Supernovae occur in highly evolved, massive stars and typically release 1051 to 1052 erg. Their light curves show that the stellar radius is about one A.U. at the time of the explosion. The typical energy density in the star is about 1011 or 1012erg cm-3 when the blast reaches the stellar surface. Much of the energy is present in thermal form. Since the density of the material is high, thermal equilibrium is attained rapidiy between the radiation field and the thermal motions. The temperature in the interior of the star becomes about 106K, and most of the energy is present in the form of radiation.

At this time the star has a large optical depth, of order 107. Therefore the effective diffusion speed for radiation is very low, about 3000 cm s-1. But the effective sound speed is large, of order 109 cm s-1, and the large input of energy has destroyed the gravitational equilibrium. So the star begins violently to expand, and the pressure of the stored radiation field does work in producing mass motion of the material. Only a small fraction of the radiant energy is released from the exploded star. The photosphere, in this phase, lies in the region where the gas changes from being ionized to non-ionized, so that the photo-spheric temperature remains low, of order 104K. There is little chance of observing any high-temperature phenomena at this stage in the evolution of a supernova.

Observations of Lyman-α absorption show that any gas present in the space between clusters of galaxies must be hot, and x-ray observations indicate that there may be present gas whose temperature at low redshifts is 4 × 108 K and whose density is about half the critical value for cosmology. The interpretation of these observations is reviewed, and difficulties with proposed heating mechanisms are emphasized.

The discovery of extended X-ray sources associated with clusters of galaxies which resulted from the Uhuru X-ray sky survey was one of the most important observations to come from that programme. Following Uhuru, the Ariel V and HEAO-1 sky surveys have found many more cluster X-ray sources and the recently launched Einstein observatory has begun to increase further the number of identifications. However there is in any case evidence from the X-ray cluster luminosity function that all rich clusters of galaxies will emit X-rays at some level.

Preliminary results from the Einstein observatory (Murray, 1979) suggest that the extended X-ray emission from centrally condensed (cD) clusters is itself centrally condensed and spherically symmetrical in appearance. However irregular clusters have non-uniform X-ray surface brightness distributions. In addition there are some galaxies in clusters of irregular morphology that have associated X-ray halos.

Acceleration in astrophysics usually means converting a significant fraction of the energy of some source into particles whose individual kinetic energy greatly exceeds the average temperature of the medium. There are three general classifications of acceleration processes. The first is hydrodynamic, second coherent electromagnetic, and third stochastic electromagnetic processes. We shall discuss each of these briefly in terms of the spectrum of accelerated particles. This can be related to an efficiency by the relationships N(>E) α E┌ or an energy efficiency N(>E) α EI-г In astrophysics we frequently emphasize Г without realizing the constraints this imposes upon the efficiency of the acceleration mechanism. So often the relatively flat spectra result in efficiency requirements that challenge the ingenuity of those who wish to invent acceleration mechanisms.

At this time we have no direct evidence for the presence of hot gaseous haloes or winds associated with galaxies. We do know that hot gas exists in conjunction with cold gas in the disks of the spirals and that this gas is hot enough to form a substantial corona. There are also a number of indirect observations which would suggest that hot gas flows and possibly bound hot gas occur in both elliptical and spiral galaxies.

In the case of elliptical galaxies the expected accumulated mass loss from the stars is not observed. Typical upper limits to the mass of cold gas at less than 1040K are around 108 M based on 21cm emission studies of the galaxies (reviewed by Van Woerden 1977). We would expect almost two orders of magnitude more material than this to have been ejected from the stars. Burke (1968), Johnson and Axford (1971) and Mathews and Baker (1971) postulated the existance of a hot galactic wind with temperatures of a few times 1060K powered by supernovae, in order to clear material from these galaxies. The evidence for hot galactic haloes around spiral galaxies is even more indirect and is based on the existance of high latitude cold clouds in our own galaxy. The velocities and number of these clouds imply that they almost certainly lie high above the galactic cold gas which extends only to a height of 130 Fc in the solar neighborhood. Spitzer therefore suggested in 1956 that an intercloud gas would have to exist to keep these clouds confined, and that to have such a large scaleheight it would have to be hot with temperatures of around 1060K. (An alternative suggestion by Pickelner (1955) was that the halo was cold but supported by turbulent velocities of around 70 km s-1.) The Spitzer Halo was assumed to be maintained by energetic particles from SN in the plane.

