Alfv\'en Polar Oscillations of Relativistic Stars

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\'en oscillations is discrete in contrast to the spectrum of axial Alfv\'en 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.