We investigate the properties of the equation of state of strange-quark matter and $u\text{−}d$ quark matter, the sound velocity of quark matter, the stability region for star matter, the maximum mass of quark stars (QSs), and the tidal deformability for QSs by using a quark quasiparticle model. Our results indicate that the recently discovered heavy compact stars PSR $\mathrm{J}0348+0432$, MSR $\mathrm{J}0740+6620$, and PSR $\mathrm{J}2215+5135$, and especially the GW190814s secondary component $m_2$ can be well described as QSs within the quasiparticle model.

We study the thermodynamic properties of asymmetric quark matter, large mass quark stars (QSs), and proto-quark stars (PQSs) within the quasiparticle model. Considering the effects of temperature within quasiparticle model can significantly influence the EOS and the entropy of strange quark matter (SQM), quark fractions in SQM, as well as the tidal deformability and the maximum mass of PQSs along the star evolution line. Our results indicate that the recent discovered heavy compact stars PSR J0348+0432, MSR J0740+6620, PSR J2215+5135, and especially the GW190814’s secondary component $$m_2$$m 2 can be well described as QSs within the quasiparticle model. The tidal deformability for the QSs describing the heavy compact stars is extremely large, which can not well describe GW170817 as QSs, and the effects of the temperature in the heating process along the star evolution will further increase the tidal deformability and the maximum mass of PQSs.

In this work, we explore the properties of isospin asymmetric quark matter in quark stars (QSs). The isospin chemical potential, the isospin asymmetry, the quark matter symmetry energy, the equation of state (EOS) of strange quark matter (SQM), and the maximum mass of QSs are also studied by using different quark phenomenological models. Our results indicate that the parameter space of the quark phenomenological models for the quark matter symmetry energy and the EOS of the star matter can be reduced by considering the recent mass-radius estimates of PSR $\mathrm{J}0740+6620$, PSR $\mathrm{J}0030+0451$, 4U 1702-429, and the central compact star within the supernova remnant HESS J1731-347.

Symmetry energy is an important part of the equation of state of isospin asymmetry matter. However, the huge uncertainties of symmetry energy remain at suprasaturation densities, where the phase transitions of strongly interacting matter and the quark matter symmetry energy are likely to be taken into account. In this work, we investigate the properties of symmetry energy by using a hybrid star with the hadron-quark phase transition. The interaction among strange quark matter (SQM) in hybrid stars is based on a 3-flavor NJL model with different vector and isovector channels, while the equation of state (EOS) of the nuclear matter is obtained by considering the ImMDI-ST interaction by varying the parameters $x$, $y$, and $z$. Our results indicate that the various parameters and coupling constants of the interactions from the ImMDI-ST and NJL model can lead to widely different trends for the symmetry energy in the hadron-quark mixed phase and the different onsets of the hadron-quark phase transition. In addition, it has been found that the radii and tidal deformabilities of hybrid stars constrain mostly the density dependence of symmetry energy while the observed maximum masses of hybrid stars constrain mostly the EOS of symmetric nuclear and quark matter.

We investigate the global properties of hybrid stars and quark-matter cores by using a quasiparticle model that rules out the possibility of the existence of absolutely stable strange quark matter within the hybrid stars. Results from our study indicate that the coupling constant $g$ can stiffen the equation of state of hybrid star matter and thus increase the hybrid star maximum mass and its tidal deformability, whereas it also decreases the mass and radius of the pure quark. By breaking the absolutely stable condition, we provide the maximum mass, minimum radius $R_{1.4}$, and minimum tidal deformation ${\mathrm{\Lambda }}_{1.4}$ of the hybrid stars as well as the maximum mass and radius of the quark-matter core with different $g$ values within the allowable regions (the energy per nucleon of both $u$-$d$ quark matter and strange quark matter must exceed 930 MeV) on the $g\text{−}{B}^{1/4}$ plane. In addition, we find that a step change of the sound velocity occurs in the hadron-quark mixed phase, and the approximate rule that the polytropic index $\gamma \le 1.75$ can also be used as a criterion for separating hadronic from quark matter in our work. Our results also confirm that the sizable quark-matter cores ($R_{QC}>6.5\mathrm{km}$) containing the mixed phase can appear in $2M_{\odot }$ massive 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 $R_{\mathrm{IV}}$ make main contributions 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. The approximate rule that the polytropic index $\gamma \le 1.75$ can also be used as a criterion for separating hadronic matter from quark matter in our work. Using the hybrid star matter EOS, we predict the radius and mass information of quark-matter cores inside hybrid stars. 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 ${\mathrm{\Lambda }}_{1.4}$ of hybrid stars.