Singlet S-wave superfluidity of proton in neutron star matter

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.