Role of the $δ$ Meson in the Equation of State an Direct Urca Cooling of Neutron Stars

Abstract

The direct Urca (dUrca) process is a key mechanism driving rapid neutrino cooling in neutron stars, with its baryon density activation threshold determined by the microscopic model for nuclear matter. Understanding how nuclear interactions shape the dUrca threshold is essential for interpreting neutron star thermal evolution, particularly in light of recent studies on exceptionally cold objects. We investigate the impact of incorporating the scalar isovector $δ$ meson into the neutron star equation of state, which alters the internal proton fraction and consequently affects the dUrca cooling threshold. Since proton superfluidity is known to suppress dUrca rates, we also examine the interplay between the nuclear interaction mediated by the $δ$ meson and the $^1S_0$ proton pairing gap. We perform a Bayesian analysis using models built within a relativistic mean-field approximation, incorporating constraints from astrophysical observations, nuclear experiments, and known results of \textit{ab initio} calculations of pure neutron matter. We then impose a constraint on the dUrca threshold based on studies of fast-cooling neutron stars. The inclusion of $δ$ meson expands the range of possible internal compositions, directly influencing the stellar mass required for the central density to reach the dUrca threshold. Furthermore, we observe that the observation of relatively young and cold neutron stars provides insights into $^1S_0$ proton superfluidity in the core of neutron stars.