Strange quark stars within the Nambu-Jona-Lasinio model

We investigate the properties of charge-neutral $\beta$-equilibrium cold quark matter within the Nambu-Jona-Lasinio model. The calculations are carried out for different ratios of coupling constants characterizing the vector and scalar 4-fermion interaction, $\xi\equiv G_V/G_S$. It is shown that for $\xi < 0.4$ matter is self-bound and for $\xi < 0.65$ it has a first order phase transition of the liquid-gas type. The Gibbs conditions in the mixed phase are applied for the case of two chemical potentials associated with the baryon number and electric charge. The characteristics of the quark stars are calculated for $\xi = 0, 0.5$ and 1. It is found that the phase transition leads to a strong density variation at the surface of these stars. For $\xi = 1$ the properties of quark stars show behaviors typical for neutron stars. At $\xi\goo 0.4$ the stars near to the maximum mass have a large admixture of strange quarks in their interiors.