The understanding of stellar structure, evolution and pulsations is a key piece of the proper understanding of the Universe. The interpretation of the luminosity and spectra of galaxies, the properties of star populations and of starbursts, the calibration of distances, the nucleosynthetic prescriptions etc... are all requiring good models of stellar structure and evolution. The many interesting and new results in the field have been presented in several recent reviews by Maeder (1991), Chiosi et al. (1992), Maeder & Conti (1994). Table 1 below presents a list of the recent grids of stellar models. The various columns give the author’s name, then the mass range, the metallicity Z range, the kind of convective assumption adopted, where “Schw.” means Schwarzschild’s criterion, “oversh” means with convective overshooting, “all” means that different assumptions have been used. In the last column, a few remarks are given. It is interesting to note that the models mentioned above often arrive to very different conclusions about the kind of mixing supported by the observations. Authors of models with overshooting generally conclude that overshooting is best supported, authors of models without overshooting favour the absence of overshooting, while authors who consider various convective assumptions generally favour semiconvection (Stothers & Chin 1991; Mowlawi & Forestini 1994).

In this review we discuss in some detail the evolution of low mass stars, and other related topics, limiting ourselves to the class of stars with solar and super-solar metal content that likely constitute the basic component of elliptical galaxies and bulges. In particular, we deal with the stars responsible of the UV flux observed in elliptical galaxies and the role played by the chemical composition and mass loss by stellar wind in producing hot progenies with effective temperatures in the range indicated by the UV data. In this context, we briefly report on recent chemo - spectro - photometric models for elliptical galaxies. In addition to this, we discuss the subject of galaxy ages by means of the ultraviolet properties and narrow band indices. Finally, we briefly report on a new formulation of diffusive mixing in stellar interiors and its effects on the structure and evolution of intermediate- and high-mass stars.

We review observational evidence on the interaction between stellar pulsation and evolution. We discuss to what extent observations of pulsating stars with variable amplitudes and pulsation periods have implications on our understanding of stellar structure and evolution. The probable link between mass loss and pulsation in AGB stars and in hot luminous stars appears to be the strongest way in which pulsations affect evolution. We point out the possibility that forced oscillations in the components of binaries may have important consequences on evolution, that could offer an explanation for some classes of peculiar evolved objects.

A major driving force behind the efforts invested in stellar pulsation calculations in the recent years was certainly the success story of the new generation of opacity data. The new opacities did not only solve old problems but they also increased the complexity of quantitative stellar pulsation studies. Besides surveying the consequences of the new generation of stellar opacities for pulsation theory we also address more formal aspects of dealing with stellar oscillations. The section reviewing recent literature on the application of stellar pulsation theory to different classes of pulsating variables is strongly biased towards the high-luminosity part of the Hertzsprung-Russell (HR) diagram. We finish by mentioning recent changes in our beliefs concerning the envelope structure of oscillating white dwarfs.

By assuming that the RR Lyrae stars have fairly strong dipole magnetic fields with the symmetry axis oblique to the rotation axis of the star, we show that the oscillation mode which would be a pure radial oscillation in absence of the magnetic field has a quadrupole component, which is axisymmetric with respect to the magnetic axis. The aspect angle of the quadrupole component changes due to the stellar rotation, and this apparent variation is interpreted as the Blazhko effect in RR Lyrae stars.

Until very recently the physical mechanism driving oscillations in β Cep and other early type stars has been a mystery. The breakthrough came with the publication of new OPAL and OP opacity data. Model calculations with the new opacities have demonstrated that the pulsations are driven by the familiar K-mechanism, acting in the metal opacity bump at T ≈ 2 × 105K. The mechanism excites the low order p- and g-modes in the upper part of the instability strip and the high order g-modes in the lower part of the strip. The theoretical instability domains agree well with the observed domains of the β Cep and the SPB stars. In this review I present these recent theoretical results and discuss their consequences for our understanding of B stars pulsations.

We identify the pulsation mode of BW Vul by means of both the moment method and the method of photometric amplitudes and find a radial pulsation. We briefly study the non-linear behaviour of BW Vul.

