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 Tcp(ρ) and Tcn(ρ) of singlet-state proton and triplet-state neutron pairing in a stellar core and consider a strong proton pairing (with maximum T cp >∼ 5 × 10 9 K) and a moderate neutron pairing (T cn ∼ 6× 10 8 K). When the internal stellar temperature T falls below T cn , the neutrino luminosity LCP due to Cooper pairing of neutrons behaves ∝ T , 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 Tcn(ρ) 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.