In-Depth Study of the Baryon-Quark Phase Transition in Supernova Matter based on the PNJL Quark Model

Determining the equation of state (EOS) of supernova matter is crucial for studying the baryon-quark phase transition (PT) in the inner core of newborn hot neutron stars, thereby deepening the astrophysical investigations on compact objects. For this purpose, we model the baryon-quark PT under the Maxwell construction (MC) by considering a statistical model based on the Thomas-Fermi (TF) approximation for baryonic matter and the Polyakov-Nambu-Jona-Lasino (PNJL) quark model. Furthermore, we adopted interactions MS96 and MS90 for baryonic matter, as well as the vector interaction effects for quark matter. In this work, we focus on the analysis of thermal contributions to the hot hybrid EOS (HHEOS), extracting the thermal index as a basic evaluation parameter. Notably, our study highlights that the HHEOS is strongly affected by the baryonic interaction, neutrino trapping, and especially the quark vector interaction.