The magnetosphere of an oscillating neutron star. Non-vacuum treatment

Abstract

We generalize a formula for the Goldreich-Julian charge density (ρGJ), originally derived for a rotating neutron star, for arbitrary oscillations of a neutron star with an arbitrary magnetic field configuration under the assumption of low current density in the inner parts of the magnetosphere. As an application, we consider the toroidal oscillation of a neutron star with a dipole magnetic field and calculate the energy losses. For some oscillation modes, the longitudinal electric field cannot be cancelled by putting charged particles in the magnetosphere without the presence of a strong electric current (j ≃ ρGJ × c/ωr). It is shown that the energy losses are strongly affected by plasma in the magnetosphere, and cannot be described by vacuum formulae.