Using spin-down of neutron stars as a probe of the phases of ultra-dense matter

Spin frequency is the most accurately measurable property of neutron stars. The range of possible frequencies is determined by internal properties, such as the amplitude of ``r-modes,'' which spin the star down by emitting copious gravitational radiation. I will discuss the damping of r-modes by non-linear contributions to the bulk viscosity, which grow with the oscillation amplitude and may become large enough to stop the growth of the r-modes. I will present our results for the viscous damping of the r-modes taking into account the high-amplitude bulk viscosity for different cases of hadronic stars, strange stars and hybrid stars and its effect on the spin-down evolution of the star.