Enhanced cooling of neutron stars via Cooper-pairing neutrino emission

Abstract

We simulate cooling of superfluid neutron stars with nucleon cores where the direct Urea 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 strong proton pairing (with maximum Tcpmax ≳ 5 × 109 K) and moderate neutron pairing (Tcnmax ∼ 6 × 108 K). When the internal stellar temperature T falls below Tcnmax, the neutrino luminosity LCP due to Cooper pairing of neutrons behaves ∝T8, just as that produced by the modified Urea 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(ρ) we can explain observations of cooling isolated neutron stars in the scenario in which the direct Urea process or a similar process in kaon/pion condensed or quark matter are absent.