  We study the cooling of superfluid neutron stars whose cores consist of
nucleon matter with the Akmal-Pandharipande-Ravenhall equation of state. This
equation of state opens the powerful direct Urca process of neutrino emission
in the interior of most massive neutron stars. Extending our previous studies
(Gusakov et al. 2004a, Kaminker et al. 2005), we employ phenomenological
density-dependent critical temperatures T_{cp}(\rho) of strong singlet-state
proton pairing (with the maximum T_{cp}^{max} \sim 7e9 K in the outer stellar
core) and T_{cnt}(\rho) of moderate triplet-state neutron pairing (with the
maximum T_{cnt}^{max} \sim 6e8 K in the inner core). Choosing properly the
position of T_{cnt}^{max} we can obtain a representative class of massive
neutron stars whose cooling is intermediate between the cooling enhanced by the
neutrino emission due to Cooper pairing of neutrons in the absence of the
direct Urca process and the very fast cooling provided by the direct Urca
process non-suppressed by superfluidity.
