We present the first massive frequency analysis of the 1200 first overtone RR Lyrae stars in the Large Magellanic Cloud observed in the first 4.3 yr of the MACHO project. Besides the many new double-mode variables, we also discovered stars with closely spaced frequencies. These variables are most probably nonradial pulsators.

OGLE-1 photometry of RR Lyrae stars has been analyzed in search of multiperiodic pulsations. A second periodicity corresponding to a nonradial mode has been found in 11 RRab and 2 RRc variables.

We present the results of a photometric study of RR Lyrae variables in the field of the globular cluster M55. We have discovered nine new RR Lyrae stars, increasing the number of known variables in this cluster to 15 objects. Five of the newly discovered variables belong to Bailey type RRc and two to type RRab. Two background RRab stars are probable members of the Sagittarius dwarf galaxy. Fourier decomposition of the light curves was used to derive basic properties of the present sample of RR Lyrae variables. From an analysis of the RRc variables we obtain a mean mass of M = 0.53 ± 0.03 M⊙, luminosity log L = 1.75 ± 0.01 L⊙, Teff = 7193 ± 27 K, and helium abundance Y = 0.27 ± 0.01. We also derive the value of the color excess for M55 to be equal to E(B − V) = 0.11 ± 0.03. We estimate the values of the visual apparent distance moduli to be 13.65 ± 0.11 from RRab stars and 13.91 ± 0.08 from RRc stars. The light curves of three of the RRc variables exhibit changes in amplitude of over 0.1 mag on time scales of less than a week, rather short for the Blazhko effect, but with no evidence for another radial pulsational frequency. However, we do detect other periodicities which are clearly visible in the light curve after removing variations with the first overtone radial frequency. This is strong evidence for the presence of nonradial pulsations, a behavior common for 8 Scuti stars, but not yet observed among RR Lyr variables.

The recent detection of a frequency splitting around the pulsation frequency and its harmonics points towards the magnetic model to explain the Blazhko effect. Here we show that it is urgent to confirm with modern observational techniques the existence of the magnetic field in RR Lyrae.

We report here the discovery of a new frequency not belonging to the Blazhko series and suggest an interpretation based on coupling between a radial and a nonradial mode from multicolor observations.

We surveyed nonradial mode properties in evolutionary sequences of RR Lyrae star models, focusing attention on modes that may be driven by the opacity mechanism and on those that may be excited as a consequence of the 1:1 resonance with the radial pulsation. Our survey shows that all RR Lyrae star models share all qualitative properties of the nonradial modes. There is always a large number of unstable low degree modes with frequencies close to unstable radial modes. However, owing to higher mode inertia, for most of nonradial modes the driving rates are much lower than those for radial modes. The exceptions are the strongly trapped (STU) modes which begin with ℓ degrees 7 to 10 (depending on the model) at frequencies somewhat above the fundamental radial mode, and with ℓ = 5 or 6 at frequencies somewhat above the radial mode overtones. We argued that these modes are not likely candidates for identification of oscillations recently detected in some RR Lyrae stars. More likely candidates seem, in spite of their lower driving rates, the ℓ = 1 modes.

We found also that parameters which determine the chances of the excitation of nonradial modes through the 1:1 resonance do not vary much over the range of RR Lyrae star parameters. According to our estimate the excitation has a high probability. In fact, some nonradial modes should be excited in the majority of the RRab pulsators and in a significant fraction of (~ 30%) of RRc pulsators. The actual number is likely greater because we ignored the effect of rotation, which increases the probability of resonant excitation. The instability may lead to a periodic light curve modulation, that is to the Blazkho effect, if the nonlinear interaction results in a periodic energy exchange between the radial and the nonradial modes. A light curve modulation may also take place in the case of a constant amplitude limit cycle if the nonradial mode is of low degree and it is not symmetric about the rotation axis.

See Dziembowski & Cassisi (1999) for the full paper.

To answer the topical question we survey synoptically the recent literature in pulsation theory. We restrict the topics to those which are not dealt with otherwise in this volume. We address research on roAp stars, EC 14026 variables, strange modes, luminous blue variables, pulsation-rotation coupling, and pulsations in compact objects seen from the classical, as well as the relativistic, viewpoint.

By performing detailed frequency-dependent radiative transfer computations we are able to calculate light curves in particular bandpasses from stellar pulsation models calculated by the Vienna nonlinear convective pulsation code. As a sample application we discuss UBVI light curves of RR Lyrae stars. The properties of these light curves are analyzed by means of standard Fourier decomposition, and a comparison to recent observations is performed. As main results we find a good agreement with important observed RR Lyrae properties like pulsation amplitudes and Fourier parameters in B, V, and I bands. Additionally, from the synthetic color curves we derive linear transformation laws between amplitudes as well as Fourier parameters in the different bandpasses.

We present a detailed analysis of theoretical period–luminosity (PL) and period–luminosity–color (PLC) relations of classical Cepheids, as derived from nonlinear, nonlocal, time-dependent convective pulsating models with different masses and chemical compositions. The predicted PL and PLC relations turn out to depend on the pulsator metallicity and, to a minor extent, on the adopted averages (magnitude-weighted or intensity-weighted) over the light cycle in different bands. We show that the determination of the reddening and true distance modulus of a galaxy from the observed PL and PLC relations is constrained by the metallicity sensitivity of these relations. Moreover, the metallicity sensitivity itself provides us with a powerful tool for deriving self-consistent evaluations of distance, reddening and metallicity of the host galaxy, once Cepheid measurements in at least three photometric bands are available. To illustrate this point, we apply our relations to the BVK data for Cepheids in the Magellanic Clouds, assuming to be unaware of their metallicities. The three filter method is finally adopted to evaluate the metallicity of galactic Cepheids (BVI data) as a function of their position.

