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We simulate cooling of superfluid neutron stars with nucleon cores where direct Urca process is forbidden. We adopt density dependent critical temperatures $T_{cp}(rho)$ and $T_{cn}(rho)$ of singlet-state proton and triplet-state neutron pairing in a stellar core and consider a strong proton pairing (with maximum $T_{cp}^{max} ga 5 times 10^9$ K) and a moderate neutron pairing ($T_{cn}^{max} sim 6 times 10^8$ K). When the internal stellar temperature $T$ falls below $T_{cn}^{max}$, the neutrino luminosity $L_{CP}$ due to Cooper pairing of neutrons behaves $propto T^8$, just as that produced by modified Urca process (in a non-superfluid star) but is higher by about two orders of magnitude. In this case the Cooper-pairing neutrino emission acts like an enhanced cooling agent. By tuning the density dependence $T_{cn}(rho)$ we can explain observations of cooling isolated neutron stars in the scenario in which direct Urca process or similar process in kaon/pion condensed or quark matter are absent.
The minimal cooling paradigm for neutron star cooling assumes that enhanced cooling due to neutrino emission from any direct Urca process, due either to nucleons or to exotica such as hyperons, Bose condensates, or deconfined quarks, does not occur.
In this review, I present a brief summary of the impact of nucleon pairing at supra-nuclear densities on the cooling of neutron stars. I also describe how the recent observation of the cooling of the neutron star in the supernova remnant Cassiopeia A
Neutrino emission in processes of breaking and formation of neutron and proton Cooper pairs is calculated within the Larkin-Migdal-Leggett approach for a superfluid Fermi liquid. We demonstrate explicitly that the Fermi-liquid renormalization respect
Neutrino emissivities in a neutron star are computed for the neutrino bremsstrahlung process. In the first part the electro-weak nucleon-nucleon bremsstrahlung is calculated in free space in terms of a on-shell $T$-matrix using a generalized Low ener
We study the cooling of isolated neutron stars with particular regard to the importance of nuclear pairing gaps. A microscopic nuclear equation of state derived in the Brueckner-Hartree-Fock approach is used together with compatible neutron and proto