Effect of a neutron-star crust on the r-mode instability - art. no. 084030

The presence of a viscous boundary layer under the solid crust of a neutron star dramatically increases the viscous damping rate of the fluid r-modes. We improve previous estimates of this damping rate by including the effect of the Coriolis force on the boundary-layer eigenfunction and by using mor e realistic neutron-star models. If the crust is assumed to be perfectly ri gid, the gravitational radiation driven instability in the r-modes is compl etely suppressed in neutron stars colder than about 1.5x10(8) K. Energy gen eration in the boundary layer will heat the star, and will even melt the cr ust if the amplitude of the r-mode is large enough. We solve the heat equat ion explicitly (including the effects of thermal conduction and neutrino em ission) and find that the r-mode amplitude needed to melt the crust is alph a (c) approximate to 5 x 10(-3) for maximally rotating neutron stars. Ii th e r-mode saturates at an amplitude larger than alpha (c), the heat generate d is sufficient to maintain the outer layers of the star in a mixed fluid-s olid state analogous to the pack ice on the fringes of the Arctic Ocean. We argue that in young, rapidly rotating neutron stars this effect considerab ly delays the formation of me crust. By considering the dissipation in the ice flow, we show that the final spin frequency of stars with r-mode amplit ude of order unity is close to the value estimated for fluid stars without a crust.