Revisiting the hot matter in the center of gamma-ray bursts and supernovae

Aims. Hot matter with nucleons can be produced in the inner region of the neutrino-dominated accretion flow in gamma-ray bursts or during the proto-neutron star birth in successful supernovae. The composition and equation of state of the matter depend on the dynamic beta equilibrium under various neutrino opacities. The strong interaction between nucleons may also play an important role. We plan to extend the previous studies by incorporating these two aspects in our model. Methods. The modification of the beta-equilibrium condition from neutrino optically thin to thick was modeled by an equilibrium factor chi ranging between the neutrino-freely-escaping case and the neutrino-trapped case. We employed the microscopic Brueckner-Hartree-Fock approach extended to the finite temperature regime to study the interacting nucleons. Results. We show the composition and chemical potentials of the hot nuclear matter for different densities and temperatures at each stage of beta equilibrium. We also compare our realistic equation of states with those of the free-gas model. We find that it is important to properly describe the neutrino opacity and the strong interaction between nucleons, and they should be taken into account in model calculations.