Neutrino emissivity of $^{3}P_{2}$-$^{3}F_{2}$ superfluid cores in neutron stars

TL;DR

This paper investigates how the admixture of the $^{3}F_{2}$ state affects collective spin oscillations and neutrino emission in superfluid neutron star cores, revealing new oscillation modes and their impact on star cooling.

Contribution

It introduces a new eigenmode of spin oscillations in triplet superfluid neutron condensates and analyzes their role in neutrino emission processes, including the effects of tensor interactions.

Findings

Existence of a new high-frequency spin oscillation mode at $\, ilde{ u}\,\simeq\sqrt{58/35}\Delta$.

Neutrino emission includes contributions from pair recombination and collective mode decays.

High-frequency oscillation decays are influenced by tensor forces but do not significantly alter total energy losses.

Abstract

The influence of the admixture of the $^{3}F_{2}$ state onto collective spin oscillations and neutrino emission processes in the triplet superfluid neutron liquid is studied in the BCS approximation. The eigen mode of spin oscillations with $\omega\simeq\sqrt{58/35}\Delta$ is predicted to exist in the triplet superfluid neutron condensate besides the already known mode $\omega\simeq\Delta/\sqrt{5}$. Excitation of the high-frequency spin oscillations in the condensate occurs through the tensor interactions between quasiparticles. Neutrino energy losses through neutral weak currents are found to consist of three separate contributions caused by a recombination of broken Cooper pairs and by weak decays of the collective modes of spin oscillations. Neutrino decays of the low-frequency spin waves can play an important role in the cooling scenario of neutron stars. Weak decays of the high-frequency oscillations that occur only if the tensor forces are taken into account in the pairing interactions does not modify substantially the total energy losses. Simple expressions are suggested for the total neutrino emissivity.