Cooling of neutron stars (NSs) with the cores composed of neutrons, protons, and electrons is simulated assuming $^1$S$_0$ pairing of neutrons in the NS crust, and also $^1$S$_0$ pairing of protons and weak $^3$P$_2$ 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) { \it Low-mass}, { \it slowly cooling} NSs where the direct Urca process of neutrino emission is either forbidden or almost fully suppressed by the proton superfluidity. (II) { \it Medium-mass} NSs which show { \it moderate} cooling via the direct Urca process suppressed by the proton superfluidity. (III) { \it Massive} NSs which show { \it 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.
Categories: astro-ph