r‐Modes of Neutron Stars with a Solid Crust

We investigate the properties of $r$-mode oscillations of a slowly rotatingneutron star with a solid crust, by taking account of the effects of theCoriolis force. For the modal analysis we employ three-component neutron starmodels that are composed of a fluid core, a solid crust and a surface fluidocean. 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 thoseconfined in the fluid core, which are most important for the $r$-modeinstability. The $r$-modes do not have any appreciable amplitudes in the solidcrust 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 andeigenfrequency as functions of the angular rotation velocity $\Omega$. Thisindicates that the extrapolation formula, which is obtained in the limit of$\Omega\to 0$, cannot be used to examine the $r$-mode instability of rapidlyrotating neutron stars with a solid crust unless the effects of mode couplingwith the crustal torsional modes are correctly taken into account.Comment: 10 pages, 3 figures, revised version accepted for publication in the Ap