Alfv\'en Polar Oscillations of Relativistic Stars

TL;DR

This paper investigates the polar Alfvén oscillations in relativistic stars with strong magnetic fields, revealing a discrete spectrum and minimal impact on fluid modes, using numerical evolution of perturbation equations.

Contribution

It provides the first detailed numerical analysis of axisymmetric polar Alfvén oscillations in relativistic stars with strong magnetic fields, highlighting their discrete spectrum.

Findings

Polar Alfvén oscillations have a discrete spectrum.

Fluid modes like f and p are unaffected by strong magnetic fields.

Numerical evolution of perturbation equations is used to analyze oscillations.

Abstract

We study polar Alfv\'en oscillations of relativistic stars endowed with a strong global poloidal dipole magnetic field. Here we focus only on the axisymmetric oscillations which are studied by evolving numerically the two-dimensional perturbation equations. Our study shows that the spectrum of the polar Alfv\'{e}n oscillations is discrete in contrast to the spectrum of axial Alfv\'{e}n oscillations which is continuous. We also show that the typical fluid modes, such as the f and p modes, are not significantly affected by the presence of the strong magnetic field.