The standard theory of stellar coronae requires the presence of vigorous surface convection. In consequence, the expectation of such a theory is that stellar x-ray emission — if due to a corona — should be limited to a subset of stars (principally those of main sequence spectral types F and G), and therefore should be relatively rare. This theory also makes detailed predictions about coronal heating, which are subject to test if spatially resolved coronal data are available. We are now in a position to subject the standard coronal scenarios to observational scrutiny on both counts: Skylab and later observations have supplied us with spatially resolved data of the solar corona, while the succession of high-energy x-ray astronomy satellites, culminating with EINSTEIN, now gives us a long-awaited glimpse of stellar x-ray emission throughout the K-R diagram.

I will maintain that these new data imply that coronal x-ray emission dominantly derives from plasma structure confined by stellar surface magnetic fields; that coronal heating is likely to be non-acoustic in character and involves the confining magnetic fields; that stellar x-ray emission is not well correlated with the level of surface convection activity. These results of course cast serious doubt upon the viability of the standard theory of stellar coronal formation. In the following, I will try to very briefly summarize the solar and stellar data, to present the context in which they were initially obtained, and very briefly sketch the new coronal picture we are pursuing. The results presented here are excerpted from lectures presented by R. Rosner and myself recently at Erice, Italy (viz. Vaiana 1979) and from the preliminary results of the EINSTEIN Stellar Survey (Vaiana et al. 1979). The latter, part of a larger effort in x-ray astronomy led by R. Giacconi, involves the work of many people, including F.R. Harnden, L. Golub, P. Gorenstein, R. Rosner, F. Seward, K. Topika at CFA, as well as a number of EINSTEIN guest investigators.

Aside from violent phenomena, regular forms of motions originate often in instabilities and the linear theory with terms ∞ exp (st) yields already significant information. The system, here a spherical star, will be the seat of an instability if R (s) > 0. In general, s will be complex as both conservative (adiabatic) and non-conservative (non-adiabatic) factors are present. However if the latter (small) are neglected, the eigen-values s2 often denoted -σ2 are real. If at least one σ2 < 0, then the star is dynamically unstable.

Radial perturbations. If an appropriate average value Γ1 > 4/3, then all σ2 are positive. If Γ < 4/3 (formation phase: ionization; late evolution: nuclear equilibrium; degeneracy in white dwarfs and neutron stars or radiation in very large masses plus general relativistic effects) the fundamental eigenvalue of only becomes negative.

The relation between a linear series and thermal (i.e. secular) stability of stellar models is discussed. Models of accreting degenerate dwarfs are considered as an example of transition from instability to stability. This transition occurs while the accretion rate increases. Such models are relevant for novae and symbiotic stars.

I shall limit this presentation to the secular i.e. thermal instabilities of stellar models in the hydrostatic and thermal equilibria. The time dependence of a small perturbation of an equilibrium model is assumed to be exponential, but the eigenvalues do not have to be real. In general they are complex. That means that thermal instability, if present, may either lead to an exponential growth of a perturbation, or may lead to oscillations with a growing amplitude. The complex nature of the eigenvalues makes a search for them difficult and no general prescription is available for a search to be complete and successful. However, a search for real eigenvalues is much easier. Some information about the presence of purely exponential modes may be achieved even without searching for them by means of calculating a linear series of stellar models. I shall describe this concept in this communication.

In this review we discuss the problems raised by the discovery that the sun was, in the past, unstable towards non-radial oscillations.

In 1972, Fowler (1972), in an attempt to explain the low-neutrino flux measured in Davis’ experiment (now 1.6 snu, while the standard solar model predicts 4.4 snu) suggested that the sun could have undergone, some 10 years ago, a change in structure because of sudden mixing of the inner core. During the same year Dilke and Gough (1972) suggested the sun is unstable to low-order gravity modes (g+ modes) of non-radial oscillation and that the mixing is triggered when the amplitude of the oscillation becomes large enough.

Shell flashes will be discussed here with regard to three different stages of evolution: 1. normal stars, 2. white dwarfs accreting H-rich matter and 3. neutron stars accreting matter.

