Non-axisymmetric magnetic modes of neutron stars with purely poloidal magnetic fields

TL;DR

This paper investigates non-axisymmetric oscillations in neutron stars with purely poloidal magnetic fields, identifying stable and unstable magnetic modes and analyzing their dependence on magnetic field strength and internal stratification.

Contribution

It introduces a method to compute non-axisymmetric magnetic modes in magnetized neutron stars using finite series expansions and identifies the nature of these modes.

Findings

Discovered stable and unstable magnetic modes in neutron stars.

Mode frequencies and growth rates are proportional to surface magnetic field strength.

Stable stratification influences the stability of magnetic modes.

Abstract

We calculate non-axisymmetric oscillations of neutron stars magnetized by purely poloidal magnetic fields. We use polytropes of index $n=1$ and 1.5 as a background model, where we ignore the equilibrium deformation due to the magnetic field. Since separation of variables is not possible for the oscillation of magnetized stars, we employ finite series expansions for the perturbations using spherical harmonic functions. Solving the oscillation equations as the boundary and eigenvalue problem, we find two kinds of discrete magnetic modes, that is, stable (oscillatory) magnetic modes and unstable (monotonically growing) magnetic modes. For isentropic models, the frequency or the growth rate of the magnetic modes is exactly proportional to $B_{\rm S}$, the strength of the field at the surface. The oscillation frequency and the growth rate are affected by the buoyant force in the interior, and the stable stratification tends to stabilize the unstable magnetic modes.