Hyperon bulk viscosity in the presence of antikaon condensate

We investigate the hyperon bulk viscosity due to the non-leptonic process $n + p \rightleftharpoons p + \Lambda $ in $K^-$ condensed matter and its effect on the r-mode instability in neutron stars. We find that the hyperon bulk viscosity coefficient in the presence of antikaon condensate is suppressed compared with the case without the condensate. The suppressed hyperon bulk viscosity in the superconducting phase is still an efficient mechanism to damp the r-mode instability in neutron stars.