Direct Urca neutrino radiation from superfluid baryonic matter

Dense matter in compact stars cools efficiently by neutrino emission via the direct Urca processes n → p + e + ν̄e and p + e → n + νe. Below the pairing phase transition temperature Tc these processes are suppressed at asymptotically low temperatures exponentially. We compute the emissivity of the Urca process at one loop for temperatures T ≤ Tc, in the case where the baryons are paired in the S0 partial wave. The Urca process is suppressed linearly, rather than exponentially, within the temperature range 0.1 ≤ T/Tc ≤ 1. The charge-current Cooper pairbreaking process contributes up to 25 − 50% of the total Urca emissivity in the superfluid state.