Effects of temperature on the structure of neutron stars at high temperature

In Newtonian physics, higher temperature leads to higher thermal pressure, which provides stronger support against the gravitational contraction of stars. However, in the temperature range of tens of MeV involved in the evolution of a proto-neutron star or a higher massive neutron star, the effects of temperature are richer. We showed that, for a high temperature neutron star (HTNS) constructed with a realistic equation of state (EOS), the HTNS may expand or contract during cooling, the central density may increase or decrease, the quasi-normal mode oscillation frequencies may increase or decrease, and in particular, (i) independent of the EOS, for a HTNS of a given mass, there exists a maximum temperature \(T_{max}\) that it could ever attend at birth (with the value of \(T_{max}\) different for different EOS), and (ii) for the Hempel EOS and the Shen EOS, there is a range of mass that the HTNS may gravitationally collapse after a period of radiative cooling; however, for the Lattimer–Swesty EOS and Banik EOS, no delayed collapse is possible. Our study, which describes the cooling of HTNSs with simple quasi-stationary TOV sequences, provides an understanding of the effects of the thermal energy/pressure at high temperature, and a demonstration that different EOSs can lead to qualitatively different evolution paths.