Thermal evolution of neutron stars is known to depend on the properties of superdense matter in neutron star cores. We suggest statistical analysis of isolated cooling middle-aged neutron stars and old transiently accreting quasi-stationary neutron stars warmed up by deep crustal heating in low-mass X-ray binaries. The method is based on simulations of the evolution of stars of different masses and on averaging the results over respective mass distributions. This gives theoretical distributions of isolated neutron stars in the surface temperature—age plane and of accreting stars in the photon thermal luminosity—mean mass accretion rate plane to be compared with observations. This approach permits to explore not only superdense matter but also the mass distributions of isolated and accreting neutron stars. We show that the observations of these stars can be reasonably well explained by assuming the presence of the powerful direct Urca process of neutrino emission in the inner cores of massive stars, introducing a slight broadening of the direct Urca threshold (for instance, by proton superfluidity), and by tuning mass distributions of isolated and accreted neutron stars.

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