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We derive analytic approximations for the neutrino luminosities and the heatcapacities of neutron stars with isothernal nucleon cores as functions of themass and radius of stars. The neutrino luminosities are approximated for thethree basic neutrino emission mechanisms, and the heat capacities for the fivebasic combinations of the partial heat capacities. The approximations are validfor for a wide class of equations of state of dense nucleonmatter. The resultssignificantly simplify the theoretical interpretation of observations ofcooling neutron stars as well as of quasistationary thermal states of neutronstars in X-ray transients. For illustration, we present an analysis of theneutrino cooling functions of nine isolated neutron stars taking into accountthe effects of their magnetic fields and of the presence of light elements intheir heat blanketing envelopes. These results allow one to investigate thesuperfluid properties of neutron star cores.

Neutrino luminosities and heat capacities of neutron stars in analytic form