Oscillations of magnetic stars: II. Axisymmetric toroidal and non-axisymmetric shear Alfven modes in a spherical shell

TL;DR

This paper investigates shear Alfven waves in a spherical shell with a dipolar magnetic field, deriving analytical expressions for modes and analyzing their behavior at low diffusivities, revealing singularities and mode categorizations.

Contribution

It provides analytical solutions for axisymmetric toroidal modes and characterizes non-axisymmetric modes, extending previous work on magnetic oscillations in spherical shells.

Findings

Analytical expressions for low-diffusivity eigenmodes.

Identification of singular behavior at vanishing diffusivities.

Classification of non-axisymmetric modes into poloidal and toroidal types.

Abstract

We carry out numerical and mathematical investigations of shear Alfven 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.