Properties of quark-matter cores in massive hybrid stars

Using the constraints from astrophysical observations and heavy-ion experiments, we investigate the equation of state (EOS) of hybrid star matter and the properties of quark-matter cores in hybrid stars. The quark matter interactions in hybrid stars are described based on 3-flavor Nambu-Jona-Lasinio model with various vector and vector-isovector coupling constants. In this work, we find that the hybrid star matter EOS is more sensitive to the strength of the vector interaction, and the EOS becomes stiffer with increasing vector strength $R_V$. The vector-isovector interaction characterized by the coupling constant $R_{IV}$ make main contribution to the hadron-quark mixed phase. Meanwhile, we note that a step change of both the sound velocity and the polytropic index $\gamma$ occurs in the hadron-quark phase transition, and it is restored with the decrease of nucleon and lepton degrees of freedom in the high density quark phase. Although the coupling constants increase the hybrid star maximum mass up to $2.08M_{\odot}$, they also decrease the mass and radius of the quark core and the mixed core. With different quark coupling constants, we also find that the maximum mass and radius of the quark matter core in a stable hybrid star can reach $0.80M_{\odot}$ and 6.95 km, which are close to half of the maximum mass and radius of the complete star. However, properties of quark matter have no effect on the $M = 1.4M_{\odot}$ hybrid star as a result of no quark matter inner core, which can also be confirmed by the criterion of the polytropic index, and thus our results also indicate that the quark interactions have no effect on the tidal deformability $\Lambda_{1.4}$ of hybrid stars.