Cooling of Neutron Stars

We introduce the theoretical basis for modeling the cooling evolution of compact stars starting from Boltzmann equations in curved space-time. We open a discussion on observational verification of different neutron star models by consistent statistics. Particular interest has the question of existence of quark matter deep inside of compact object, which has to have a specific influence on the cooling history of the star. Besides of consideration of several constraints and features of cooling evolution, which are susceptible of being critical for internal structure of hot compact stars we have introduced a method of extraction of the mass distribution of the neutron stars from temperature and age data. The resulting mass distribution has been compared with the one suggested by supernove simulations. This method can be considered as an additional checking tool for the consistency of theoretical modeling of neutron stars. We conclude that the cooling data allowed existence of neutron stars with quark cores even with one-flavor quark matter