). The PG survey forms a mainstay in the investigations of late stages of stellar evolution. Work (Flemming et al., 1986) has already cast light on the important question of the space density of DA’s and continuing work is seeking values for similar population parameters for the subdwarfs: Evolutionary links between the subdwarf stage and white dwarfs will thereby be illuminated.