Nucleon effective mass in neutron stars cooling

The cooling of neutrons stars, which are composed of ultra-high-density nuclear matter, strongly depends on the equation of state because the dominant cooling sources are neutrinos produced in their interiors. Here, we investigate the cooling properties of neutron stars, focusing on effective nucleon masses, whose impacts have been recently examined in supernova explosion and proto-neutron star cooling. The uncertainties of effective masses originate from the difference in the attractive interaction of scalar meson and the definition of the Dirac and Landau masses. At first, we employ so-called Walecka models that allow these two masses to be introduced within a unified framework and evaluate the resulting cooling curves. Based on the Walecka model, we compute the emissivity of the neutrons and the direct Urca process and their cooling curves. We demonstrate that the Dirac and Landau masses affect cooling of massive neutron stars, although most previous cooling simulations do not distinguish them. We also perform cooling simulations with two realistic equation of states based on relativistic mean-field (RMF) theory, whose differences arise from properties of only effective masses among characteristic parameters. These results are broadly consistent with those obtained from the Walecka models, indicating that the treatment of effective nucleon masses may be an important source of uncertainty in neutron-star cooling.