Torsional oscillations of magnetized neutron stars: Impacts of Landau-Rabi quantization of electron motion

Torsional oscillations of magnetized neutron stars have been well studied since they may be relevant to the physical interpretation of some of the observed quasiperiodic oscillations in the magnetar giant flares. In the crustal region of a magnetar, the strong magnetic field can alter the equation of state and composition due to the Landau-Rabi quantization of electron motion. In this paper, we study this effect on the crust-confined, torsional oscillation modes of neutron stars with mixed poloidal-toroidal magnetic fields in general relativity under the Cowling approximation. Furthermore, the inner and outer crusts are treated consistently based on the nuclear-energy density functional theory. Depending on the magnetic-field configurations, we find that the Landau-Rabi quantization of electrons can change the frequencies of the fundamental torsional oscillation mode of $1.4{M}_{\ensuremath{\bigodot}}$ neutron star models with a normal fluid core by about 10% when the magnetic field strength at the pole reaches the order of ${10}^{16}\text{ }\text{ }\mathrm{G}$. The shift can even approach 20% at a field strength of ${10}^{15}\text{ }\text{ }\mathrm{G}$ for neutron stars with a simple model of superconducting core where the magnetic field is assumed to be expelled completely.