Direct Urca neutrino rate in color superconducting quark matter

If deconfined quark matter exists inside compact stars, the primary cooling mechanism is neutrino radiation via the direct Urca processes d -> u+e+ -> nu(e) and u+e -> d+nu(e). Below a critical temperature, T-c, quark matter forms a color superconductor, one possible manifestation of which is a condensate of < ud > quark Cooper pairs in an electric-charge neutralizing background of electrons. We compute the neutrino emission rate from such a phase, including charged pair-breaking and recombination effects, and find that on a material temperature domain below T-c the pairing-induced suppression of the neutrino emission rate is not uniformly exponential. If gapless modes are present in the condensed phase, the emissivity at low temperatures is moderately enhanced above that of completely unpaired matter. The importance of charged current pair-breaking processes for neutrino emission both in the fully gapped and partially gapped regimes is emphasized.