Perturbation of the Non-Radial Oscillations of a Gaseous Star by an Axial Rotation, a Tidal Action or a Magnetic Field

Abstract

The study of the linear and adiabatic oscillations of a gaseous star gives rise to an eigenvalue problem for the pulsation σ, if perturbations proportional to eiσt are considered. In the presence of a rotation, a tidal action or a magnetic field, the equations are not separable in spherical coordinates. To get approximate expressions for the influence of these factors on the non-radial oscillations of a star, the author and his collaborators J. Denis and M. Goossens have used a perturbation method (Smeyers and Denis, 1971; Denis, 1972; Goossens, 1972; Denis, 1973). Their procedure corresponds to a generalization of the method proposed by Simon (1969) to study the second order rotational perturbation of the radial oscillations of a star.Two types of perturbations are taken into account: volume perturbations due to the local variations of the equilibrium quantities and to the presence of a supplementary force in the equation of motion (Coriolis force, Lorentz force); surface perturbations related to the distortion of the equilibrium configuration and to the change of the condition at the surface in the presence of a magnetic field. The resulting expressions are accurate up to the second order in the angular velocity in the case of a rotational perturbation, to the third order in the ratio of the mean radius of the primary to the distance of the secondary in the case of a tidal perturbation, and to the second order in the magnetic field in the case of a perturbing magnetic field. These expressions can in principle be applied to any mode.Numerical results have been obtained for a homogeneous model and for a polytropic model n = 3. In particular, the splitting of the frequencies of the fundamental radial mode and of the f-mode belonging to l = 2 and m = 0 has been studied for the critical value of y, in the case of a component of a synchronously rotating binary system.