In a recent paper (Richer 1978, hereafter Paper I) the results of a search for faint blue objects in and around the globular cluster NGC 6752 were reported. The aim of the program was to isolate a sample of white dwarf candidates in this cluster which could then be studied in further detail. The plate material for this survey consisted of a set of deep UBV plates (only one in each color) obtained at the prime focus of the Cerro Tololo Interamerican Observatory 4-meter telescope. Limiting magnitudes reached by the plates were about U=22.4, B=23.0, V=22.0. A reanalysis of the photometry presented in Paper I (using a reduction program supplied by W. Harris [see Stetson and Harris 1977]) has now yielded a total of 68 candidate objects within 20′ of the cluster center having B≤22.7 and (U–B) ≤ –0.4. Although the accuracy of the photometry is low (about ±0.2 magnitudes), it seems clear that the preponderance of the objects do not have UBV colors typical of white dwarfs. Of the 68 candidate objects, 36 had a measurable V magnitude, and only 11 of these lay in the area of the color-color diagram known to be occupied by white dwarfs (Eggen and Greenstein 1965). The remaining 25 were generally well above the black body line in the two-color diagram and are probably QSO’s or peculiar blue stellar objects. Among these 11 good candidates, 7 are within 14’ of the cluster center and hence have a probability of greater than 50% of being cluster members according to the star counts of King et al (1968) assuming that white dwarfs have a radial distribution in NGC 6752 similar to other cluster members.

Close-binary central stars of planetary nebulae are of interest to participants in this Colloquium because of recent suggestions that the cataclysmic binaries, containing a white dwarf and a lower-main-sequence star, may be descended from such objects (e.g. Paczynski 1976; Ritter 1976; Webbink 1978; Meyer and Meyer-Hofmeister 1978; Livio, Salzman, and Shaviv 1979). The proposed scenario is. that a binary system of initially large separation (P.= 1-10 yr) forms a “common-envelope” binary after the primary has evolved to the red-giant stage and developed a degenerate core. The secondary star spirals inward inside the red-giant envelope, eventually transferring enough angular momentum to the envelope to eject it. The result is a close binary containing the hot degenerate core of the red giant and a cool main-sequence companion, surrounded by the ejected envelope, which is ionized by the hotter star. Much later, when the cool companion begins to evolve, it will start to transfer matter to the hot star (by now a white dwarf), and cataclysmic activity ensues.

In our previous papers (Tutukov, Ergma, 1979; Ergma and Tutukov, 1979) we have proposed a simple analytical method to investigate the thermal evolution of shells accreted onto the surface of a neutron star. We have used this method for investigation of thermal evolution of shells accreted onto the surface of a carbon-oxygen white dwarf.

It is now generally accepted that a nova outburst is caused by a thermonuclear runaway (TR) in the accreted hydrogen rich envelope of a carbon white dwarf. Over the past few years we have studied the evolution of such runaways and have shown that the calculated evolutionary sequences are in substantial agreement with the observations (Starrfield, et. al. 1978; Sparks, et. al. 1978). In the published work we have varied the white dwarf mass, the envelope mass, the accreted envelope mass, and the chemical composition in the envelope (Starrfield, et. al. 1976; Gallagher and Starrfield 1978). In all cases we find that a TR results in mass ejection and the luminosity variations of this ejected material can reproduce the observed light curves of the fast and slow novae.

It is now well known that an accreting white dwarf experiences a shell flash near its suface. Such phenomena are related with rekindling of white dwarfs, slow and fast nova explosions etc. depending on its strength. Though many authors computed evolution through such shell flashes, they treated them only under specific conditions.

When gas is accreted onto a carbon-oxygen white dwarf, a hydrogen shell-flash is triggered. Recently such phenomena are studied by many authors in relation to nova explosions and rekindling of white dwarfs. Unless all of the accreted gas is ejected by the process of the nova, a helium zone is formed as a result of hydrogen shell-burning. As the hydrogen shell-flashes recur many times, the helium zone grows gradually in mass. Then the helium shell-flash will be ignited as in the deep interior of ordinary red giant stars. We have investigated such process, simulating it by helium accretion at a constant rate. In the present paper we show that the helium shell-flashes result in a variety of strengths depending upon situations.

