Since 1984, efforts have been underway at Lowell Observatory to monitor Ap stars for rapid oscillations utilizing a photoelectric photometer on 0.6- to 1.8-meter telescopes. These variables, first discovered and designated as a subgroup of Ap stars by D.W. Kurtz, pulsate with periods between 4 and 15 minutes and light variations less than about 0.m016 in B. This strongly suggests high overtone p-mode oscillations as the cause of rapid variability. To attempt to increase the known number, Ap stars of spectral type B9 and later are being monitored. As members currently span the range A5 to F0, it is important to establish within what limits rapid oscillations are present. So far, only one new member has been found at Lowell (HD 134214), bringing the known total to eleven. The coordination of observations for known members has proved to be useful; no fewer than five rapidly oscillating Ap stars have been observed via multi-site, coordinated photometry. In this context, the status of this observing program and its future goals are presented.

In the late sixties, Spica (α Virginia, a 4.01454-day SB2 and interferometric binary, with a B1 IV primary component) was showing a light variation that consisted of two periodic terms. One term had the form of a double wave with the above-mentioned orbital period, the other was sinusoidal in shape and had a period equal to 0.1738 days. The double-wave term was clearly an ellipsoidal variation, caused by aspect changes of the tidally distorted primary, whereas the short-period term could only be explained as due to the primary's β Cephei-type pulsations. However, in 1972 these pulsations became undetectable.

A survey of K giants is being conducted to search for both short- and long-term oscillations. Our radial velocity spectrometer has a short-term precision on bright stars of 4 m/s after an exposure of 3 minutes on the CCD detector. Extensive sets of observations have been reduced for Arcturus, Pollux, and Aldebaran. Power spectra show no apparent oscillations within these data sets for frequencies between 0.15 and 2.0 mHz. However, the nightly averages over a 4 month time base show a three-fold increase in variance for Arcturus when compared to Pollux. A periodogram reveals a period of 1.844 0.005 days (or its alias of 2.174 days).

We have reviewed the observational data for ∊ Eri to derive our best estimates of luminosity, radius, temperature, composition, and age, as well as the uncertainties associated with each of these. These quantities are then used in stellar structure models to try to reproduce the global oscillation frequencies observed by Noyes et al. We find that we can reproduce the observed frequencies and splittings at least as well as the computations of Guenther and Demarque, yet for significantly different stellar parameters, most notably the age.

Because Epsilon Eridani (Z = 0.013) appears about 0.2 mag above the Z = 0.02 zero-age main sequence, zero-age models of Epsilon Eridani must be evolved off the ZAMS to ages much older than its rapid rotation and high chromospheric activity suggests. To resolve this conflict we propose that either Epsilon Eridani is part of a binary system or that its metal content has been underestimated. To test these hypotheses we use not only the stellar constraints of luminosity and effective temperature but also impose that the characteristic frequency spacing of the oscillation spectra of the models match the value observed by Noyes et al. (1984).

In a previous paper on Procyon A, we analyzed the best available observational data (summarized here in Table 1), discussed its evolutionary status in terms of theoretical evolutionary tracks, and evaluated on the basis of these models its expected characteristic p-mode frequency spacing (Demarque and Guenther 1986). We reached the following conclusions:

1. (1) that the published astrometric mass of Procyon A is inconsistent with stellar models and seems too large by about 15 per cent.

2. (2) that evolutionary models have too high effective temperatures unless convective overshoot at the edge of the convective core, of the order of a tenth of a pressure scale height, is taken into account.

3. (3) that the p-mode characteristic frequency spacing for Procyon A should be in the range 25–30 μHz.

The aim of this paper is to explore theoretically the potential ability of the p-mode and g-mode non-radial oscillation spectrum to throw light on two fundamental problems raised by our first study: Procyon A's evolutionary status, and its mass-luminosity relation.

Suppression of convection near the poles of magnetic A stars and inhibition of winds near the equator influence chemical composition gradients resulting from diffusion, leading to appreciable horizontal variation in the equilibrium configurations of the stars. We conjecture that it is this variation which is responsible for the apparent alignment of non-radial pulsations with the magnetic axes of the stars, and also for a possible previous misidentification of the modes. We suggest that nonadiabatic excitation can be sufficient to overcome energy leakage into the atmosphere.

I present evolutionary tracks and curves of constant central hydrogen abundance in diagrams based on frequencies of high-order, low-degree p modes. For stars with masses between 0.7 and 1.5 M⊙, a clean separation is obtained between the effects of varying mass and varying evolutionary state.

Theoretical calculations show that the detailed pattern of frequencies from stellar oscillations can in principal produce data that can determine stellar masses independent of other input data.

