Torsional oscillations of magnetized neutron stars with mixed poloidal-toroidal fields

Abstract

The quasiperiodic oscillations found in the three giant flares of soft gamma-ray repeaters observed to date have been interpreted as torsional oscillations caused by a starquake related to a magnetospheric reconnection event. Motivated by these observations, we study the influence of the magnetic field geometry in the frequencies of the torsional oscillations of magnetized neutron stars. We use realistic tabulated equations of state for the core and crust of the stars and model their magnetic field as a dipole plus a toroidal component, using the relativistic Grad-Shafranov equation. The frequencies of the torsional modes are obtained by the numerical solution of the eigenvalue problem posed by the linear perturbation equations in the Cowling approximation. Our results show how the asteroseismology of these stars becomes complicated by the degeneracy in the frequencies due to the large relevant parameter space. However, we are able to propose approximately equation-of-state--independent relations that parametrize the influence of the magnetic field in the torsional oscillations, as well as a testable scenario in which the rearrangement of the magnetic field causes an evolution of the frequencies. Finally, we show that there is a magnetic field configuration that maximizes the energy in the perturbation at linear order, which could be related to the trigger of the giant flare.