As the most compact stars in the Universe, neutron stars are powerful investigative instruments of both theories of gravitation and the behavior of highly dense matter. The core of neutron stars, still unknown in its composition and behavior, hosts a number of neutrino emission processes that have an impact on the cooling and the exhibited luminosity of neutron stars. Neutrinos are key agents in our understanding of neutron star matter; they appear in core-collapse and proto-neutron star simulations, the cooling of isolated or accreting neutron stars, and even at the merger stages in a binary system. It is, therefore, crucial to understand in what conditions neutrinos are emitted or absorbed and also how they transport in neutron stars.
In this presentation, we shall discuss the neutrino emission of Urca processes in finite-temperature neutron stars, with a focus on the so-called Modified Urca. After a quick introduction to neutron star physics, I will introduce the nuclear physics essential to understand neutron star cooling and the role of neutrino emission processes in its modeling. I will then present in details the derivation of the Modified Urca neutrino emissivity and mean free path for different regimes of temperature, density, and electron fraction of neutron star matter. Our results are calculated using an importance sampling Monte-Carlo integration approach and represent a significant improvement from the analytical neutrino rates established from drastic approximations. Finally, I will present a simple approximation for the nucleon distribution function that can help anticipate the regimes of temperature and density in which the Modified Urca process should be calculated or neglected for finite-temperature neutron stars.
