Properties of r modes in rotating magnetic neutron stars. I. Kinematic Secular Effects and Magnetic Evolution Equations

TL;DR

This paper investigates the kinematic effects and magnetic field evolution in rotating neutron stars with r-mode oscillations, highlighting how secular velocity fields can generate strong magnetic fields rapidly, influencing the star's stability.

Contribution

It introduces detailed analysis of secular kinematic effects and magnetic field evolution equations in r-mode oscillations of neutron stars, extending previous work.

Findings

Secular velocity fields produce toroidal fluid drifts.

Magnetic fields can reach equipartition within a year.

Full numerical analysis will be presented in a companion paper.

Abstract

The instability of r-mode oscillations in rapidly rotating neutron stars has attracted attention as a potential mechanism for producing high frequency, almost periodic gravitational waves. The analyses carried so far have shown the existence of these modes and have considered damping by shear and bulk viscosity. However, the magnetohydrodynamic coupling of the modes with a stellar magnetic field and its role in the damping of the instability has not been fully investigated yet. Following our introductory paper (Rezzolla, Lamb and Shapiro 2000), we here discuss in more detail the existence of secular higher-order kinematical effects which will produce toroidal fluid drifts. We also define the sets of equations that account for the time evolution of the magnetic fields produced by these secular velocity fields and show that the magnetic fields produced can reach equipartition in less than a year. The full numerical calculations as well as the evaluation of the impact of strong magnetic fields on the onset and evolution of the r-mode instability will be presented in a companion paper.