Since Landolt's discovery of the first ZZ Ceti star, the ranks of the compact pulsators have swollen to include planetary nebula nuclei, hot pre-white dwarf stars, hot and cool white dwarf stars, and possibly even neutron stars. The discovery of multi-periodic variations in these objects has helped to usher in a new era of rapid progress in the field of stellar seismology. For the compact stars this rapid progress is the result of a combination of four fortunate circumstances: their physical structure is relatively simple; typical amplitudes are small enough to be both readily observable and amenable to linear analysis; the wealth of observed periods in each object provides many independent clues to the underlying structure of the compact stars; and the periods are short enough that we can observe many cycles in a night, thereby completely resolving the period structure in many of these stars.

In this review I will discuss the current state of our understanding of these objects, with special emphasis on their distribution in the H-R diagram, range of pulsation properties, possible mode selection mechanisms, excitation of the pulsations, problems of convection, and particularly the measurement and interpretation of period changes. In addition to the results of recent research, I will review the techniques used to obtain them, pointing out both their strengths and weaknesses. I will close with a discussion of some of the important problems facing us in the study of these objects, and attempt to identify potentially fruitful directions for future research.

The rate of change of period with time for the g-mode pulsations in ZZ Ceti stars depends directly on the cooling timescale for a DA white dwarf, and therefore a measurement of its value can yield an evolutionary timescale for the white dwarf. We have obtained an upper limit for the rate of change of the period of the dominant pulsation in the light curve of the ZZ Ceti star G117-B15A of |dP/dt| ≤ 9.9 × 10−15 s/s at the 68% confidence level, equivalent to a timescale for period change of

Asymptotic analysis of the equations of nonradial adiabatic oscillation shows that there is a “characteristic period spacing” for g-modes with the same degree (l) and consecutive values of the radial wavenumber (n). If modes with the same l but different n are present in a pulsating star, then comparison of the characteristic period spacing in appropriate stellar models with period differences between the observed pulsation periods can provide mode identifications, and thereby constrain other physical properties of the star. A simple empirical model of the observed period spectrum of the hot white dwarf star PG1159-035 yields two statistically significant mean period intervals of 21.0±0.3 or 8.8±0.1s. We also evaluate the period interval for models of hot white dwarfs that are representative of PG1159 stars. The observed intervals correspond very closely to those derived from the theoretical models. This analysis indicates that the mass of PG1159-035 is 0.60M⊙ and that it is either a dipole (l=1) or l=3 pulsator (or both!), pulsating in high radial overtone g-modes.

In order to see if there could be agreement between results of stellar evolution theory and those of nonradial pulsation theory, calculations of white dwarf models have been made for hydrogen surface masses of 10−4M⊙. Earlier results by Winget et al. (1982) indicated that surface masses greater than 10−8M⊙ would not allow nonradial pulsations, even though all the driving and damping is in surface layers only 10−12 of the mass thick. We show that the surface mass of hydrogen in the pulsating white dwarfs (ZZ Ceti variables) can be any value as long as it is thick enough to contain the surface convection zone.

We present here a new method for analysing stellar variability: a geometrical study of the attractor associated with a variable star. In contrary to Fourier analysis, which focuses on times scales, this approach attemps to define the shape of the attractor in its phase space. It presents the advantage of being almost unsensitive to gaps in the data as long as uninterrupted sequences contain several tens of characteristic times. But, its noise sensitivity calls for very accurate photometry (10−4), still extremely difficult to perform up to now.

A preliminary test has been done on the variable white dwarf GD 66 on data obtained by classical photometry from the ground.

Variable stars can be broadly classified into two categories: (a) High amplitude pulsators like Cepheids and RR Lyrae variables, (b) Low amplitude pulsators like Sun and Sun-like stars. The study of stellar pulsations has opened the possibility of using the oscillatory modes to probe the internal structure and dynamics of these stars. The cause of pulsational instability for a majority of stars is the partial ionisation of the abundant elements present in the envelope of the stars, while some instabilities are driven by the transfer of momentum from the medium to the oscillating elements. Various mechanisms responsible for exciting and limiting the solar and stellar oscillations are discussed.

Present theories suggest two different classes of excitation mechanisms which may be responsible for the observed amplitudes of solar p-mode oscillations—self-excitation of the modes (e.g. the κ mechanism), and stochastic excitation by turbulent convection. I discuss here the agreement and disagreement between the predictions of these two mechanisms and the observed mode amplitudes and linewidths.

The contribution of each element participating in p-p chain and each region of star to oscillation excitation by nuclear energy is investigated. The gravity modes the most easily excited by this way are indicated.

A simple prescription for the dynamics of convection perturbed by stellar pulsation is used in an estimation of the growth rates of solar five-minute modes. Convection appears to enhance the excitation of the modes, and the maximum in the growth rate versus frequency found previously when oscillatory convective perturbations were ignored is still present.

The excitation mechanism of the 5 min. oscillations is not yet understood. So far two mechanisms have been discussed. The first one is the linear vibrational instability. The second one is the non linear coupling between convection and pulsation discussed by Goldreich and Keeley (1977) and Goldreich and Kumar (1986).

Analysing the results of numerical simulations of solar granular convection we found, superimposed on the convective flow, an oscillatory phenomenon with a well defined period of 260 ± 15 sec.