Bulk viscosity of Mixed nucleon-hyperon-quark Matter in Neutron stars

We calculate the coefficient of bulk viscosity by considering the non-leptonic weak interactions in the cores of hybrid stars with both hyperons and quarks. We first determine the dependence of the production rate of neutrons on the reaction rate of quarks in the non-leptonic processes, that is $\Gamma_{n}=K_{s}\Gamma_{s}+\Gamma_{\Lambda}+2\Gamma_{\Sigma^{-}}$. The conversion rate, $K_{s}$ in our scenario is a complicated function of baryon number density. We also consider medium effect of quark matter on bulk viscosity. Using these results, we estimate the limiting rotation of the hybrid stars, which may suppress the r-mode instability more effectively. Hybrid stars should be the candidates for the extremely rapid rotators .