R-modes of a neutron star with a magnetic dipole field

Abstract

We study $r$-modes of a rotating magnetized neutron star, assuming a magnetic dipole field whose axis is aligned with the axis of rotation. We approach the problem by applying a singular perturbation theory to the oscillations of rotating stars. In this treatment, we divide the star into a thin surface magnetic layer and a non-magnetic core. We integrate linearized ideal MHD equations in the surface magnetic layer and non-magnetic oscillation equations in the core, and match the two integrations at the interface to obtain a complete solution. For a polytropic neutron star model of mass $M=1.4M_{\odot }$ and radius $R=10^6$cm, the magnetic dipole field becomes effective on the modal properties of the $r$-modes only when the field strength $B_S$ is much greater than $10^{14}$G. We also find that the damping effects caused by very short magnetic perturbations in the surface layer are not important for the $r$-mode instability of rapidly rotating neutron stars if the field strength $B_S$ is smaller than $10^{12}$G.

arXiv commentAccepted for publication in MN

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• Non-radial oscillations of the magnetized rotating stars with purely toroidal magnetic fields
• A $r$-mode in a magnetic rotating spherical layer: application to neutron stars
• Generation of strong magnetic fields by r-modes in millisecond accreting neutron stars: induced deformations and gravitational wave emission
• Axisymmetric toroidal modes of general relativistic magnetized neutron star models
• Limits on Magnetic Field Amplification from the r-Mode Instability
• Differential rotation and r-modes in magnetized neutron stars
• Evolution of newborn rapidly rotating magnetars: effects of r-mode and fall-back accretion
• Non-axisymmetric magnetic modes of neutron stars with purely poloidal magnetic fields
• Long term evolution of CFS-unstable neutron stars and role of differential rotation on short time-scales
• Axisymmetric spheroidal modes of neutron stars magnetized with poloidal magnetic fields