Astronomy and Astrophysics – Astrophysics
Scientific paper
2000-06-08
Astrophys.J. 546 (2001) 1121-1125
Astronomy and Astrophysics
Astrophysics
10 pages, 3 figures, revised version accepted for publication in the ApJ
Scientific paper
10.1086/318292
We investigate the properties of $r$-mode oscillations of a slowly rotating neutron star with a solid crust, by taking account of the effects of the Coriolis force. For the modal analysis we employ three-component neutron star models that are composed of a fluid core, a solid crust and a surface fluid ocean. For the three-component models, we find that there exist two kinds of $r$-modes, that is, those confined in the surface fluid ocean and those confined in the fluid core, which are most important for the $r$-mode instability. The $r$-modes do not have any appreciable amplitudes in the solid crust if rotation rate of the star is sufficiently small. We find that the core $r$-modes are strongly affected by mode coupling with the crustal torsional (toroidal) modes and lose their simple properties of the eigenfunction and eigenfrequency as functions of the angular rotation velocity $\Omega$. This indicates that the extrapolation formula, which is obtained in the limit of $\Omega\to 0$, cannot be used to examine the $r$-mode instability of rapidly rotating neutron stars with a solid crust unless the effects of mode coupling with the crustal torsional modes are correctly taken into account.
Lee Umin
Yoshida Shijun
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