Non-axisymmetric Torsional Oscillations of Relativistic Stars

Hajime SOTANI and Kostas D. KOKKOTAS

We examine the non-axisymmetric Alfv¥'{e}n oscillations of relativistic stars with a strong dipole magnetic fields. In general, to consider the non-axisymmetric oscillations one has to take into account both the axial and polar perturbations even for a non-rotating star, because due to the presence of magnetic field the both perturbations are coupled with each other. However, since this coupling becomes important only for the case with strong magnetic field and first we want to know the feature in spectrum for non-axisymmetric axial-type oscillations on the magnetized neutron stars, as a first step we neglect such a coupling. In such a way that we have done the 2D simulation, we find that the spectrum of non-axisymmetric axial-type Alfv¥'{e}n oscillations is discrete as well as the axisymmetric polar Alfv¥'{e}n oscillations, in contrast to the spectrum of axisymmetric axial Alfv¥'{e}n oscillations which is continuum. We also show the dependence of Alv¥'{e}n frequency on the strength of magnetic field and find that such frequencies are smaller than those of the axisymmetric axial Alfv¥'{e}n oscillations. That is, in order to explain the observed evidence of quasi-periodic oscillations in the soft gamma repeaters, the non-axisymmetric axial oscillations could also play an important role.