Evolution of proto-neutron stars with the hadron-quark phase transition

The Poyakov-Nambu-Jona-Lasinio (PNJL) model was developed recently, which includes both the chiral dynamics and (de)confinement effect and gives a good description of lattice QCD data. In this study we use the PNJL model to describe the quark phase, and first use it to study the evolution of proto-neutron star (PNS) with a hadron-quark phase transition. Along the line of a PNS evolution, we take several snapshots of PNS profiles, presenting the fractions of different species, the equations of state (EOS), and the mass-radius relations at different stages. The calculation shows the mixed phase may exist during the whole evolving process, and the onset density of quark phase decreases with the radiation of neutrinos in the heating stage. In the cooling stage, the EOS of the mixed phase softens and the center density increases. In this process a part of nuclear matter transforms to quark matter, which may lead to a PNS collapsing into a black hole.