G. Kovacs

A survey of bump Cepheid model pulsations

The periodical nonlinear behavior of a number of sequences of radiative Cepheid models is computed and Fourier analyzed. The Fourier phases and amplitudes exhibit systematic and characteristic variations when plotted as a function of the period ratio P2/P0, but not as a function of the period or the effective temperature. The dominant role played by the 2:1 resonance between the fundamental mode and the second overtone is clearly established. The astrophysical consequences of the observed tightness of the Fourier phase phi(21) versus period relation are thoroughly discussed. It is demonstrated that the dispersion of phi(21) can be used to estimate the width of the instability strip, independently of the Cepheid temperature and luminosity calibrations. Comparison of such an estimation with the traditional determination of that width provides a new test for pulsation and evolution theories. 57 refs.

The Cepheid bump progression and amplitude equations

It is shown that the characteristic and systematic behavior of the low-order Fourier amplitudes and phases of hydrodynamically generated radial velocity and light curves of Cepheid model sequences is very well captured not only qualitatively but also quantitatively by the amplitude equation formalism. The 2:1 resonance between the fundamental and the second overtone plays an essential role in the behavior of the models 8 refs.

Modal selection in stellar pulsators. II. Application to RR Lyrae models

The numerically produced dynamical evolution of several RR Lyrae models from various initial conditions is subjected to a time-dependent Fourier analysis. This generates the temporal behavior of the amplitudes and phases of the few long-lived transient modes in addition to those of the ultimately surviving mode. It is shown that the amplitude equation formalism of Bucher and Goupil (1985) gives a remarkably good description of the observed behavior of the models. It is concluded (1) that the essence of the dynamical behavior of the model is played in a low-dimensional subspace of phase space, (2) that the nonlinearities in the pulsation are so weak as to involve only the lowest essential nonlinearities, and (3) that the assumptions made by Buchler and Kovacs (1986) in their discussion of the modal selection problem are satisfied. 23 references.

Cepheid radial velocity curves revisited

Les vitesses radiales de 57 Cepheides galactiques de type I sont analysees pour etudier les variations systematiques de leur decomposition de Fourier avec la periode.

Periodic stellar pulsations : stability analysis and amplitude equations

The stability properties of nonlinear periodic stellar pulsations are studied within the amplitude equation formalism. Both nonresonant and resonant pulsations are considered. A comparison to a sequence of classical Cepheid models shows that the formalism provides a good qualitative and quantitative description of the behavior of the Floquet coefficients and that it also captures the most important features of the Floquet eigenvectors. It thus helps shed new light on the behaviour (bifurcations) of pulsating stars. In addition, the predictive powers of the analytical approach allow a systematic search for models with specific pulsational properties

The Evolution to Steady Nonlinear Pulsation in Stellar Models

The numerically generated dynamical evolution of an RR Lyrae model from different initial conditions is subjected to a time-dependent Fourier analysis, which yields the temporal behavior of the amplitudes and phases of the few longlived transient modes in addition to the ultimate winner. It is shown that the amplitude equation formalism of Buchler and Goupil gives an almost perfect fit to the observed transient behavior of the amplitudes and phases of the excited modes. Prospects and applications are discussed.

Finally a Double-Mode RR Lyrae Model?

It is shown that in a certain range of physical parameters a proper choice of the artificial viscosity parameters can lead to double-mode pulsation of RR Lyrae models. Here we present one such model and exhibit its double-mode behavior both through the stability analysis of the periodic limit cycles and through straightforward numerical integrations.