Using the parity doublet model (PDM) for hadronic matter and a modified Nambu-Jona-Lasinio (NJL) model for quark matter, we investigate the potential existence of two- and three-flavor quark matter in neutron star cores. Both models respect chiral symmetry, and a sharp first-order phase transition is implemented via Maxwell construction. We find stable neutron stars with quark cores within a specific parameter space that satisfies current astronomical observations. Typical neutron stars with masses around $1.4M_{\odot }$ may possess deconfined quark matter in their centers. The hybrid star scenario with a two-flavor quark core offers enough parameter space to allow the neutron stars with large quark cores exceeding $\sim 1M_{\odot }$ and to allow the early deconfinement position before $2{\rho }_0$, where ${\rho }_0$ is the nuclear saturation density. The observations of gravitational wave event GW170817 suggest a relatively large chiral invariant mass $m_0=600\mathrm{MeV}$ in the PDM for scenarios involving three-flavor quark matter cores. The maximum mass of the hybrid star with a quark core is found to be approximately $2.2M_{\odot }$ for both two- or three-flavor quark matter in their centers.

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• Nuclear astrophysics
• Nuclear matter in neutron stars
• QCD phase transitions
• Quark matter