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

TL;DR

This study evaluates how future high-precision neutron star radius measurements can constrain the dense matter equation of state, by embedding a minimal hadronic npeμ EOS in a CSS-based first-order hadron-quark transition within a flexible nine-parameter meta-model. Using mock radii for a 2.0 solar-mass star and Bayesian inference, it shows that precise radii, especially for massive NSs, dramatically tighten constraints on the hadron-quark transition density $\rho_t$, the quark-matter mass fraction, and several high-density hadronic EOS parameters, though the degree of improvement depends on the assumed prior range for $\rho_t$. The work also finds that NS radii are largely insensitive to the stiffness of quark matter (the speed of sound in QM) and that the inferred results are strongly prior-dependent, with two prior choices reflecting BES/RHIC guidance. Overall, high-precision radius data can meaningfully probe the hadron-quark interface and supranuclear matter, while remaining limited in revealing QM stiffness and in the absolute likelihood of sizable quark cores without stronger priors or complementary observations.

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 $σ\simeq 0.1$~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 $σ= 1.0$ 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 $ρ_t$, 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 $ρ_t$. 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 $ρ_t$.

Figures (12)

• Figure 1: Posterior PDFs of the three quark matter EOS parameters inferred from mock NS radius data of $R_{2.0}=11.9$ km, with the precision $\sigma$ varying from 1.0 to 0.1 km.
• Figure 1: (color online) Comparisons of the mass-radius sequences using the same core EOS without a hadron-quark phase transition but different crustal EOSs: (1) the same NV+BPS (blue) and (2) the CUTER crustal EOS (black). Both panels use the EOS parameters $E_{\rm sym}(\rho_0)=31,7$ MeV, $K_{\rm sym}=-100$ MeV, $J_{\rm sym}=800$ MeV, $K_0=240$ MeV, and $J_0=-190$ MeV. The left (right) panel uses $L=58.7$ (40) MeV.
• Figure 2: (color online) Posterior PDFs of four hadronic EOS parameters inferred from the same data sets as in Fig. \ref{['PDF-QM-rt1']}.
• Figure 2: (color online) Probability distribution function (PDF) of density $\rho_{cc}$ (left), isospin asymmetry $\delta_{cc}$ (middle) and pressure $P_{cc}$ (right) at the crust-core transition point, respectively, generated from using 40,000 EOSs for the outer core matter in neutron stars.
• Figure 3: color online) Quark matter mass fraction of hybrid stars inferred from the mock radius data of a massive NS of mass 2.0M$_{\odot}$ with a mean radius $R_{2.0}=11.9$ km and the precisions indicated.