Unsolved problems of theoretical stellar pulsations are briefly reviewed for pulsators in six regions of the Hertzsprung-Russell diagram. Only a small selection is included in the discussion of them, and the emphasis is mostly on theoretical problems. The problem of the pulsations of Mira stars, and the mode in which it pulsates is reviewed in more detail together with some new calculations that illustrate the difficulties. Finally an extensive discussion is made for the pulsation mechanism of the white dwarf (DA and DB) pulsators. A new interpretation is advocated, which unfortunately is not tractable by linear nonadiabatic calculations because during the pulsation cycle it involves the turning off and on of Convection with a short time scale relative to the pulsation period. Most of the theoretical problems involve the time dependence of convection, a topic still without any concise and practical way of convenient implementation.

Much of our knowledge of the hydrodynamics of stellar oscillations is summarized in the now-classical article by Ledoux & Walraven in volume 51 of the Handbuch der Physik. It is from that article that I, and many others, first learned the subject. Most of what we have learned since, aside, perhaps, from what we have learned from nonlinear studies, derives from that work. Even today, what is written in that work is hardly out of date. It is not possible to do justice to even the most outstanding contents of Ledoux & Walraven’s article in a single talk, so I highlight some aspects of further developments that have been of more recent interest, trying to set them into a context of current understanding.

We review briefly the different prescriptions which have been proposed to predict the extent of convective penetration (or overshoot) in stellar interiors, and we confront them with the results of numerical simulations and with helioseismic data. It appears that the penetrative motions are structured in plumes, and that thermal diffusion plays an important role in controlling the temperature stratification in the stable domain. The most recent high-resolution simulations suggest that these plumes are less space-filling than thought before, and that they are therefore less efficient in establishing an adiabatic temperature profile. This property is compatible with the solar profiles obtained through acoustic sounding.

In slowly rotating stars, the coupling of helium settling and meridional circulation leads to a particular hydrodynamical process which was not introduced in previous computations of abundance variations. The μ-gradients induced by element settling can lead to a quasi-paralysis stage in which the efficiencies of both the meridional circulation and the microscopic diffusion are strongly reduced. Such an effect was studied in the eighties for nuclear-induced μ-gradients by Mestel et al., who called it “creeping paralysis”. Below convective zones, this process has important consequences. Here we discuss the case of the halo stars and the sun.

The DJEHUTY project is an intensive effort at the Lawrence Livermore National Laboratory (LLNL) to produce a general purpose 3-D stellar structure and evolution code to study dynamic processes in whole stars.

In this paper, we present the results of a theoretical investigation on tidally excited oscillation modes in close binaries. We apply our results to the slowly pulsating B star HD 177863 and present evidence for the resonant excitation of the second-degree -mode in this star.

A theoretical description is presented of the modulation of a radial oscillation in a uniformly rotating star in a close binary that is subject to the tidal action of a companion moving in a circular orbit. The star is assumed to rotate non-synchronously with the companion’s orbital motion. A tidal modulation of a radial oscillation has been observed in the star θ Tucanae by Sterken (1997) and De Mey et al. (1998).

Through tidal deformation of the equilibrium state, the p-mode oscillations may show apparently complicated features. I discuss the fundamental characteristics of the tidally forced oscillation, and show the possibility that it leads to a triplet fine structure in the frequency spectrum of p-modes.

A study of the rapid variations of the line profiles of λ Scorpii leads to the following new result: we find evidence for the presence of at least 5 periodicities in the intrinsic variations of λ Scorpii, which seem to be part of an equidistant multiplet. The modes associated to these periodicities are interpreted as non radial pulsation modes.

We introduce our observational study of the orbital motion of β Cen. Using 463 high signal-to-noise, high-resolution spectra obtained over a timespan of 12 years it is shown that the radial velocity of β Cen varies with an orbital period of 357.0 days. We derive for the first time the orbital parameters of β Cen and find a very eccentric orbit (e = 0.81) and similar component masses with a mass ratio M1/M2 = 1.02. Both the primary and the secondary exhibit periodic line-profile variations.

We developed a procedure to disentangle the different radial velocity variations due to orbital motion, rotation, and pulsation based on an iterative mutual subtraction of orbital and short-term contributions. The method was successfully tested on a data set of over 2200 spectra of the eclipsing β Cep star EN Lac spanning a time interval of about 90 years. We further applied the procedure to early type binaries. For the A1 III star 21 Her we found short-term variations which indicate the presence of rotationally split nonradial pulsation (NRP) modes.

We report the discovery of both intermediate-order gravity mode and low-order pressure mode pulsation in the same star, HD 209295. It is therefore both a γ Doradus and a δ Scuti star, which makes it the first confirmed member of two classes of pulsating star.

This object is located in a close binary system with an unknown, but likely degenerate companion in an eccentric orbit, and some of the γ Doradus pulsation frequencies are exact integer multiples of the orbital frequency. We suggest that these pulsations are tidally excited. HD 209295 may be the progenitor of an intermediate-mass X-Ray binary.

The colour behaviour of θ Tucanae with orbital phase is shown. A break in the residuals is checked as the criterion for stopping the period search. A resonance of the dominant pulsational mode and the period of ellipticity is reported, with a Resonance number of 72.

We give a brief review on the present status of our research of A-F pulsating components of semi-detached Algol-type systems. We suggest a new asteroseismic approach for estimating the evolutionary stage of the mass-accreting components of Algols during rapid and slow mass-transfer phases, asynchronization and differential rotation.