A shell flash Is a thermal instability, a nuclear run-away process, occurring in any nuclear burning shell, as long as It is sufficiently thin in geometrical extent and sufficiently thick for a high enough heat capacity. (in contrast to the off-center helium shell flash, another kind of shell flash which occurs for degenerate matter, the shell flash discussed here does take place for an Ideal gas including radiation pressure and does not require degeneracy.) The first shell flash discovered was the helium shell flash, about 15 years ago, by Schwarzschild and Härm (1965); Hayashi, Hoshi, and Suglmoto (1965); and Weigert (1965, 1966).

There have been several interesting developments during the last year with regard to global oscillations of the sun. However, because of the very full program of this Joint Discussion and the resulting tight schedule, only one point will be addressed here: the observational evidence for global oscillations of the sun with periods ≤ 1 hr and > 5 min.

The most decisive test currently available for identifying global oscillations is their examination for coherence of phase over an extended period of time. This test discriminates against both nonsolar phenomena, such as effects caused by observing through the earth’s atmosphere, and solar phenomena which occur in the frequency range of interest but which are not global oscillations of the sun. The search for this coherence has been conducted using 2 sets of observations from SCLERA, the 1973 observations of Hill and Stebbins (1975) and the 1978 observations described by Caudell et al. (1979). The results of these examinations strongly support the interpretation of the reported oscillations as solar in origin and as global in character.

The above observations consist of time chains of diameter measurements made at SCLERA. A list of references may be found in Hill and Stebbins (1975) and Hill (1978) which describe the telescope, the method for defining the solar diameter, the means of measuring the solar diameter, and the data reduction techniques used to produce the final Fourier transforms and associated power spectra of the diameter measurements.

Oscillations of the Sun with the period of 160m first observed in Crimea in 1974 and described in a set of papers by Kotov, Severny and Tsap (Severny et al. 1976, 1978; Kotov et al. 1978) were observed also by Brookes et al. (1976) and have been afterwards observed during the last three years in Stanford (Scherrer et al. 1979) and Kitt Peak (Snider et al. 1978). This fact excludes possible instrumental origin of the effect. Moreover, the phase coherence (after elimination of integer number of 160m-periods) between these four observatories makes the assumption of Earth atmospheric origin of the oscillations (Fossat and Grec 1978) very unlikely. Besides that, (1) the dependence of amplitude of oscillations on the phase of solar rotation and (2) slow, synchronous (at Crimea and Stanford) drift of the phase of maximum from year to year, pointing to a true period slightly higher 160m (160m 0.1), make the “telluric hypothesis” of the effect completely inconsistent.

Rather than review β Cepheids, this paper will address the issue that β Cephei variability is only a readily detectable tip of a much larger iceberg of variability among β stars. This variability being widespread, it becomes crucial to differentiate β Cepheids from other variable subgroups by observational criteria if one is ever to make physical inferences concerning the instability mechanism involved. Shobbrook (1978) has raised this point indirectly in discussing the importance of defining the width of the instability strip: if the strip is narrow, the pulsational instability is more likely to arise in the stellar core; if it is wide, it is probably excited in the envelope. Enormous efforts have gone into delineating the evolutionary and HR-D confines of ß Cepheids. In this paper it will be suggested that the situation is more complicated than the traditional outlook holds.

The excitation mechanism for the pulsations of β Cephei stars and variable B stars is not yet understood. Recently, Stellingwerf (1978) found that an opacity bump located near the He+ ionization zone has a significant effect on the stability of radial pulsations in massive stars. However, the opacity bump, according to current opacities, is probably not enough to excite radial pulsations. On the other hand, some observational facts suggest that nonradial pulsations may participate in the variations of β Cephei stars and variable B stars. Therefore, it is interesting and important to examine the effect of the opacity bump on nonradial pulsations in massive stars.

Delta Scuti stars are short-period pulsating A/F stars situated on or above the main sequence. They often pulsate with two more excited modes. The knowledge of the period lengths and period ratios is very important to deduce the nature of the pulsation modes, e.g. is the pulsation radial or nonradial? Furthermore, these values provide valuable information on the interior structure of these stars.

The determination of the period ratios from the light curves is difficult, since only a few cycles can be covered during a night. The small amplitudes of about 0.01 mag in some variables also makes the multiperiod analysis difficult. While every star should be considered on its own merit, a rough estimate of about 5 nights per deduced period appears to be a minimum requirement. Even then different analyses can give different results. A recent example is the star 38 Cnc (=BT Cnc). An excellent set of observations by Guerrero, Mantegazza and Scardia (1979) gave three periods with nonradial period ratios and a good fit. Our subsequent analysis of the same data gave three radial periods with an even better fit!

