Viscosity and r-mode damping in stars with quark matter

The effect of shear and bulk viscosity on $r$-mode oscillations in compact stars with quark matter is presented. We consider both the ungapped and gapped color-flavor-locked (CFL) phase of quark matter. In ungapped quark phase $r$-mode is damped for temperatures $10^8$ K $-5\times 10^9$ K even for rapid rotations whereas in CFL phase $r$-mode is not damped in the temperature range $10^{10}$ K $-10^{11}$ K. We find viscous damping of $r$-mode in quark matter leads to larger critical frequencies and smaller spin-periods compared to rotating neutron stars.