r-modes of neutron stars with a solid crust

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 Ω. This indicates that the extrapolation formula, which is obtained in the limit of Ω → 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.