Oscillations of magnetic stars^*

II. Axisymmetric toroidal and non-axisymmetric shear Alfvén modes in a spherical shell

Laboratoire d'Astrophysique de Toulouse et Tarbes, Observatoire Midi-Pyrénées, 14 avenue É. Belin, 31400 Toulouse, France e-mail: daniel.reese@ast.obs-mip.fr

Received: 29 March 2004
Accepted: 16 July 2004

Abstract

We carry out numerical and mathematical investigations of shear Alfvén waves inside of a spherical shell filled with an incompressible conducting fluid, and bathed in a strong dipolar magnetic field. We focus on axisymmetric toroidal and non-axisymmetric modes, in continuation of a previous work by Rincon & Rieutord (2003, A&A, 398, 663). Analytical expressions are obtained for toroidal eigenmodes and their corresponding frequencies at low diffusivities. These oscillations behave like magnetic shear layers, in which the magnetic poles play a key role, and hence become singular when diffusivities vanish. It is also demonstrated that non-axisymmetric modes are split into two categories, namely poloidal or toroidal types, following similar asymptotic behaviours as their axisymmetric counterparts when the diffusivities become arbitrarily small.