Non-axisymmetric Torsional Oscillations of Relativistic Stars

We examine the non-axisymmetric Alfven oscillations of relativistic stars with a strong dipole magnetic fields, where we have done the 2D simulation. We find that the spectrum of non-axisymmetric axial-type Alfven oscillations is discrete as well as the axisymmetric polar Alfven oscillations, in contrast to the spectrum of axisymmetric axial Alfven oscillations which is continuum. We also show the dependence of Alfven frequency on the strength of magnetic field and find that such frequencies are smaller than those of the axisymmetric axial Alfven oscillations. That is, 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.