Quark Deconfinement Phase Transition in Hot Neutron-Star Matter: Effects of Neutrino Trapping

We study the effect of trapped neutrinos on the properties of the deconfinement phase transition from hot $\beta$-equilibrated, electrically neutral hadronic matter to quark matter. To describe the thermodynamic properties of hot hadronic matter, an extended relativistic mean field (RMF) theory is used, which also incorporates the isovector–Lorentz-scalar $\delta$-meson effective field. The three-flavor quark phase is described within the framework of the local Nambu--Jona-Lasinio (NJL) model. It was assumed that the surface tension at the quark-hadron interface is so strong that the phase transition occurs according to Maxwell's construction. The thermodynamic properties of the quark and hadronic phases were calculated for both neutrino-trapped and neutrino-transparent regimes at various temperatures ranging from 0 to 100 MeV and baryon number densities from 0 to 1.8 fm$^{-3}$. The impact of trapped neutrinos on the thermodynamic properties of the coexistence state has been investigated. It has been demonstrated that the baryon chemical potential in the coexistence state decreases as temperature increases. The critical endpoint parameters in the $T-n_B$ plane of the phase diagram were obtained for the case of trapped neutrinos (74 MeV; 0.269 fm$^{-3}$) and for the case of the absence of neutrinos (75.6 MeV; 0.255 fm$^{-3}$).