General Relativistic Magnetospheres of Slowly Rotating and Oscillating Magnetized Neutron Stars

TL;DR

This paper investigates how toroidal oscillations in slowly rotating, magnetized neutron stars affect their magnetospheres, revealing significant impacts on electric fields, charge densities, and energy losses, with implications for pulsar variability.

Contribution

It provides an analytical model of the relativistic magnetosphere of oscillating neutron stars, linking stellar oscillations to observable pulsar phenomena and energy loss mechanisms.

Findings

Oscillations modify the electric field and charge density in the magnetosphere.

Energy losses depend linearly on oscillation amplitude, with certain modes causing larger losses.

Stellar oscillations may explain intermittent pulsar behavior linked to star glitches.

Abstract

We study the magnetosphere of a slowly rotating magnetized neutron star 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 analyze 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 $\sim8$ larger than the rotational energy losses, even for a velocity oscillation amplitude at the star surface as small as $\eta=0.05 \ \Omega \ R$. The results obtained in this paper clarify the extent to which stellar oscillations are reflected in the time variation of the physical properties at the surface of the rotating neutron star, mainly by showing the existence of a relation between $P\dot{P}$ and the oscillation amplitude. Finally, we propose a qualitative model for the explanation of the phenomenology of intermittent pulsars in terms of stellar oscillations that are periodically excited by star glitches.