THE COOLING OF NEUTRON-STARS BY THE DIRECT URCA PROCESS

Recent work has shown that many modern nuclear equations of state give proton fractions that are large enough for the direct Urca process to operate in the interiors of neutron stars. We include the direct Urca process in calculations of neutron star cooling and find that the surface temperature of a young neutron star drops catastrophically after approximately 10(2) yr if the direct Urca process is allowed and nucleons do not become superfluid. If nucleon superfluidity occurs throughout the direct Urca region, the surface temperature drops to a value determined by the superfluid transition temperature after approximately 10(2) yr and decreases slowly for the next approximately 10(5) yr, at which time surface photon cooling takes over. The surface temperatures of all of the candidates for thermal X-ray emission from cooling neutron stars are determined by the transition temperature for superfluidity and almost nothing else if these stars cool by direct Urca. By comparison with observational data, we find that superfluid transition temperatures of the order of 10(9) K are required in the whole direct Urca inner core. If neutron stars are created with a range of masses, it is possible that the more massive cool by direct Urca and the less massive do not, resulting in two populations of stars differing in their thermal properties.