Bayesian Analysis of the Neutron Star Equation of State and Model Comparison: Insights from PSR J0437+4715, PSR J0614+3329, and Other Multi-Physics Data

TL;DR

This paper develops a Bayesian framework to constrain the neutron star equation of state (EoS) by integrating terrestrial nuclear data with multimessenger astrophysical observations. It compares five EoS families—Taylor, $n/3$, Skyrme, RMF, and CS—and updates priors sequentially with $ ext{χ}$EFT PNM, terrestrial empirical inputs, NICER radii, and GW170817 data, revealing tight constraints on nuclear matter parameters such as $L_0$, $K_{\mathrm{sym}0}$, $K_0$, and $Q_0$. Bayesian model comparison favors the Skyrme model under the combined data (Set4), yielding precise NS observables: $R_{1.4}=11.85\pm0.11$ km and $\Lambda_{1.4}=354\pm25$, with central densities around $3\rho_0$ for $1.4\,M_\odot$ stars and $6$–$7\rho_0$ for maximum-mass stars. The work demonstrates the power of jointly leveraging theory, laboratory measurements, and multi-messenger signals to tightly constrain the high-density EoS and informs future NS measurements and nuclear theory developments.

Abstract

We perform a comprehensive Bayesian analysis to constrain the neutron star (NS) equation of state (EoS) using a wide range of terrestrial and astrophysical data. The terrestrial inputs include quantities related to symmetric nuclear matter (SNM) and symmetry energy up to two times saturation density ($ρ_0\sim$0.16 fm$^{-3}$), derived from finite nuclei and heavy-ion collisions (HICs). The astrophysical constraints incorporate NS radii and tidal deformabilities from recent NICER observations and GW170817, respectively. We consider five different EoS models: Taylor, $n/3$, Skyrme, RMF, and sound speed(CS), are analyzed by sequentially updating the priors with (i) $χ$EFT based pure neutron matter, (ii) terrestrial, empirical and earlier astrophysical data, (iii) case (ii) including NICER radii of PSR J0437+4715 and J0614+3329, (iv) all data combined, and (v) excluding empirical nuclear inputs. We also perform Bayesian model comparison which favors the Skyrme model under all combined data (scenario (iv)), yielding tight constraints on symmetry energy parameters: $L_0 = 56 \pm 3$~MeV, $K_{\mathrm{sym}0} = -132 \pm 15$~MeV and also on SNM parameters: $K_0 = 265 \pm 12$~MeV, $Q_0 = -366 \pm 43$~MeV. The mass-radius and mass-tidal deformability posterior distributions are also well constrained. The radius and tidal deformability of a $1.4\,M_\odot$ neutron star are found to be $R_{1.4} = 11.85 \pm 0.11$~km and $Λ_{1.4} = 354 \pm 25$, respectively.

Figures (7)

• Figure 1: A flowchart for translating the coupling constants into the NMPs within the RMF framework, enabling the use of prior distributions on NMPs rather than on the couplings.
• Figure 2: The marginalized posterior distributions of the NMPs, obtained through Bayesian inference using the Set4 scenario dataset, for all the considered EoS models with all NMPs expressed in MeV except $\rho_0$ which is in fm$^{-3}$.
• Figure 3: The 95% confidence interval plots for (a) the pressure of the symmetry energy, $P_{\rm sym}$, (b) the pressure of SNM, $P_{\rm SNM}$, (c) the symmetry energy, $J(\rho)$, and (d) the pressure of PNM, $P_{\rm PNM}$, as a function of the baryon density $\rho$, evaluated using the posterior distributions from the Set4 scenario. The corresponding experimental data incorporated into the Bayesian framework are also shown.
• Figure 4: The 95$\%$ confidence interval posterior distributions of (a) the pressure of $\beta$-equilibrated matter, $P$, (b) the proton fraction, $Y_{\rm p}$, and (c) the squared sound speed, $c_s^2$, as functions of the baryon density $\rho$ obtained using the data in Set4 scenario. The onset of Urca cooling occurs above the solid black line. The vertical red dashed line indicates the transition density $\rho_{t2}=0.34$ fm$^{-3}$ for CS model.
• Figure 5: The 95$\%$ confidence interval distributions for the radius, R(km) (left panel) and tidal deformability, $\Lambda$ (right panel) as a function of neutron star mass, $M(M_\odot)$, evaluated using the posterior distributions of the Set4 scenario. The astrophysical observations incorporated in the Bayesian framework are also shown.