We assume that the outburst of classical novae is the result of transfer of H-rich material from a red secondary star to a He or C/O white dwarf and the development of a thermonuclear runaway in the e-degenerate “base of the accreted H-rich envelope. Based on these assumptions, we have investigated this problem in several stages of increasing theoretical complexity and physical realism.

In this paper we discuss the third stage of our research on the nova outburst as described in the preceeding paper (Kutter and Sparks, page 290), i.e. we accrete hydrogen-rich material (normal solar composition) with Keplerian velocity onto a helium white dwarf at a rate of 10-8 M⊙/yr. When material with high angular momentum from a circumstellar disk is accreted onto a white dwarf with negligible angular momentum, a tremendous shear instability is created, and hydrogen-rich material is mixed with helium-rich material of the white dwarf on a scale that is short compared to the accretion time scale. Following Kippenhahn and Thomas (1978), we assume that in the mixing region marginal stability is established. Mathematically this is expressed by setting the Richardson number (the ratio of the work done against buoyancy to the kinetic energy of the turbulence) equal to ¼.

The first magnetic field in a white dwarf was discovered nine years ago (Kemp et al. 1970). Since that time magnetic fields have been detected in a total of 12 single white dwarfs and four white dwarfs in close binary systems. These magnetic fields have been found both through the Zeeman splitting and shifting of spectral lines and through the continuum circular (and sometimes linear) polarisation which a field may produce in the optical flux of a star in which it occurs. The fields so far detected appear to range between 3 MG and more than 100 MG. For stars with fields less than about 40 MG, both the observed Zeeman shifts of spectral lines and the observed circular polarisation appear to be reasonably well understood. For stars with fields above this level, attempts so far to identify absorption features in the spectra and to account for the continuum polarisation have not been very successful; indeed, there is considerable dispute about the fundamental mechanism producing the continuum polarisation, especially the linear component.

Work in progress at Steward Observatory covering three aspects of magnetism in degenerate dwarfs is reviewed. First, the identification of the Minkowski bands in Grw + 70° 8247 with Zeeman transitions in hydrogen. Second, a determination of field strengths in the more strongly magnetic white dwarfs. Third, some observations and speculations concerning the origin of white dwarf and neutron star magnetic fields.

The Zeeman theory of hydrogen and neutral helium lines is used to analyse the spectrum of the magnetic DBA white dwarf Feige 7. On the assumption of a centered dipole field distribution and a uniform chemical composition, the atmospheric helium to hydrogen ratio by number, , is found to be ~ 102. However, it is argued that either one, or both of these assumptions are likely to be in error.

Garstang and Kemic (1974) derived formulae for the splitting of hydrogen and helium lines in the presence of large magnetic fields. We applied their method in calculating the eigenvectors for some transitions of neutral carbon, where a correction factor for the coupling and mixing of the energy levels has to be applied. For CI – lines in the visible region of the spectrum, well separated components can be expected for a field strength up to 2 • 107G. Fig. 1 shows the splitting of three lines for B = 107 G.

The 4 known AM Her stars or polars (AM Her, ANUMa, W Pup, and 2A0311-227) are characterized by large circular polarizations of 10-35%, (Tapia 1977a, b, Krzeminski and Serkowski 1977), an emission line spectrum with strong H and He lines (Crampton and Cowley 1977, Greenstein et al. 1977), complex photometric variations (Szkody 1978, Priedhorsky and Krzeminski 1978, Warner & Nather 1972), long term high and low states and short orbital periods (80-180 min.). Models of these systems envision a close binary containing a magnetic white dwarf primary (B ~ 108G) and late type main sequence secondary transferring material into an accretion funnel over one or both poles of the white dwarf (Stockman et al. 1977, Lamb & Masters 1979, Liebert et al. 1978).

VV Puppis, a dwarf-nova binary with a 100 min period (Herbig 1960) was observed on two occasions. On 2nd February 1979, VV Puppis was in a faint inactive state. On the other hand it was bright and active on 14th June 1979. Spectral and polarimetry observations were made on both these occasions using IDS (modified as polarimeter) at the f/15 Cassegrain focus of the 4 meter Anglo-Australian Telescope. Spectral range covered was from 3600 Å to 7000 Å with a resolution of 10 Å. The star and sky apertures both were of size 3 × 4 sec of arc and 40 sec apart.

