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 quasistationary neutron stars in X-ray transients for constraining the position and relative broadening alpha of the direct Urca threshold of powerful neutrino emission in neutron star cores. We show that most likely explanation of observations corresponds to alpha = 0.08 - 0.10 and to the neutron star mass, at which the direct Urca process is open, M_D = (1.6 - 1.8) M_sun.