Nonrelativistic and Relativistic Treatments for Propagation of Torsional Resonant Alfven Waves in Strongly Magnetized Neutron Stars

Abstract

We study the propagation and transmission of torsional Alfven waves in magnetars. First, we consider a simple two-layer model composed of an outer crust and vaccum magnetosphere. In this model, we derive the classical formulation for the transmission coefficient of Alfven waves using an MHD approximation. We then include a displacement current in Maxwell’s equations, which can be shown to become important in the magnetically relativistic region of the crust, B 4πρc. The effects of strong magnetic fields of magnetars are specifically quantified and discussed. Second, we consider a three-layer model in order to investigate the propagation properties of Alfven waves excited in the deep crust. This model is adopted for the inner crust, outer crust, and vacuum magnetosphere. It is shown that the outer crust plays a significant role as a resonant cavity if a certain condition holds. Some nonrelativistic resonance of Alfven modes with low frequencies obtained in this work is probably associated with the observed QPOs from soft gamma-ray repeaters. The estimated energy flux carried by relativistic Alfven waves is in good agreement with the observed values, E = 10–10 erg s−1, of giant flares.