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

Umin Lee
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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.

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Umin Lee. 2004-11-30. R-modes of a neutron star with a magnetic dipole field. https://doi.org/10.1111/j.1365-2966.2004.08614.x

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