The chiral restored quark stars can exist in the universe

In this paper, the equation of state (EOS) of deconfined quark stars is studied in the framework of the two-flavor NJL model, and the self-consistent mean field approximation is employed by introducing a parameter $\alpha$ combining the original Lagrangian and the Fierz-transformed Lagrangian, $\mathcal{L}_R= (1-\alpha)\mathcal{L}+\alpha\mathcal{L}_F$, to measure the weights of different interaction channels. It is believed that the deconfinement of phase transition happens along with the chiral phase transition. Thus, due to the lack of description of confinement in the NJL model, the vacuum pressure is set to confine quarks at low densities, which is the pressure corresponding to the critical point of chiral phase transition. We find that deconfined quark stars can reach over two-solar-mass, and the bag constant therefore shifts from $(130 ~\mathrm{MeV})^4$ to $(150 ~\mathrm{MeV})^4$ as $\alpha$ grows. In addition, the tidal deformability $\Lambda$ is yielded ranging from 253 to 482 along with the decrease of $~\alpha$, which satisfies the astronomical constraint of $\Lambda<800$ for 1.4-solar-mass neutron stars.