Bayesian Inference of Hybrid Star Properties from Future High-Precision Measurements of Their Radii

Abstract

Future high-precision X-ray and gravitational-wave observations of neutron stars (NSs) are expected to constrain NS radii with uncertainties as small as $\sigma \simeq 0.1$~km. Such unprecedented precision offers a unique opportunity to extract new information about the nature and equation of state (EOS) of supradense matter in NS cores. Using mock radius data with uncertainties ranging from $\sigma = 1.0$ to $0.1$~km, together with a flexible meta-model NS EOS that allows for a first-order hadron-quark phase transition, we perform a Bayesian statistical analysis to assess the impact of radius measurements on EOS constraints. We find that high-precision radius measurements, particularly for massive NSs, significantly tighten constraints on the hadron-quark transition density $\rho_t$, the quark matter mass fraction in NS cores, and several parameters characterizing the EOS of supranuclear hadronic matter, although the degree of improvement depends on the assumed prior range of $\rho_t$. In contrast, even with the highest precision considered, NS radii -- including those of massive stars -- remain largely insensitive to the stiffness of quark matter, independent of the measurement accuracy or the prior range adopted for $\rho_t$.