The rapidly oscillating Ap (roAp) stars are upper mainsequence stars that pulsate in non-radial p modes of high overtone. We present an observer’s overview of the roAp phenomenon and discuss significant developments since the last major observational reviews of Kurtz (1990a) and Matthews (1991).

The δ Scuti stars pulsate with a large number of low-order radial and nonradial p-modes. There also exists some evidence for the presence of g-modes.

The pulsational variability outside the classical δ Scuti star instability strip (A1V - F0V on the main sequence) is examined. New measurements do not confirm the short-period variability of the hot B9p star ET And. However, a number of cool, early-F stars shows variability around one day: the γ Dor variables. An explanation involving nonradial g modes appears the most promising.

An examination of available information on the multi-periodicity of δ Scuti stars shows no systematic behaviour in which pulsation modes axe excited to an observable level with luminosity and temperature. The asteroseismological potential of δ Scuti vaxiables is briefly examined.

So far, the period changes of five luminous Pop. I δ Scuti variables have been studied. While stellar evolution predicts period increases, decreases have been observed and reported for all five stars. The statistical significance of this result and alternative explanations axe briefly examined.

During the final evolution of most stars, they shed their outer skin and expose their core of the hot ashes of nuclear burning. As these hot and very dense cores cool into white dwarf stars, they go through episodes of multiperiodic, nonradial g-mode pulsation. The tools of stellar seismology allow us to use the pulsation spectra as powerful probes into the deep interiors of these stars. Progress in white dwarf seismology has required significant international cooperation, since another consequence of the complex pulsations of these stars is decoding the true pulsation frequencies requires a coordinated global effort involving high-speed photometric observations. Through one such effort, the Whole Earth Telescope project, we have located subsurface composition changes, detected differential rotation and magnetic fields, and measured fundamental quantities such as stellar mass, luminosity, and distance to extraordinary accuracy.

We present the first results of our project of calculating the evolutionary and seismological properties of δ Scuti models using Livermore OPAL opacities. We calculate the radial and low-degree nonradial nonadiabatic pulsation frequencies for a 1.8 and 2.0M⊙ model. Our radial first overtone/fundamental mode period ratios are × 0.772, which agree well with observed period ratios. We find a dense spectrum of unstable nonradial modes including both low order g-type modes and low to intermediate order p—type modes, confirming that we need a selection mechanism allowing only some modes to grow to observable amplitudes.

Recently, Clemens suggested that the similarity in period structure of the hotter DAV (ZZ Ceti) stars could be explained if they pulsated in a common set of modes. Here, I use theoretical pulsation periods from a new grid of evolutionary DA white dwarf models to determine the internal structure of G 117–B15A and R 548. Both stars have hydrogen layer masses of × 1.5 × 10−4M* and oxygen-rich cores with a composition gradient starting near 0.75M*.

Ground based optical spectroscopy as well as EUVE and HST observations are used for model atmosphere analyses of PG1159 stars in order to confine the GW Vir instability strip.

Observations of solar p-mode oscillations over the last two decades have provided a fundamentally new and unique means of probing the Sun’s interior structure. The history of understanding solar oscillations as trapped normal-mode pulsations will be briefly discussed. The large number of excited modes seen in the Sun have been used to constrain the solar core structure, determine the convection zone depth and to fix the variation of angular velocity with depth and latitude. Standard stellar structure and evolution theory does remarkably well in matching the helioseismic results. Further work promises to reveal the solar helium abundance. Upcoming network and space observations should provide the stability and resolution necessary to return detailed information on near-surface structures associated with solar activity.

We recently reported strong evidence for solar-like oscillations in the G0 IV star η Boo (Kjeldsen et al. 1995, AJ 109, 1313). We measured small temperature fluctuations produced by oscillations through their effect on the equivalent widths of the Balmer lines. Here we address several issues that were raised at this conference.

We consider the synthetic power spectra of multi-mode solar-type acoustic oscillations in stars, computed within a general framework of the linear response of the dynamical system to an arbitrary excitation force which is decomposed in spherical harmonics in space and harmonic functions in time. We discuss possible signatures in the observational data which might be used as diagnostics of the excitation source.