Analytic approximations of neutrino luminosities and heat capacities of neutron stars with nucleon cores

We derive analytic approximations of neutrino luminosities and heat capacities of neutron stars with nucleon cores valid for a wide class of equations of state of dense nucleon matter. The neutrino luminosities are approximated for the three cases in which they are produced by (i) direct Urca or (ii) modified Urca processes in non-superfluid matter, or (iii) neutrino-pair bremsstrahlung in neutron-neutron collisions (when other neutrino reactions are suppressed by strong proton superfluidity). The heat capacity is approximated for the two cases of (i) non-superfluid cores and (ii) the cores with strong proton superfluidity. The results can greatly simplify numerical simulations of cooling neutron stars with isothermal interiors at the neutrino and photon cooling stages as well as simulations of quasi-stationary internal thermal states of neutron stars in X-ray transients. For illustration, a model-independent analysis of thermal states of the latter sources is outlined.