Proton pairing in neutron stars from chiral effective field theory

TL;DR

This paper investigates how three-body nuclear forces influence proton pairing in neutron star matter, showing they reduce the pairing gap and critical temperature, with implications for neutron star cooling.

Contribution

It provides a chiral effective field theory-based calculation of proton pairing gaps in neutron stars, emphasizing the impact of three-body forces and model uncertainties.

Findings

Three-body forces decrease the proton pairing gap.

The maximum density for proton pairing is reduced.

Critical temperature for proton superconductivity is estimated as (3.7 - 6.0)×10^9 K.

Abstract

We study the ${}^{1}S_0$ proton pairing gap in beta-equilibrated neutron star matter within the framework of chiral effective field theory. We focus on the role of three-body forces, which strongly modify the effective proton-proton spin-singlet interaction in dense matter. We find that three-body forces generically reduce both the size of the pairing gap and the maximum density at which proton pairing may occur. The pairing gap is computed within BCS theory, and model uncertainties are estimated by varying the nuclear potential and the choice of single-particle spectrum in the gap equation. We find that a second-order perturbative treatment of the single-particle spectrum suppresses the proton ${}^{1}S_0$ pairing gap relative to the use of a free spectrum. We estimate the critical temperature for the onset of proton superconductivity to be $T_c = (3.7 - 6.0)\times 10^{9} $ K, which is consistent with previous theoretical results in the literature and marginally within the range deduced from a recent Bayesian analysis of neutron star cooling observations.