Role of the δ meson in the equation of state and direct Urca cooling of neutron stars

¹ CFisUC, Department of Physics, University of Coimbra, 3004-516 Coimbra, Portugal
² Université de Caen Normandie, CNRS/IN2P3, LPC Caen, 14050 Caen, France
³ IUF, service du Ministère de l’Enseignement supérieur et de la Recherche, 1 rue Descartes, 75231 Paris Cedex 5, France

^⋆ Corresponding author: lscurto@student.uc.pt

Received: 24 March 2025
Accepted: 13 September 2025

Abstract

Context. The direct Urca (dUrca) process is a key mechanism driving rapid neutrino cooling in neutron stars. Its baryon density activation threshold is determined by the microscopic model for nuclear matter. Nuclear interactions shape the dUrca threshold, and it is essential to understand this for interpreting the thermal evolution of neutron stars, in particular in light of recent studies of exceptionally cold objects.

Aims. We investigated the impact of incorporating the scalar-isovector δ meson into the neutron star equation of state. This alters the internal proton fraction and consequently affects the dUrca cooling threshold. Proton superfluidity is known to suppress dUrca rates, and we therefore also examined the interplay between the nuclear interaction mediated by the δ meson and the ¹S₀ proton-pairing gap.

Methods. We performed a Bayesian analysis using models built within a relativistic mean-field approximation that incorporated constraints from astrophysical observations, nuclear experiments, and known results of ab initio calculations of pure neutron matter. We then imposed a constraint on the dUrca threshold based on studies of fast-cooling neutron stars.

Results. The inclusion of the δ meson expands the range of possible internal compositions and directly influences the stellar mass required for the central density to reach the dUrca threshold. Furthermore, we find that the observation of relatively young and cold neutron stars provides insights into the ¹S₀ proton superfluidity in the core of neutron stars.