Superfluid response and the neutrino emissivity of baryon matter: Fermi-liquid effects

TL;DR

This paper extends the theory of superfluid baryon matter's response to weak fields by including Fermi-liquid effects, analyzing neutrino emission processes relevant to neutron star cooling, and highlighting the impact of interactions on emissivity.

Contribution

It generalizes Leggett's superfluid Fermi-liquid theory to finite temperature and timelike momentum transfer, providing new insights into neutrino emissivity in neutron star matter.

Findings

Neutrino emission mainly via axial-vector neutral currents.

Fermi-liquid interactions modify the temperature dependence of emissivity.

Emissivity remains comparable to BCS approximation despite interactions.

Abstract

The linear response of a nonrelativistic superfluid baryon system on an external weak field is investigated while taking into account of the Fermi-liquid interactions. We generalize the theory developed by Leggett for a superfluid Fermi-liquid at finite temperature to the case of timelike momentum transfer typical of the problem of neutrino emission from neutron stars. A space-like kinematics is also analysed for completeness and compared with known results. We use the obtained response functions to derive the neutrino energy losses caused by recombination of broken pairs in the electrically neutral superfluid baryon matter. We find that the dominant neutrino radiation occurs through the axial-vector neutral currents. The emissivity is found to be of the same order as in the BCS approximation, but the details of its temperature dependence are modified by the Fermi-liquid interactions. The role of electromagnetic correlations in the pairing case of protons interacting with the electron background is discussed in the conclusion.