Most theoretical models of the AM Her variables (AM Her, AN UMa, W Pup and 2A0311-22) rely on strong cyclotron emission at the fundamental cyclotron frequency and higher harmonics to produce the observed, strongly-polarized optical continuum (e.g. Lamb and Masters 1979). The cyclotron lines, which presumably originate in the hot, isothermal accretion shock at the surface of the white dwarf (kT ≳ 10 keV, h/R* ≲ 0.1), should be blurred into a continuous spectrum by both optical depth effects and electron Doppler broadening. Thus the lack of even weak cyclotron features in the optical spectra of these objects is still compatible with a cyclotron origin.

There has been considerable interest recently in the AM Herculis binaries, which are believed to contain a strongly magnetic white dwarf accreting matter from a lower-main-sequence companion (Tapia 1977, Chanmugam and Wagner 1977, Stockman et al. 1977). Models for these systems feature an accretion column above a magnetic pole of the white dwarf. A shock-heated region, with a temperature kT ≈ 20 keV (Raymond et al. 1979) and a height h – 106cm (Masters 1978), believed to be formed in AM Her just above the magnetic pole is likely to be responsible for the emission of the hard X-rays observed (Swank et al. 1977). It has been further suggested that this region should emit optically thick cyclotron emission in the ultraviolet because of the presence of the strong magnetic field ~ 108 gauss (Masters 1978, Lamb and Masters 1979). Such UV emission has not been observed (Raymond et al. 1979).

The ZZ Ceti stars are the pulsating white dwarfs lying within a narrow instability strip, extending in temperature from 13,500 to 10,500 K, on the white dwarf cooling sequence. That white dwarfs should be pulsationally unstable cannot be considered surprising, since theoretical investigations of white dwarf pulsations began at least as early as 1949 (Sauvenier-Goffin 1949). As the predicted pulsation periods demonstrate, however, the nature of the pulsations was not correctly foreseen. With very few exceptions (e.g. Harper and Rose 1970) the early investigations assumed that the most likely pulsations to be excited were radial pulsations. Thus, the calculated periods were quite short, typically 2-10 seconds. The first of the pulsating white dwarfs actually to be observed was HL Tau-76 (Landolt 1968). A portion of its light curve is shown in Figure 1. The typical interval between successive pulses is about 750 seconds, not 2-10 seconds. This is a serious discrepancy, and one that exists for all of the ZZ Ceti stars discovered since HL Tau-76. Clearly, then, the observational data requires us to modify our understanding of pulsating white dwarfs. A considerable body of this observational data now exists. The purpose of the present paper is to present the data, and to show that it provides a reasonably coherent picture of the pulsating white dwarfs.

Attention is focused on those aspects of the theory that may be relevant in understanding the nature of ZZ Ceti-type variable white dwarfs. Recent calculations show that the opacity mechanism can drive a large variety of oscillation modes, including the ones that fit observed periods. An estimate of nonlinear effects shows that resonant mode coupling plays a dominant role in determining the finite amplitude behaviour of oscillations and is also probably responsible for rapid amplitude changes observed in these variables.

Spectra of seven ZZ Ceti DA variables have been obtained with the multichannel spectrophotometer, several also with 7 Å resolution with the SIT digital spectrophotometer, one with the IUE. The colors fit hydrogen model atmospheres well; the combined IUE and MCSP energy distribution of G29-38 show no peculiarity from 10,000 to 2000 Å. Hydrogen model atmospheres yield <log T> = 4.073±0.008; the dispersion is σ = ±0.02, quite near the total observational and model-fitting error. Using an estimate of the intrinsic 2σ as a half-width the instability strip for hydrogen degenerates lies at 11,800±600 K (for log g = 8). This applies, of course, only to the northern ZZ Ceti stars observed. Another measure of how normal these variables appear is the equivalent width of Balmer lines, which are normal for that T, and are at the line-strength maximum (estimated for log g = 8.2). Possibly the mean Hα is slightly strong; since the Balmer jump is also at maximum strength, a slightly anomalous low boundary temperature might be present. This is also suggested by marginally more positive U-B color for their G-R (or larger log g). I have counts from MCSP data giving the frequency of 162 DA effective temperatures. The ZZ Ceti stars represent 7 of 27 stars in the bin ±0.05 wide in log T centered on 4.05. They are a substantial fraction, but not necessarily all, stars at that temperature. An attempt to observe Ha emission with the Boksenberg IPCS at the Palomar coudé failed for lack of photons.