Standard and Enhanced Cooling of Neutron Stars with Superfluid Cores

Calculations are performed of the cooling of neutron stars with standard and enhanced neutrino energy losses in the presence of neutron and proton superfluidities in the stellar cores. The effects of superfluidity on the heat capacity and the neutrino luminosity produced by the direct and modified Urca processes and by the neutrino bremsstrahlung emission in nucleon-nucleon collisions are taken into account. The constraints are analyzed on the critical temperatures $\tn$ and $\tp$ of the transition of neutrons and protons to the superfluid state, which can be obtained from a comparison of observational data on thermal radiation from neutron stars with theoretical cooling curves for the standard and enhanced neutrino energy losses. Possible ranges of $\tn$ and $\tp$ for the pulsar Geminga are discussed.