Electromagnetic fields in the exterior of an oscillating relativistic star -- II. Electromagnetic damping

TL;DR

This paper analytically investigates electromagnetic damping mechanisms in oscillating relativistic stars, revealing that relativistic effects significantly enhance electromagnetic energy loss rates compared to Newtonian predictions, especially for certain oscillation modes.

Contribution

It provides fully analytic expressions for electromagnetic energy losses in relativistic oscillating stars with dipolar magnetic fields, extending classical estimates to a relativistic framework.

Findings

Relativistic corrections reduce electromagnetic damping timescales by at least an order of magnitude.

Electromagnetic damping is less effective than gravitational damping for most oscillation modes.

Analytic solutions for electric and magnetic fields are derived for various oscillation modes.

Abstract

An important issue in the asteroseismology of compact and magnetized stars is the determination of the dissipation mechanism which is most efficient in damping the oscillations when these are produced. In a linear regime and for low-multipolarity modes these mechanisms are confined to either gravitational-wave or electromagnetic losses. We here consider the latter and compute the energy losses in the form of Poynting fluxes, Joule heating and Ohmic dissipation in a relativistic oscillating spherical star with a dipolar magnetic field in vacuum. While this approach is not particularly realistic for rapidly rotating stars, it has the advantage that it is fully analytic and that it provides expressions for the electric and magnetic fields produced by the most common modes of oscillation both in the vicinity of the star and far away from it. In this way we revisit and extend to a relativistic context the classical estimates of McDermott et al. Overall, we find that general-relativistic corrections lead to electromagnetic damping time-scales that are at least one order of magnitude smaller than in Newtonian gravity. Furthermore, with the only exception of $g$ (gravity) modes, we find that $f$ (fundamental), $p$ (pressure), $i$ (interface) and $s$ (shear) modes are suppressed more efficiently by gravitational losses than by electromagnetic ones.