# Singlet S-wave superfluidity of proton in neutron star matter

## TL;DR

This paper investigates proton superfluidity in neutron star matter, showing hyperons influence the energy gap and density range, thus affecting the superfluid properties and equation of state of neutron stars.

## Contribution

It provides a detailed analysis of how hyperons affect proton superfluidity and the density range of superfluidity in neutron star matter using BCS theory.

## Key findings

- Hyperons slightly decrease the proton pairing gap in most densities.
- At higher densities, hyperons increase the pairing gap significantly.
- Hyperons extend the density range where proton superfluidity exists.

## Abstract

The possible $^{1}S_{0}$ protonic superfluidity is investigated in neutron star matter, and the corresponding energy gap as a function of baryonic density is calculated on the basis of BCS gap equation. We have discussed particularly the influence of hyperon degrees of freedom on $^{1}S_{0}$ protonic superfluidity. It is found that the appearance of hyperons leads to a slight decrease of $^{1}S_{0}$ protonic pairing energy gap in most density range of existing $^{1}S_{0}$ protonic superfluidity. However, when the baryonic density $\rho_{B}>$0.377 (or 0.409) fm${^{-3}}$ for TM1 (or TMA) parameter set, $^{1}S_{0}$ protonic pairing energy gap is significantly larger than the corresponding values without hyperons. And the baryonic density range of existing $^{1}S_{0}$ protonic superfluidity is widen due to the appearance of hyperons. In our results, the hyperons not only change the EOS and bulk properties but also change the size and baryon density range of $^{1}S_{0}$ protonic superfluidity in neutron star matter.