Neutrino emission due to Cooper-pair recombination in neutron stars revisited

TL;DR

This paper revisits neutrino emission from Cooper-pair recombination in neutron stars, demonstrating that superfluid Fermi liquid effects and Ward identity compliance lead to a suppressed emissivity primarily governed by axial-vector currents.

Contribution

It provides a systematic expansion of neutrino emissivities considering superfluid Fermi liquid effects, confirming weak current conservation and quantifying suppression factors.

Findings

Neutrino emissivity on neutron pairs is suppressed by ~v_{F,n}^2.

Proton pair processes are similarly suppressed by ~v_{F,p}^2.

Axial-vector currents dominate the emission processes.

Abstract

Neutrino emission in processes of breaking and formation of neutron and proton Cooper pairs is calculated within the Larkin-Migdal-Leggett approach for a superfluid Fermi liquid. We demonstrate explicitly that the Fermi-liquid renormalization respects the Ward identity and assures the weak vector current conservation. The systematic expansion of the emissivities for small temperatures and nucleon Fermi velocity, v_{F,i}, i=n,p, is performed. Both neutron and proton processes are mainly controlled by the axial-vector current contributions, which are not strongly changed in the superfluid matter. Thus, compared to earlier calculations the total emissivity of processes on neutrons paired in the 1S_0 state is suppressed by a factor ~(0.9-1.2) v_{F,n}^2. A similar suppression factor (~v_{F,p}^2) arises for processes on protons.