  We model the thermal states of both isolated neutron stars and accreting
neutron stars in X-ray transients in quiescence and confront them with
observations. We use an equation of state and superfluid baryon gaps, which are
consistently calculated. We conclude that the direct Urca process is required
to be consistent with low-luminous accreting neutron stars. In addition, proton
superfluidity and sufficiently weak neutron superfluidity are necessary to
explain the cooling of middle-aged neutron stars and to obtain a realistic
distribution of neutron star masses.

High Energy Astrophysical Phenomena;Nuclear Theory