Constraints on QCD-based equation of state of quark stars from neutron star maximum mass, radius, and tidal deformability observations

Neutron stars (NSs), the densest known objects composed of matter, provide a unique laboratory to probe whether strange quark matter is the true ground state of matter. We investigate the range of parameters relevant for the equation of state of strange stars taking into account a quantum chromodynamics (QCD)-informed model. The sampling of the parameter space was performed using quasirandom Latin hypercube sampling, ensuring uniform coverage. The parameters are related to the energy density difference between quark matter and the QCD vacuum, the strength of strong interactions, and the gap parameter for color superconductivity. To restrict them, we incorporate observational constraints on the maximum mass of NSs (from both observations of binary systems and NS mergers), the radii of $1.4{M}_{\ensuremath{\bigodot}}$ NSs [inferred from gravitational wave (GW) and electromagnetic observations], and tidal deformations (from GW170817). Our results indicate that strong quark interactions play a crucial role in the description of NSs, with a minimum deviation of at least 20% from the behavior of free quarks. Additionally, we find that color superconductivity is relevant, and derive a maximum gap parameter reaching approximately 230 MeV for a strange quark mass of 100 MeV. Furthermore, we determine that the surface-to-vacuum energy density jump for quark stars lies within the range (1.1--2.2) ${\ensuremath{\rho}}_{\mathrm{sat}}$, where ${\ensuremath{\rho}}_{\mathrm{sat}}\ensuremath{\simeq}2.7\ifmmode\times\else\texttimes\fi{}{10}^{14}\text{ }\text{ }\mathrm{g}\text{ }{\mathrm{cm}}^{\ensuremath{-}3}$ is the nuclear saturation density. As a byproduct of the observational constraints, we find that the radius of a $1.4{M}_{\ensuremath{\bigodot}}$ quark star lies in the range (10.0--12.3) km, while its dimensionless tidal deformability falls within the interval (270--970). In addition, all the above constraints are fully consistent with the small mass and radius inferred electromagnetically for the central compact object XMMU J173203.3-344518 (NS) in the supernova remnant HESS J1731-347, with $M=0.7{7}_{\ensuremath{-}0.17}^{+0.20}{M}_{\ensuremath{\bigodot}}$ and $R=10.4{0}_{\ensuremath{-}0.78}^{+0.86}\text{ }\text{ }\mathrm{km}$. The above results may offer important inputs for studies on quark and, in a complementary way, hybrid stars, serving as parameter references for more detailed investigations into their astrophysical signatures, including tidal deformations, cooling curves, quasinormal modes, and ellipticities. We briefly discuss these implications.