Statistical theory of thermal evolution of neutron stars - II. Limitations on direct Urca threshold

We apply our recently suggested statistical approach to thermal evolution of isolated neutron stars and accreting quasi-stationary neutron stars in X-ray transients for constraining the position and relative broadening a of the direct Urca threshold of powerful neutrino emission in neutron star cores. We show that most likely explanation of observations corresponds to alpha approximate to 0.08-0.10 and to the neutron star mass, at which the direct Urca process is open, M-D approximate to 1.6-1.8 M-circle dot.