Bump masses and radii are derived for 18 BL Her stars from the observed bump phase and the accurately known fundamental period. The mean mass M/M⊙ = 0.60 ± 0.09 agrees precisely with predictions from standard stellar evolution theory and gives a new test of the theoretical models. The derived radius of V553 Centauri is in good agreement with the radius recently determined by an independent modified Baade-Wesselink method by Balona. Finally, a preliminary discussion of possible continuations of the BL Her bump progression is given.

BL Her Stars are primarily Population II Cepheids with periods between one and three days. On the H-R diagram they are about 1mbrighter than the RR Lyrae variables but below the W Virginis variables. They are not as blue as the so-called anomalous Cepheids. Typically these stars are metal deficient, but notable exceptions are the prototype BL Her and V553 Cen with solar type abundances (Smith, et al. 1978). Their evolutionary status given by Sweigart and Gross (1976) puts them on the immediate post-horizontal-branch stage with energy supplied by both He and H burning shells.

A theoretical counterpart to the Barnes-Evans relation between stellar surface brightness and V-R color has been calculated from model atmospheres for parameters appropriate to RR Lyrae stars. Such a relation can be used to derive stellar angular diameters from V,R photometry and, when applied to variable stars and combined with a radial velocity curve,, to derive radii, distances, and absolute magnitudes by the method of Barnes et al. (1977, MNRAS,178, 661). This was done for RR Lyr and X Ari using the photometry of Moffett and Barnes (1980, private communication) and radial velocities from the literature. The resulting absolute magnitudes are <MV> ± + 0.59 + 0.25 for X Ari and <MV> = 0.61 + 0.35 for RR Lyr. The method is shown to be a very accurate way of determining radii, distances, and absolute magnitudes for RR Lyrae stars which compares very favorably to the variations of the Baade-Wesselink technique currently in use.

On the basis of a frequency analysis of light variations of AR Her a double-mode pulsation is proposed as an explanation of the Blazhko effect. The analysis revealed a number of components, which can all be interpreted as a result of nonlinear superposition of the fundamental mode, and a mode with period P = 1/(2/P0 + 1/PB) ~ P0/2, where P0 = 0d.470 and Pb = 31d.55 denote the fundamental and the Blazhko effect periods, respectively.

The P ⋍ P0/2 mode can be identified as the second or the third radial overtone. In both these cases the “beat” masses derived from a comparison of the calculated (nonadiabatic) and observed period ratios for RR Lyrae variables with Blazhko effect are different from their evolutionary masses.

The Cepheid-like pulsations of some of the R CrB stars should in principle make it possible to determine their masses and hence to place constraints on possible evolution scenarios. We briefly review the evidence for these pulsations and discuss the problem of how these low-mass, hydrogen-deficient carbon stars could have evolved to their present position in the H-R diagram. Linear and nonlinear pulsation calculations are reviewed. It is found that for these large luminosity to mass ratio (L/M) stars a region of pulsation instability extends considerably hotter than for normal high luminosity Cepheids. The envelopes of these models are so nonadiabatic that the identification of modes becomes very difficult since there is frequently no clearly defined nodal structure. For the most extreme L/M cases it is found that the models are unstable in the sense that they appear on the verge of ejecting the outer layers.

The radial pulsations of very luminous, low-mass models (L/M ˜ 104, solar units), which are possible representatives of the R CrB stars, have been examined. These pulsations are extremely nonadia–batic. We find that there are in some cases at least one extra (“strange”) mode which makes interpretation difficult. The blue instability edges are also peculiar, in that there is an abrupt excursion of the blue edge to the blue for L/M sufficiently large. The range of periods of the model encompasses observed periods of the Cepheid-like pulsations of actual R CrB stars.

