A $r$-mode in a magnetic rotating spherical layer: application to neutron stars

TL;DR

This study investigates how magnetic fields influence r-mode oscillations in neutron stars, revealing that strong magnetic fields above 10^{14} G significantly affect the instability, with implications for gravitational wave emission.

Contribution

The paper provides a numerical analysis of magnetic and rotational effects on r-modes in neutron stars, identifying a specific magnetic field threshold for perturbing the instability.

Findings

Magnetic fields above 10^{14} G perturb r-mode instability in neutron stars.

The influence of magnetic fields depends on the Lehnert number and Ekman number scaling.

Internal shear layers and Alfvén wave wavelengths are key to understanding the magnetic effects.

Abstract

The impact of the combination of rotation and magnetic fields on oscillations of stellar fluids is still not well known theoretically. It mixes Alfv\'en and inertial waves. Neutron stars are a place where both effects may be at work. We wish to decipher the solution of this problem in the context of $r$-modes instability in neutron stars, as it appears when these modes are coupled to gravitational radiation. We consider a rotating spherical shell filled with a viscous fluid but of infinite electrical conductivity and analyze propagation of modal perturbations when a dipolar magnetic field is bathing the fluid layer. We perform an extensive numerical analysis and find that the $m=2$ $r$-mode oscillation is influenced by the magnetic field when the Lehnert number (ratio of Alfv\'en speed to rotation speed) exceeds a value proportional to the one-fourth power of the Ekman number (non-dimensional measure of viscosity). This scaling is interpreted as the coincidence of the width of internal shear layers of inertial modes and the wavelength of the Alfv\'en waves. Applied to the case of rotating magnetic neutron stars, we find that dipolar magnetic fields above $10^{14}$ G are necessary to perturb the $r$-modes instability.