2020A&A...642A..42S

In this work, we revisit the thermal relaxation process for neutron stars. Such a process is associated with the thermal coupling between the core and the crust of neutron stars. The thermal relaxation, which takes place at around 10-100 years, is manifested as a sudden drop in the star's surface temperature. Such a drop is smooth for slowly cooling objects and very sharp for fast-cooling ones. In our study, we focused particularly on the cooling of neutron stars whose mass is slightly greater than the value above which the direct Urca (DU) process sets in. Considering different mechanisms for neutrino production in each region of the star, and working with equations of state with different properties, we solved the thermal evolution equation and calculated the thermal relaxation time for an ample range of neutron star masses. By performing a comprehensive study of neutron stars just above the onset of the DU process, we show that stars under these conditions exhibit a peculiar thermal relaxation behavior. We demonstrate that such stars exhibit an abnormally late relaxation time, characterized by a second drop in its surface temperature taking place a later age. We qualified such behavior by showing that it is associated with limited spatial distribution of the DU process in such stars. We show that as the star's mass increases, the DU region also grows, and the star exhibits the expected behavior of fast-cooling stars. Finally, we show that one can expect high relaxation times for stars in which the DU process takes place in a radius no larger than 3 km.