Recent evidence suggests that δ Set stars and most dwarf Cepheids are population I objects of normal mass. The remaining dwarf Cepheids, including CY Aqr, DY Peg, SX Phe and GD 428, have low masses, are metal-deficient, and are in a presently undetermined stage of evolution (Breger 1979, McNamara and Feltz 1978, but see also Simon 1979).

Many δ Set and dwarf Cepheid variables are multiperiodic and, in principle, multiple periods can be used to infer physical properties of these stars. The component periods must be determined accurately and reliably, and several workers (Breger, Fitch, Kurtz, Pelt, Percy, Shob-brook, Stellingwerf, Stobie and Warman) are active in developing and applying new methods of period analysis; see Wizinowich and Percy (1979) for a representative example.

One result of these analyses is the discovery that in some stars, modes may vary in amplitude or appear or disappear completely within a few days (Stobie and Shobbrook 1976). Methods of period analysis must allow for this possibility if they are to be accurate and reliable.

It has been known for a long time that white dwarfs are pulsationally unstable if nuclear burning takes place in their envelopes. Perturbation of energy generation rate promotes pulsational instability and this effect is frequently referred to as ε-mechanism. In recent years, with the advent of high-speed photometry, many rapidly varying white dwarfs have been discovered. However, periods of variability were found to be significantly longer than the periods of radial pulsations which were the only type of oscillations considered before the discovery. Furthermore, the case of ε-mechanism as being responsible for the observed variability has never been made strong for any of the observed objects.

Variable white dwarfs are found among: Io single DA-type objects in the effective temperature range 10000-15000K; 2o members of close, usually but not always, cataclysmic binary systems. Although, following an early suggestion by Warner and Robinson (1972), the excitation of nonradial oscillation is postulated in both cases, the two types represent very different physical situations and they will be discussed here separately.

The main data concerning the amplitudes and periods of super-giant variations are reviewed. The period-luminosity-colour relation of intermediate-term variations is compatible with pulsation motions. The Q-values seem to be larger than those corresponding to the fundamental mode and there are arguments favouring non-radial oscillations.

Calibration of the Period-Luminosity relation for Classical Cepheids is still far from settled: the debate continues as to whether there is a unique relation from galaxy to galaxy and what the precise form is in any one system. In the Milky Way we suffer from poor sample size; in the Magellanic Clouds it is still a matter of low accuracy in the observations. Work is in progress at several observatories to alleviate both of these problems through studying not only galactic Cepheids but also those in the LMC, SMC, M33 and NGC 300.

Arellano & Percy (CTI0/DD0) have begun a photoelectric monitoring of the apparently brightest F & G supergiants in the Milky Way. The aim is to detect near-by very-low-amplitude Cepheids which are binaries or are intrinsically low amplitude variables. This should provide a better qualitative hold on the sense of the amplitude dependence on effective temperature, as well as the true fequency of the cepheid phenomenon.

Suppose one of the current high angular resolution instruments were capable of measuring the instantaneous angular diameter of a Cepheid throughout its pulsation cycle. By comparing the angular diameter variation to the linear displacement variation, obtained from the integrated radial velocity curve, one could determine both the linear radius and the distance of the variable. This distance would be independent of all other astrophysical distance scales and would be geometric, i.e. independent of the effects of interstellar obscuration.

Although none of the current instruments has this capability, the same result can be accomplished indirectly through use of the stellar surface brightness. Recall that the visual surface brightness can be expressed in terms of the apparent visual magnitude and the stellar angular diameter. At any phase in the Cepheid pulsation, knowledge of the visual surface brightness and the apparent magnitude permits inference of the angular diameter.

From stars with measured angular diameters it is known that the visual surface brightness parameter Fv correlates remarkably well with the Johnson V-R color index (Barnes and Evans 1976; Barnes, Evans and Parsons 1976; Barnes, Evans and Moffett 1978). Johnson VR photometry may thus be used to determine the visual surface brightness and hence the stellar angular diameter. As shown in the referenced works, such angular diameters are essentially independent of the choice of interstellar obscuration corrections. This approach to stellar angular diameters and then to variable star distances is therefore nearly equivalent to direct measurements.