Universal relations for hybrid stars and their quark cores: a systematic scan of the quark-matter parameter space

Abstract

Universal, equation-of-state (EOS) insensitive relations among the global properties of compact stars are well established for hadronic neutron stars and for self-bound strange stars. We ask whether analogous relations hold for the quark core of a hybrid star, and whether the core can be constrained from the surface. Describing quark matter with the three-flavor MIT bag model with repulsive vector interactions, matched to the hadronic DD2 EOS through a Maxwell construction, we scan the full $(B^{1/4},G_V)$ plane and obtain 1112 hybrid EOSs with maximum masses above $2\,M_\odot$, broadly compatible with current multimessenger constraints. For every stable configuration we evaluate the mass, radius, moment of inertia, and tidal deformability both at the stellar surface and at the boundary of the quark core. Global quantities follow the relations of hadronic stars---the $I$--Love relation to within $0.5\%$---while core quantities follow those of self-bound strange stars with median deviations of $6$--$9\%$. We explain the latter by expanding the structure of the core in powers of its compactness: to first order, the core mass, baryon mass, moment of inertia, and tidal deformability depend only on the compactness and on the properties of the hadron--quark interface, chiefly the ratio $ξ=p_{\rm tr}/\varepsilon_+$ of transition pressure to quark energy density. The strange-star relations are the $ξ\to0$ member of this family, and the deviations from them measure $ξ$. The fractional core mass and radius of all configurations follow the normalized mass profile of the star, and no global observable allows the core size to be inferred. Evanescent cores dominate the viable parameter space, while sizable cores require low bag constants and strong vector couplings.