  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.

Astrophysics