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Neutrino Emissivity of Non-equilibrium beta processes With Nucleon Superfluidity

We investigate the influence of nucleon superfluidity on the neutrino emissivity of non-equilibrium beta processes. Calculations are performed of the reduction factors for direct and modified Urca processes with three types of nucleon superfluidity in $npe$ matter. The numerical results are given since the analytical solution is impossible. We find that the behavior of the superfluid influence is closely related to the chemical departure from beta equilibrium. For small chemical departure, the superfluid reduction factor almost only depends on the gap but is hardly affected by the departure. While for the departure large enough, it rapidly enhances the neutrino emissivity. The onset of the "enchanced" emission has some corresponding thresholds which seem to be linked to the ratio of the energy gap to the chemical departure.