Direct Urca processes involving singlet proton superfluidity in neutron star cooling

A detailed description of the baryon direct Urca processes A: $n\rightarrow p+e+\bar{\nu}_{e}$, B: $\Lambda\rightarrow p+e+\bar{\nu}_{e}$, C: $\Xi^{-}\rightarrow\Lambda+e+\bar{\nu}_{e}$ related to the neutron star cooling is given in the relativistic mean field approximation.The contributions of the reactions B and C on the neutrino luminosity are calculated by means of the relativistic expressions of the neutrino energy losses.Our results show that the total neutrino luminosities of the reactions A, B, C within the mass range 1.603-2.067$M_{\odot}$ (1.515-1.840$M_{\odot}$ for TM1 model) for GM1 model are larger than the corresponding values for neutron stars in npe$\mu$ matter. Although the hyperon direct Urca processes B and C reduce the neutrino emissivity of the reaction A, it illustrates the reactions B and C still make the total neutrino luminosity enhancement in the above mentioned areas.Furthermore, when we only consider the $^{1}S_{0}$ proton superfluidity in neutron star cooling, we find that although the neutrino emissivity of the reactions A and B is suppressed with the appearance of $^{1}S_{0}$ proton superfluidity, the total contribution of the reactions A, B, C can still quicken a massive neutron star cooling.These results could be used to help prove appearing hyperons in PSR J1614-2230 and J0348+0432 from neutron star cooling perspective.