Oscillations of rotating magnetised neutron stars with purely toroidal magnetic fields

TL;DR

This study explores the oscillation spectrum of rotating neutron stars with purely toroidal magnetic fields, revealing hybrid magneto-inertial modes, magnetic suppression of r-mode instability, and magnetic shifts in the f-mode, relevant for understanding magnetar oscillations.

Contribution

It provides a fully consistent numerical analysis of oscillation modes in rotating, magnetized neutron stars with purely toroidal fields, including mode hybridization and magnetic effects.

Findings

Identification of magnetically-restored Alfvén modes.

Discovery of hybrid magneto-inertial modes in rotating stars.

Magnetic fields suppress r-mode instability in slow rotators.

Abstract

We investigate the oscillation spectrum of rotating Newtonian neutron stars endowed with purely toroidal magnetic fields, using a time evolution code to evolve linear perturbations in the Cowling approximation. The background star is generated by numerically solving the MHD equilibrium equations and may be nonspherical by virtue of both rotation and magnetic effects; hence our perturbations and background are fully consistent. Whilst the background field is purely toroidal, the perturbed field is mixed poloidal-toroidal. From Fourier analysis of the perturbations we are able to identify a number of magnetically-restored Alfv\'en (or $a$-) modes. We show that in a rotating star pure inertial and $a$-modes are replaced by hybrid magneto-inertial modes, which reduce to $a$-modes in the nonrotating limit and inertial modes in the nonmagnetic limit. We show that the $r$-mode instability is suppressed by magnetic fields in sufficiently slowly rotating stars. In addition, we determine magnetic frequency shifts in the $f$-mode. We discuss the astrophysical relevance of our results, in particular for magnetar oscillations.