Phase structures of neutral dense quark matter and application to strange stars

In the contact interaction model, the quark propagator has only one solution, chiral symmetry breaking solution, at vanish temperature and density. Inspire by Y. Jiang and Z.-F. Cui, we introduce 2+1 flavors quark condensates feedback on coupling strength, the Wigner solution appears in some region of parameters. It enables us to tackle chiral phase transition as two-phase coexistences. At finite chemical potential, we analyze the chiral phase transition to the conditions of electric charge neutrality and $\beta$ equilibrium. The four chemical potentials, $\mu_u$, $\mu_d$, $\mu_s$ and $\mu_e$, are constrained by three conditions, there is one independent variable that remained, we choose the average quark chemical potential as the free variable. All quark masses and number densities suffer discontinuities at the phase transition point. The strange quarks appear after the phase transition due to the system needs more energy to produce a d-quark than an s-quark. Take the EOS as an input, the TOV equations are solved numerically, we show that the mass-radius relation is sensitive to the EOSs. The maximum mass of strange quark stars is not susceptible to our introduced parameter $\Lambda_q$.