Viscous damping ofr-mode oscillations in compact stars with quark matter

Abstract

We determine characteristic time scales for the viscous damping of $r$-mode oscillations in rapidly rotating compact stars that contain quark matter. We present results for the color-flavor-locked (CFL) phase of dense quark matter, in which the up, down, and strange quarks are gapped, as well as the normal (ungapped) quark phase. While the ungapped quark phase supports a temperature window ${10}^{8}\text{ }\text{ }\mathrm{K}\ensuremath{\le}T\ensuremath{\le}5\ifmmode\times\else\texttimes\fi{}{10}^{9}\text{ }\text{ }\mathrm{K}$ where the $r$ mode is damped even for rapid rotation, the $r$ mode in a rapidly rotating pure CFL star is not damped in the temperature range ${10}^{10}\text{ }\text{ }\mathrm{K}\ensuremath{\le}T\ensuremath{\le}{10}^{11}\text{ }\text{ }\mathrm{K}$. Rotating hybrid stars with quark matter cores display an instability window whose width is determined by the amount of quark matter present, and they can have large spin frequencies outside this window. Except at high temperatures $T\ensuremath{\ge}{10}^{10}\text{ }\text{ }\mathrm{K}$, the presence of a quark phase allows for larger critical frequencies and smaller spin periods compared to rotating neutron stars. If low-mass x-ray binaries contain a large amount of ungapped or CFL quark matter, then our estimates of the $r$-mode instability suggest that there should be a population of rapidly rotating binaries at $\ensuremath{\nu}\ensuremath{\gtrsim}1000\text{ }\text{ }\mathrm{Hz}$ which have not yet been observed.