Revisiting the thermal relaxation of neutron stars

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.

The Influence of Intermittent Fatigue Exercise on Early and Late Phases of Relaxation From Maximal Voluntary Contraction

Twenty-two young male subjects were tested to estimate the behavior of the early and late phases of relaxation from a 3-s maximal voluntary contraction (MVC) under the influence of fatigue. Less demanding and more demanding protocols of intermittent hand grip exercise were used to fatigue muscle. Before and after fatigue, the early and late relaxation time, maximal relaxation rate, and half-relaxation time were measured. The results showed that during voluntary movement (a) the early phase of relaxation was independent of the mode of intermittent exercise and did not change significantly after fatigue; (b) the late relaxation time and absolute maximal relaxation rate were slower after both protocols, with the changes more pronounced following the more demanding protocol; and (c) the half-relaxation time and relative maximal relaxation rate were changed only in the more demanding protocol. It is concluded that unlike the relaxation following electrical stimulation of isolated muscle, the early phase of relaxation from voluntary contraction appears to be the most resistant to the type of intermittent fatiguing exercise used in the present study, whereas the late relaxation time was the most sensitive to this type of fatigue. Key words: hand grip exercise, late relaxation time, early relaxation time, half-relaxation time