Hadron-quark Phase Transition with Finite-size Effect in Neutron Stars

It is generally considered that hadron matter may undergo a deconfinement phase transition becoming quark matter at very high density in massive neutron stars. This hadron-quark phase transition has important impact on neutron stars, which has received much attention. We consider finite-size effect in this phase transition process, which contains the impact of Coulomb energy and surface energy. By including this effect, the mixed phase forms the pasta structures. The equilibrium conditions for coexisting hadronic and quark phases are derived by minimizing the total energy including the surface and Coulomb contributions. We employ the relativistic mean-field(RMF) model to describe the hadronic phase, while the Nambu-Jona-Lasinio(NJL) model is used for the quark phase. We conclude that the finite-size effect will raise the stiffness of EOS, and then increase the maximum mass of neutron stars, which depend on the value of surface tension. Our results show that finite-size effects can significantly reduce the region of the mixed phase, and the results lie between those from the Gibbs and Maxwell constructions. We show that a massive star may contain a mixed phase core and its size depends on the surface tension of the hadron-quark interface.