Recent developments in the physics input for iron core collapse models of type II supernovae are reviewed. The effect of these developments on collapse calculations is also discussed. The inner core collapses homologously, with little change in specific entropy, bounces in the neighborhood of nuclear density, and sets up; an outward moving shock. In adiabatic models an explosion may result. The inclusion of neutrino effects may produce substantial shock damping. Current results indicate that core collapse, bounce and shock propagation does not produce an explosion when neutrino effects are included.

A brief description of the current state of knowledge for Type II light curves is given, including discussion of some of the remaining problems. The use of supernovae of both types as independent distance indicators is outlined and difficulties are pointed out. A summary of new ideas regarding the origin of Type I light curves is presented.

To date, most of the hydrodynamic calculations that have followed the details of the physics during an iron core collapse (see Bowers, these proceedings, for a review) have been restricted to spherical symmetry and therefore have neglected the role that rotation may play in the hydrodynamics of the collapse (see, however, LeBlanc and Wilson, 1970). If rotation is important, the core will flatten to an oblate spheroidal shape allowing some loss of energy through gravitational radiation; the core could conceivably, dynamically evolve to a toroidal configuration, as has been observed in some models of rotating protostellar clouds (Tohline, 1980b; Boss, 1980b and references cited therein); and it may, through a rotational instability, eventually evolve into a non-axisymmetric structure. It is important to know just how much rotational energy must be present in the pre-collapse core in order for these, or any other significant deviations from spherical symmetry, to become important considerations during a core collapse.

Supernova mechanisms in accreting white dwarfs (WDs) are presented, i.e., the carbon deflagration as a plausible mechanism for producing Type I supernovae and electron captures to form quiet supernovae leaving neutron stars. These outcomes depend on accretion rate of helium, initial mass and composition of the WD. The various types of hydrogen shell-burning in the présupernova stage are also discussed.

A two dimensional hydrodynamic study indicates that convectively unstable gradients which develop during core collapse and bounce give rise to large scale core overturn. It is also shown that the concomitant release of neutrini can deposit large amounts of energy and momentum in the infalling envelope and give rise to a powerful supernova explosion.

One-dimensional hydrodynamic calculations have been done of 1E51 erg explosions in 15M⊙ stars. We have appended a steep external density gradient to the pre-supernova model of Weaver et al and find: (1) the outer shock wave decelerates throughout the pre-Sedov phase, (2) the expanding stellar envelope and the shocked interstellar material are Rayleigh-Taylor stable until the Sedov phase, and (3) steep internal density gradients are R-T unstable during the early expansion and may be the source of high velocity knots seen in Cas A.

With the help of a very simple two zone model, we demonstrate the possibility of periodic thermal relaxation (limit cycle) oscillations in the helium burning envelope of accreting neutron stars. Physically reasonable model parameters can be chosen which yield agreement with the observed features of x-ray bursts and we suggest that this limit cycle is operative in neutron stars which have an accretion rate in a specific range. For hydrogen burning a similar cycle is possible, but it operates at such high temperatures that an unrealistically large accretion rate would be required.

It has been suggested by several authors (e.g., Harwit and Salpeter, 1973) that the observed cosmic gamma-ray bursts might be produced by the collision of comet or asteroid-sized bodies with a compact object. Colgate and Petschek (1980) have discussed the tidal breakup of a solid body approaching a neutron star in central impact, with particular application to the cosmic gamma-ray burst of March 5, 1979. In this work we present the results of simplified one-dimensional hydrodynamic-radiation diffusion calculations of such an occurence.

Mass-accreting carbon-oxygen white dwarfs become thermally and dynamically unstable when they reach high enough central densities. Carbon ignition at the star’s center likely propagates subsonically and, in the case of an initially solid core, leads to collapse if the rate of increase of the core’s mass is sufficiently fast. Recent results indicate, however, that solidification of the core induces carbon-oxygen separation. The central regions are then made of pure oxygen while carbon is rejected to lower-density layers. Carbon ignition happens only after neutronization of the central (oxygen) regions. Collapse to a neutron star is then independent from the rate of mass increase and the only possible restrictions are set by the behaviour of the outer, accreted layers. X-ray sources, pulsars and Type I supernovae are likely outcomes of this process.

