Oscillations and instabilities in neutron stars with poloidal magnetic fields

Abstract

We study the time evolution of non-axisymmetric linear perturbations of a rotating magnetised neutron star, whose magnetic field is multipolar and purely poloidal. The background stellar configurations are generated self-consistently, allowing for distortions to the density distribution from rotational and magnetic forces. We find that the behaviour of axial-led perturbations is dominated by an instability generic to poloidal fields, which is localised around the `neutral line' where the background field vanishes. Rotation acts to reduce the effect of this instability. Polar-led perturbations do not appear to be unstable and in this case we find global Alfv\'en modes, whose restoring force is the magnetic field. In a rotating magnetised star there are no pure Alfv\'en modes or pure inertial modes, but hybrids of these. We discuss the nature of magnetic instabilities and oscillations in magnetars and pulsars, finding the dominant Alfv\'en mode has a frequency comparable with observed magnetar QPOs.