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

Abstract

The combined impact of rotation and magnetic fields on oscillations of stellar fluids is still<br><br>not well known theoretically. It mixes Alfv´en and inertial waves. Neutron stars are a place<br><br>where both effects may be at work. We aim to solve this problem in the context of the<br><br>r-mode instability in neutron stars, as it appears when these modes are coupled to gravitational<br><br>radiation.We consider a rotating spherical shell filled with a viscous fluid of infinite electrical conductivity<br><br>and analyse propagation of model 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 (the ratio of Alfv´en speed to rotation speed) exceeds a value proportional to the one-fourth power of the Ekman number (a 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 1014 G are necessary to perturb the r-mode instability.