The cooling of Akmal–Pandharipande–Ravenhall neutron star models

We study the cooling of superfluid neutron stars whose cores consist of nucleon matter with the Akmal–Pandharipande–Ravenhall (APR) 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 recent studies (Papers I and II), we employ phenomenological density-dependent critical temperatures T cp(ρ) of strong singlet-state proton pairing (with the maximum T max cp ∼ 7 × 109 K in the outer stellar core) and T cnt(ρ) of moderate triplet-state neutron pairing (with the maximum T max cnt ∼ 6 × 108 K in the inner core). Choosing the position of T max cnt properly, we can obtain a representative class of massive neutron stars whose cooling is intermediate between the cooling enhanced by 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.