In this paper, we use the recent updated source properties of GW170817 to constrain the hybrid equation of state (EOS) constructed by a three-window modeling between the hadronic EOS and quark EOS. Specifically, the hadronic EOS is described by the $\mathrm{NL}3\omega \rho$ model whose corresponding pure neutron star (NS) is already excluded by the constraint of tidal deformability (TD) from GW170817, and the quark EOS is calculated with the $2+1$ flavors Nambu-Jona-Lasinio (NJL) model. We also consider four other constraints on the hybrid EOS. As a result, we find the parameter set ($B^{\frac{1}{4}},\tilde{\mu },\mathrm{\Gamma }$) can be well constrained, indicating the possible existence of the hybrid star (HS) with a crossover inside. The type of the two stars in the binary system for nine representative hybrid EOSs is shown in this paper too. Furthermore, the HSs restricted by five constraints do not suggest a pure quark core but a mixed phase in the center.

As is pointed out in a recent work [ Phys. Rev. Lett. 120, 222001 (2018)], quark matter may not be strange. Inspired by this argument, we use a new self-consistent mean field approximation method to study the equation of state of cold dense matter within the framework of the two-flavor NJL model. Then the mass-radius relationship of two-flavor pure quark stars is studied. In the new self-consistent mean field approximation method we introduced, there is a free parameter $\alpha$, which reflects the weight of different interaction channels. In principle, $\alpha$ should be determined by experiments rather than the self-consistent mean field approximation itself. In this paper, thus, the influence of the variation of $\alpha$ on the critical chemical potential of chiral phase transition and the stiffness of the equation of state (EOS) are thoroughly explored. The stiffness of the EOS can be increased greatly to support a two-solar-mass pure quark star when $\alpha$ is greater than 0.9, because the contribution from the vector term is retained by the Fierz transformation. Our result is also within the constraints on the radius from the recent data analysis of the tidal deformability. This means that the current theoretical calculations and astronomical observations cannot rule out the possibility of a two-flavor pure quark star.

In this work, we use the equation of state (EOS) of the ($2+1$)-flavor Nambu-Jona-Lasinio (NJL) model to study the structure of the strange quark star. With a new free parameter $\alpha$, the Lagrangian is constructed by two parts, the original NJL Lagrangian and the Fierz transformation of it, as $\mathcal{L}=(1-\alpha ){\mathcal{L}}_{\mathrm{NJL}}+\alpha {\mathcal{L}}_{\text{Fierz}}$. To determine the range of $\alpha$, we compare the binding energies in the two-flavor and ($2+1$)-flavor cases. We also consider the constraints of chemical equilibrium and electric charge neutrality in the strange quark star and choose six representative EOSs with different $\alpha$ and $B$ (bag constant) to study their influence on the structure of the strange quark star. As a result, we find that a larger $\alpha$ and a smaller $B$ correspond to a heavier star with a stiffer EOS. Furthermore, the heaviest strange quark star is in agreement with not only the recent mass observation of PSR $\mathrm{J}0740+6620$ and the x-ray observations on radius measurements, but also the constraint on the tidal deformability of GW170817.

In this work, a modified Nambu-Jona-Lasinio (NJL) model with proper-time regularization is employed to study the properties of hypothetical nonstrange quark stars. The coupling constant of the four-fermion interaction in the conventional NJL model is modified as $G=G_1+G_2⟨\overline{\psi }\psi ⟩$ to highlight the feedback of the quark propagator to the gluon propagator. To study the dependence of the equation of state (EOS) on this modification as well as the vacuum pressure, we choose nine representative EOSs for comparison. It is found that a smaller $G_1$ leads to a stiffer EOS, and a higher vacuum pressure (i.e., a smaller bag constant) yields a softer EOS at low energy density. It is further shown that the heaviest quark star under this modified NJL model satisfies not only the recent mass measurement of PSR $\mathrm{J}0740+6620$, but also the radius constraints from x-ray timing observations. The corresponding tidal deformability is also in agreement with the observations of GW170817.

In this paper, a version of the Polyakov-Nambu-Jona-Lasinio (PNJL) model based on nonextensive statistical mechanics is presented. This new statistics summarizes all possible factors that violate the assumptions of the Boltzmann-Gibbs (BG) statistics to a dimensionless nonextensivity parameter q. Thus, when q tends to 1, it returns to the BG case. Within the nonextensive PNJL model, we found that as q increases, the location of the critical end point (CEP) exhibits non-monotonic behavior. That is, for , CEP moves in the direction of lower temperature and larger quark chemical potential. However, for , CEP turns to move in the direction of lower temperature and lower quark chemical potential. In addition, we studied the moments of the net-baryon number distribution, that is, variance ( ), skewness (S), and kurtosis (κ). Our results are generally consistent with the latest experimental data reported, especially for , when q is set to .

In this paper, we study the pseudo-Wigner solution of the quark gap equation with a recently proposed algorithm in the framework of the ($2+1$)-flavor Nambu-Jona-Lasinio (NJL) model. We find that for the current quark mass $m_{u,d}=5.5\mathrm{MeV}$ and chemical potential $\mu <{\mu }_{\mathrm{TCP}}=272.5\mathrm{MeV}$, the Nambu solution and the positive pseudo-Wigner solution obtained via this algorithm is consistent with the physical solution obtained with the iterative method. Furthermore, the algorithm we used can help to illustrate the evolution of the solutions of the gap equation from the chiral limit to nonchiral limit and gives a prediction where the crossover line is located in the phase diagram for $\mu <272.5\mathrm{MeV}$. In addition, we also study the chiral susceptibilities as well as the loss of solutions for different chemical potentials.