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

Abstract

The impact of the combination of rotation and magnetic fields on oscillations of stellar fluids is still not well known theoretically. It mixes Alfvén 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 Alfvén 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 Alfvén 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.

9 pages, 6 figures, to appear in Monthly Notices of RAS

References in corpus (3)

• Axial invariance of rapidly varying diffusionless motions in the Earth's core interior
• Ekman layer damping of r-modes revisited
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• Long term evolution of CFS-unstable neutron stars and role of differential rotation on short time-scales
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