Quark matter and quark stars at finite temperature in Nambu–Jona-Lasinio model

Abstract We extend the SU(3) Nambu–Jona-Lasinio (NJL) model to include two types of vector interaction. Using these two types of vector interaction in NJL model, we study the quark symmetry free energy in asymmetric quark matter, the constituent quark mass, the quark fraction, the equation of state (EOS) for $$\beta $$ β -equilibrium quark matter, the maximum mass of QSs at finite temperature, the maximum mass of proto-quark stars (PQSs) along the star evolution, and the effects of the vector interaction on the QCD phase diagram. We find that comparing zero temperature case, the values of quark matter symmetry free energy get larger with temperature increasing, which will reduce the difference between the fraction of u, d and s quarks and stiffen the EoS for $$\beta $$ β -equilibrium quark matter. In particular, our results indicate that the maximum masses of the quark stars increase with temperature because of the effects of the quark matter symmetry free energy, and we find that the heating(cooling) process for PQSs will increase (decrease) the maximum mass within NJL model