Neutron star cooling

In order to study the sensitivity of neutron star cooling to nucleon superfluidity and to discover whether neutron stars can cool quickly enough to satisfy the Crab pulsar blackbody observability constraint in the absence of pion condensates, we have performed cooling calculations within a variety of scenarios using a simple, constant-density model for the neutron star interior. These scenarios involve different contributions to the total luminosity and different combinations of proton and neutron superfluidity. To maximize superfluidity effects on the cooling, superfluid gaps are employed which are the maxima as functions of density for particular effective-mass values. Among the cooling processes considered are surface photon emission, neutrino pair bremsstrahlung from the Coulomb scattering of electrons off of crust nuclei, and two interior neutrino processes: the modified Urca process and neutrino pair bremsstrahlung from nucleon-nucleon scattering. Our results indicate that the major effect of proton superfluidity is to retard cooling in its early stages through suppression of the Urca process while the major effect of neutron superfluidity is to accelerate cooling in later stages through reduction of the neutron specific heat. Furthermore, we find that photons alone cannot cool neutron stars to the Crab pulsar observability limit fast enough but that any of the combinations of neutrino processes considered can, regardless of the existence of superfluidity. Thus cooling considerations alone do not currently indicate the existence of pion condensates in neutron stars. On the other hand, a reduction of the observability limit from the present value (4.7 x 106 K) to 2.0 x 106 K would be difficult to accommodate within cooling scenarios without pion condensates