Bulk viscosity in 2SC quark matter

The bulk viscosity of three-flavour colour-superconducting quark matter originating from the nonleptonic process u + s <-> u + d is computed. It is assumed that up and down quarks form Cooper pairs while the strange quark remains unpaired (2SC phase). A general derivation of the rate of strangeness production is presented, involving contributions from a multitude of different subprocesses, including subprocesses that involve different numbers of gapped quarks as well as creation and annihilation of particles in the condensate. The rate is then used to compute the bulk viscosity as a function of the temperature, for an external oscillation frequency typical of a compact star r-mode. We find that, for temperatures far below the critical temperature T-c for 2SC pairing, the bulk viscosity of colour-superconducting quark matter is suppressed relative to that of unpaired quark matter, but for T greater than or similar to T-c/30 the colour-superconducting quark matter has a higher bulk viscosity. This is potentially relevant for the suppression of r-mode instabilities early in the life of a compact star.