We review the numerical modeling of the nonlinear pulsations of classical variable stars with hydro-codes that include the effects of turbulent convection. Despite their simplicity these turbulent convective recipes appear to remove many of the difficulties that radiative codes faced. In particular, the numerical modeling of double mode pulsations has become possible.

The hydrodynamical modeling of steady double-mode (DM) pulsations has been a long-standing quest. Recent improvements in turbulent-convective pulsation codes provide a natural way to calculate nonlinear DM oscillations. The eddy viscosity plays a crucial role in these models. We present models both for RRd and beat Cepheid variables and for different chemical compositions. Simple nonresonant amplitude equations capture the DM phenomenon, giving an overview of modal selection on the HR diagram.

We review properties of stellar convection, as derived from detailed 3-D numerical modeling, and assess to what extent 1-D models are able to provide a fair representation of stellar structure in various regions of the HR diagram. We point out a number of problems and discrepancies that are inevitable when using conventional 1-D models. The problems originate mainly in the surface layers, where horizontal fluctuations become particularly large, and where convective energy transport gives way to radiation. We conclude that it is necessary (and possible) to use three-dimensional models of these layers, in order to avoid the uncertainties and inaccuracies associated with 1-D representations.

We present numerical simulations of gravito-inertial waves propagating in radiative zones of rapidly rotating stars. A first model, using the Boussinesq approximation, allows us to study the oscillations of a quasi-incompressible stratified fluid embedded in a rapidly rotating sphere or spherical shell. In a second step, we investigate the case of a γ Doradus-type star using the anelastic approximation. Some fascinating features of rapidly rotating fluids, such as wave attractors, appear in both cases.

We used our nonlinear hydrodynamical code with turbulent convection to model RR Lyrae stars. In some regime this approach produces double-mode solutions. We investigated series of models with different parameters (metallicity, luminosity, etc.). Our goal was to estimate the width of the double-mode region. The resulting tendencies can be directly compared with observational properties.

A method of calculating nonradial oscillations in rotating stars is presented. Using this method, we are able to calculate the spectrum of g-, f- and p-mode eigenfunctions of a star for different stellar rotation speeds, and also the spectrum of rotational r modes. Stability of the modes as a function of stellar rotation speed can be investigated. By regarding the response of a star which undergoes periodic deformations due to the gravitational force of an orbiting companion as a forced nonradial oscillation, the problem of determining the eigenfrequencies of the star becomes one of finding resonances with the forcing potential. Expanding the potential of the orbiting (point mass) companion in terms of the usual spherical functions, the response of the star to each tidal term , with l and m fixed, can be calculated separately. By varying the forcing frequency σ we are then able to calculate the stellar spectrum. To calculate the response of the star we numerically solve the fully non-adiabatic, but linearised hydrodynamical equations for the star, in which the Coriolis forces due to stellar rotation are fully taken into account. To this end we utilise an implicit 2D finite difference scheme which solves the equations on an (r, ϑ) grid. A calculated solution describes the steady state in which the power σT due to the external driving force is in equilibrium with the internal damping. For results and more references see Witte & Savonije (1999).

Robust double-mode pulsation has been found in several nonlinear radiative Cepheid models. This phenomenon has not been previously detected in purely radiative models.

A new type of oscillatory thermal mode has been found in red giant stars. The modes arise because of the interaction of stellar oscillations and convective energy transport. All the modes found are highly damped. However, it is possible that a different treatment of convection could lead to unstable modes capable of explaining the long secondary periods observed in some red giants.

We compare the recent OGLE 2 data of stars in the Small Magellanic Cloud (SMC) with stellar evolutionary models of low metallicity computed with the updated and numerically accurate code CESAM. The conversion between theoretical and observational data has been carefully done using the BaSel Library. This enables us to derive new observational constraints at SMC chemical composition: on the overshooting parameter αover during the main sequence, and on the mixing-length parameter αMLT for the red giant branch. The occurrence of an instability strip-crossing episode is strongly related to these mixing parameters.

Figure 1 is of the same form as Fig. 3 in Schrijvers et al. (1997): the upper part of each panel is the amplitude of the variation across the line at the mode frequency and the lower part is the phase shift of these two components across the line (in units of Φ). The parameters {Vavg, k, Ω/ω0, W} were chosen to have values representative of the δ Scuti star 4 CVn. Each panel in this array of plots has m=0, with a value of ∓ of 0, 1, or 2, and an inclination angle θi between 10° and 80°. In order to generate the synthetic line profiles, we use sampling times taken from the last week of the 1996 δ Scuti campaign on 4 CVn, and we assume that the signal-to-noise ratio of the spectrum is 250.

The effects of a low-mass companion (a planet?) revolving around a red giant at a short distance (inside its circumstellar envelope) are discussed. Calculations are given for a conical shock wave, induced by the orbital motion of the companion. Consequences for the stellar spectrum and light curve are derived, and predictions for the evolution of such a system are made.