On the subseismic approximation for low-frequency gravity modes in spherically symmetric stars

Instituut voor Sterrenkunde, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, 3001 Heverlee, Belgium

Received: 6 March 2001
Accepted: 6 April 2001

Abstract

In a comparative study of the anelastic and the subseismic approximation for the description of low-frequency gravity modes in spherically symmetric stars, Dintrans & Rieutord ([CITE]) stress that the subseismic approximation is inconsistent in that the Eulerian perturbation of the mass density is negligible as is the Eulerian perturbation of the pressure and that consequently the equation of mass conservation is not satisfied. In this paper, attention is drawn to the asymptotic theory for low-degree, low-frequency gravity modes of spherically symmetric stars developed by Smeyers et al. ([CITE]). A main conclusion is that, in the main body of a star, the subseismic approximation results as a natural consequence of the lowest-order asymptotic approximation. At the same order of approximation, the Eulerian perturbation of the mass density is derived from the equation of mass conservation and is different from zero. It also follows from the lowest-order asymptotic approximation that the Eulerian perturbation of the pressure is different from zero in a small region near the star's surface, so that the subseismic approximation is not adequate in that region.