Three types of cooling superfluid neutron stars: Theory and observations

Cooling of neutron stars (NSs) with the cores composed of neutrons, protons, and electrons is simulated assuming 1S0 pairing of neutrons in the NS crust, and also 1S0 pairing of protons and weak 3P2 pairing of neutrons in the NS core, and using realistic density profiles of the superfluid critical temperatures $T_{\rm c}(\rho)$. The theoretical cooling models of isolated middle-aged NSs can be divided into three main types. (I) Low-mass, slowly cooling NSs where the direct Urca process of neutrino emission is either forbidden or almost fully suppressed by the proton superfluidity. (II) Medium-mass NSs which show moderate cooling via the direct Urca process suppressed by the proton superfluidity. (III) Massive NSs which show fast cooling via the direct Urca process weakly suppressed by superfluidity. Confronting the theory with observations we treat RX J0822–43, PSR 1055–52 and RX J1856–3754 as slowly cooling NSs. To explain these sufficiently warm sources we need a density profile $T_{\rm c}(\rho)$ in the crust with a rather high and flat maximum and sharp wings. We treat 1E 1207–52, RX J0002+62, PSR 0656+14, Vela, and Geminga as moderately cooling NSs. We can determine their masses for a given model of proton superfluidity, $T_{\rm cp}(\rho)$, and the equation of state in the NS core. No rapidly cooling NS has been observed so far