Instabilities in neutron stars with toroidal magnetic fields

We study $m=1$ oscillations and instabilities of magnetised neutron stars, by numerical time-evolution of linear perturbations of the system. The background stars are stationary equilibrium configurations with purely toroidal magnetic fields. We find that an $m=1$ instability of toroidal magnetic fields, already known from local analyses, may also be found in our relatively low-resolution global study. We present quantitative results for the instability growth rate and its suppression by rotation. The instability is discussed as a possible trigger mechanism for Soft Gamma Repeater (SGR) flares. Although our primary focus is evolutions of magnetised stars, we also consider perturbations about unmagnetised background stars in order to study $m=1$ inertial modes. We track these modes up to break-up frequency, extending known slow-rotation results.