General relativistic plasma magnetospheres of slowly rotating and oscillating magnetized neutron stars

We study the magnetosphere of a slowly rotating magnetized neutron star with radius R and angular velocity Ω subject to toroidal oscillations in the relativistic regime. Under the assumption of a zero inclination angle between the magnetic moment and the angular momentum of the star, we analyse the Goldreich-Julian charge density and derive a second-order differential equation for the electrostatic potential. The analytical solution of this equation in the polar cap region of the magnetosphere shows the modification induced by stellar toroidal oscillations on the accelerating electric field and on the charge density. We also find that, after decomposing the oscillation velocity in terms of spherical harmonics, the first few modes with m = 0, 1 are responsible for energy losses that are almost linearly dependent on the amplitude of the oscillation and that, for the mode (l, m) = (2, 1), can be a factor ∼ 8 larger than the rotational energy losses, even for a velocity oscillation amplitude at the star surface as small as η = 0.05 Ω R. We revisit particle acceleration in the polar cap region of a neutron star by taking into account both general relativistic effects and the presence of toroidal oscillations at the star surface.