Poloidal-Field Instability in Magnetized Relativistic Stars

We investigate the instability of purely poloidal magnetic fields in nonrotating neutron stars by means of three-dimensional general-relativistic magnetohydrodynamics simulations, extending the work presented in Ciolfi et al. (2011). Our aim is to draw a clear picture of the dynamics associated with the instability and to study the final configuration reached by the system, thus obtaining indications on possible equilibria in a magnetized neutron star. Furthermore, since the internal rearrangement of magnetic fields is a highly dynamical process, which has been suggested to be behind magnetar giant flares, our simulations can provide a realistic estimate of the electromagnetic and gravitational-wave emission which should accompany the flare event. Our main findings are the following: (i) the initial development of the instability meets all the expectations of perturbative studies in terms of the location of the seed of the instability, the timescale for its growth and the generation of a toroidal component; (ii) in the subsequent nonlinear reorganization of the system, ~90% of magnetic energy is lost in few Alfven timescales mainly through electromagnetic emission, and further decreases on a much longer timescale; (iii) all stellar models tend to achieve a significant amount of magnetic helicity and the equipartition of energy between poloidal and toroidal magnetic fields, and evolve to a new configuration which does not show a subsequent instability on dynamical or Alfven timescales; (iv) the electromagnetic emission matches the duration of the initial burst in luminosity observed in giant flares, giving support to the internal rearrangement scenario; (v) only a small fraction of the energy released during the process is converted into f-mode oscillations and in the consequent gravitational-wave emission, thus resulting in very low chances of detecting this signal with present and.