Neutrino emission from triplet pairing of neutrons in neutron stars

TL;DR

This paper investigates neutrino emission from triplet neutron pairing in neutron stars, accounting for anomalous weak interactions and showing significant suppression of neutrino emissivity compared to previous estimates.

Contribution

It derives self-consistent equations for anomalous weak vertices considering $^{3}P_{2}$ pairing and quantifies the suppression of neutrino emission due to anomalous interactions.

Findings

Neutrino emission via the vector channel is suppressed and vanishes in the nonrelativistic limit.

The axial channel is moderately suppressed.

Total neutrino emissivity is reduced by a factor of approximately 0.19.

Abstract

Neutrino emission due to the pair breaking and formation processes in the bulk triplet superfluid in neutron stars is investigated with taking into account of anomalous weak interactions. We consider the problem in the BCS approximation discarding Fermi-liquid effects. In this approach we derive self-consistent equations for anomalous vector and axial-vector vertices of weak interactions taking into account the $^{3}P_{2}- ^{3}F_{2}$ mixing. Further we simplify the problem and consider the pure $^{3}P_{2}$ pairing with $m_{j}=0$, as is adopted in the minimal cooling paradigm. As was expected because of current conservation we have obtained a large suppression of the neutrino emissivity in the vector channel. More exactly, the neutrino emission through the vector channel vanishes in the nonrelativistic limit $V_F=0$. The axial channel is also found to be moderately suppressed. The total neutrino emissivity is suppressed by a factor of $1.9\times10^{-1}$ relative to original estimates using bare weak vertices.