Neutrino luminosities and heat capacities of neutron stars in analytic form

We derive analytic approximations for the neutrino luminosities and the heat capacities of neutron stars with isothermal nucleon cores as functions of the mass and radius of stars. The neutrino luminosities are approximated for the three basic neutrino emission mechanisms, and the heat capacities for the five basic combinations of the partial heat capacities. The approximations are valid for a wide class of equations of state of dense nucleon matter. The results significantly simplify the theoretical interpretation of observations of cooling neutron stars as well as of quasistationary thermal states of neutron stars in x-ray transients. For illustration, we present an analysis of the neutrino cooling functions of nine isolated neutron stars taking into account the effects of their magnetic fields and of the presence of light elements in their heat blanketing envelopes. These results allow one to investigate the superfluid properties of neutron star cores.