Role of antikaon condensation in r-mode instability

We investigate the effect of antikaon condensed matter on bulk viscosity in rotating neutron stars. We use relativistic field theoretical models to construct the equation of state of neutron stars with the condensate, where the phase transition from nucleonic to K condensed phase is assumed to be of first order. We calculate the coefficient of bulk viscosity due to the non-leptonic weak interaction n ⇀↽ p + K. The influence of antikaon bulk viscosity on the gravitational radiation reaction driven instability in the r-modes is investigated. We compare our results with the previously studied non-leptonic weak interaction n+ p ⇀↽ p+Λ involving hyperons on the damping of the r-mode oscillations. We find that the bulk viscosity coefficient due to the non-leptonic weak process involving the condensate is suppressed by several orders of magnitude in comparison with the non-superfluid hyperon bulk viscosity coefficient. Consequently, the antikaon bulk viscosity may not be able to damp the r-mode instability, while hyperon bulk viscosity can effectively suppress r-mode oscillations at low temperatures. Hence neutron stars containing K condensate in their core could be possible sources of gravitational waves.