A simple cooling model for neutron stars with superfluid cores: Comparisonwith observations

The cooling of neutron stars (NSs) with superfluid cores is simulated by ta king into account the neutrino emission produced by Cooper pairing of nucle ons. Two cooling regimes of NSs composed of matter with the same moderately stiff equation of state are studied: the standard cooling (for a 1.30M. st ar, as an example) and the cooling enhanced by the direct Urea process (for a 1.48M.) star). The critical temperatures of neutron and proton superflui dities, T-cn and T-cp, are assumed to be constant over the NS core and are treated as free parameters. They are determined by using the surface temper atures T-s of isolated NSs (RX 50822-43, PSR 1055-52, 1E 1207-52, Vela, Gem inga, PSR 0656+14, RX J0002+62), which are obtained by interpreting the obs erved thermal radiation either with a blackbody spectrum or with hydrogen a tmosphere models. The temperatures T-s of the last five objects for the "at mospheric" interpretation can be explained by the cooling of the same NS wi th the same T-cn and T-cp for all objects. The allowable values of T-cn and T-cp are severely constrained and depend on the cooling regime. The standa rd cooling requires moderately strong neutron and proton superfluidities, w hile the enhanced cooling requires moderate neutron and strong proton super fluidities. If, however, the observations are interpreted with a blackbody spectrum, only the last three objects can be explained in a similar fashion . For both the standard and enhanced cooling, the confidence regions of T-c n and T-cp turn out to be broader than those for the "atmospheric" values o f T-s and consist of two separate subregions. None of the models require si multaneously strong neutron and proton superfluidities (T-cn, T-cp greater than or similar to 3 X 10(9) K), which argues against very soft equations o f state for the NS cores.