Quark stars in the pure pseudo-Wigner phase

Abstract

In this paper, we consider the scenario of a pure quark star which is completely composed of quarks in the pseudo-Wigner phase. 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. We assume deconfinement 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 the bag constant shifts from \((130\text{ MeV})^{4}\) to \((150 \text{ MeV})^{4}\) as \(\alpha \) grows. When \(\alpha \) is around 0.9, the mass-radius relations of deconfined quark stars can meet the requirement of pulsar observations. In addition, the tidal deformability \(\Lambda \) is found to range in 253 – 482, which satisfies the astronomical constraint of \(\Lambda <800\) for 1.4-solar-mass neutron stars.