Enhanced cooling of neutron stars via Cooper-pairing neutrino emission

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.