Bayesian Inference of Fine-Features of Nuclear Equation of State from Future Neutron Star Radius Measurements to 0.1km Accuracy

TL;DR

This paper uses Bayesian inference with future neutron star radius measurements to precisely constrain nuclear matter properties and the symmetry energy parameters at high densities, revealing detailed correlations and features in the EOS.

Contribution

It introduces a Bayesian framework to infer detailed nuclear matter parameters from high-precision neutron star radius data, highlighting the impact of measurement accuracy on constraining the EOS.

Findings

Smaller radius measurement errors improve parameter inference.

Double-peak features in parameter PDFs emerge at high measurement precision.

High-precision measurements of canonical NSs better constrain the EOS around 2-3 times saturation density.

Abstract

To more precisely constrain the Equation of State (EOS) of supradense neutron-rich nuclear matter, future high-precision X-ray and gravitational wave observatories are proposed to measure the radii of neutron stars (NSs) with an accuracy better than about 0.1 km. However, it remains unclear what particular aspects (other than the stiffness generally spoken of in the literature) of the EOS and to what precision they will be better constrained. In this work, within a Bayesian framework using a meta-model EOS for NSs, we infer the posterior probability distribution functions (PDFs) of incompressibility $K_{0}$ and skewness $J_{0}$ of symmetric nuclear matter (SNM) as well as the slope $L$, curvature $K_{\rm{sym}}$, and skewness $J_{\rm{sym}}$ characterizing the density dependence of nuclear symmetry energy $E_{\rm{sym}}(\rho)$, respectively, from mean values of NS radii consistent with existing observations and an expected accuracy $\Delta R$ ranging from about 1.0 km to 0.1 km. We found that (1) the $\Delta R$ has little effect on inferring the stiffness of SNM at suprasaturation densities, (2) smaller $\Delta R$ reveals more accurately not only the PDFs but also pairwise correlations among parameters characterizing high-density $E_{\rm{sym}}(\rho)$, (3) a double-peak feature of the PDF($K_{\rm{sym}}$) corresponding to the strong $K_{\rm{sym}}-J_{\rm{sym}}$ and $K_{\rm{sym}}-L$ anti-correlations is revealed when $\Delta R$ is less than about 0.2 km, and the locations of the two peaks are sensitive to the maximum value of $J_{\rm{sym}}$ reflecting the stiffness of $E_{\rm{sym}}(\rho)$ above about 3 times the saturation density $\rho_0$ of SNM, (4) the high-precision radius measurement for canonical NSs is more useful than that for massive ones for constraining the EOS of nucleonic matter around $(2-3)\rho_0$.