The DA white dwarfs are those which show only the Stark-broadened lines of hydrogen in their spectra. They comprise about 80% of the total white dwarf population. A subset of the DA dwarfs, the ZZ Ceti stars, form a highly homogeneous class of nonradially pulsating variable stars. In this paper we shall review the observations from which both the physical properties of the stars and the characteristics of the pulsations have been derived. Data obtained since the last review of these variables (Robinson 1979) is stressed, as these data are forcing a somewhat revised understanding of the ZZ Ceti stars and their relationship to investigations of white dwarfs and to pulsating variable stars, in general.

The importance of the ZZ Ceti stars, and indeed the importance of all pulsating stars, derives from the fact that stellar pulsations probe the interiors of stars, and thus they test directly our models of stellar interiors and stellar evolution. The relative value of stellar pulsations as such a probe depends on, among other factors, the number of pulsation modes simultaneously excited in a star, as each additional mode depends on and constrains the properties of the star in a different way. Judged by this criterion, the pulsations of the ZZ Ceti stars should be unusually valuable because all ZZ Ceti stars are multi-mode variables. For example, among the ZZ Ceti stars with well studied light curves, the one with the fewest modes is R548 (= ZZ Ceti itself) with 4 pulsation modes simultaneously excited (Robinson et al. 1976), while some of the other ZZ Ceti stars can have dozens of pulsation modes simutaneously excited (cf. Robinson 1979).

A completely new kind of variable star has recently been discovered (McGraw, et. al. 1979). Designated as PG1159-035 (hereafter PG) this star is distinguished not only by the complete lack of hydrogen in its spectrum but also by an effective temperature that exceeds 8 × 104 K (McGraw, private communication). The photometric data show that this star is pulsating with two periods - 539 seconds and 460 seconds and the light curve is very reminiscent of that of a ZZ Ceti variable star (DA white dwarfs pulsating in non-radial modes). However, its spectral characteristics show that it cannot be included in this class since analysis of both optical and IUE spectra show that the major atmospheric constituents are probably helium and carbon and that its surface gravity is considerably lower than 108 cm sec−2 characteristic of a DA white dwarf. Its energy distribution suggests a small amount of reddening and since it is far out of the plane it must be at a distance at least 1 kpc. This estimate is supported by a null proper motion over a 13 year baseline (Luyten 1979, private communication to J Liebert). These data suggest that its luminosity exceeds 10 L⊙. In any case, it would need a luminosity as large as 10 L⊙ to fall on or above the white dwarf cooling curve at Te = 8 × 104 K (Lamb and Van Horn 1975). All of these facts suggest strongly that this star is unique and a new kind of pulsating variable.

The thermodynamic transport properties of special relativistic imperfect fluids, as found in dense stars, are investigated. These properties, which include thermal and electrical conductivities, electrothermal coefficients, and bulk and shear viscosities may be formulated in terms of the momentum distribution functions obtained from the solution of the Boltzmann transport equation. Spherical harmonic solutions of the relaxation form of the relativistic magnetic Boltzmann transport equation have also been obtained which give the non-equilibrium momentum distribution function perturbation f-f(0) = Δf(p) in terms of electromagnetic and thermal fields.

Over the past few years, significant advances have been made in our understanding of the nova outburst. The theoretical studies have shown not only that a thermonuclear runaway in the envelope of a white dwarf reproduces the gross features of the nova outburst (c.f.; Starrfield, Sparks, and Truran 1978, Sparks, Starrfield, and Truran, 1978, Gallagher and Starrfield 1978), but also made important predictions regarding the observed behavior of the outburst itself. The observational studies have provided us with new data concerning the evolution of the bolometric light curve of a nova during outburst, the elemental abundances in the ejecta, the formation of dust during the outburst, and the structure of nova binaries (c.f., Gallagher and Starrfield 1978).