Consequences of Rapid Rotation on Mode Identification

The present work deals with the effect of rotation on the adiabatic oscillation frequencies of stellar models. Here, rotation, as described in a perturbation theory, is said to be rapid in the sense that second order perturbation effects have to be taken into account. Rotation has two second order effects on the oscillation frequencies: departure from equidistance within a given multiplet split by rotation and an overall shift of the multiplet itself. The first effect has been investigated for realistic models of δ Scuti stars in uniform rotation (Dziembowski & Goode, 1992), whereas H. Saio’s study includes both effects for a polytrope of index 3 in uniform rotation (Saio 1981). Both effects are investigated for realistic models of δ Scuti stars. Results for the overall shift for a 2 M⊙ model in rapid uniform rotation (v up to ∼ 200 km/s) are outlined below. The rotation rate corresponding to this surface velocity is Ω = 1.44 10−4 rad/s.

The stellar seismology of the hot white dwarf star PG1159-035

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.

The Effect of a Magnetic Field on Stellar Pulsations as a Singular Perturbation Problem

The perturbation problem that describes the effect of a weak magnetic field on stellar adiabatic oscillation is considered. This perturbation problem is singular when the magnetic field does not vanish at the stellar surface, and a regular perturbation scheme fails where the magnetic pressure is comparable to the thermodynamic pressure. The application of the Method of Matched Asymptotic Expansion is used to obtain expressions for the eigenfunctions and the eigenfrequencies.