Multi-Physics Bayesian Analysis of Neutron Star Crust Using Relativistic Mean-Field Model

TL;DR

This work develops a fully Bayesian, unified RMF-based equation of state that consistently treats the outer crust, inner crust, and core of neutron stars, constrained by nuclear experiments, $\chi$EFT, and multimessenger observations. The analysis reveals that the crust–core transition is primarily governed by the symmetry-energy slope $L$ and curvature $K_{\rm sym}$ at sub-saturation densities, while the inner crust EOS emerges from collective isovector NM effects rather than any single parameter. The study provides quantitative crust properties for canonical NSs (e.g., $l_{\rm crust}\approx1.18$ km, $M_{\rm crust}\approx0.034\,M_\odot$, $I_{\rm crust}/I\approx0.05$ for $M=1.4M_\odot$) and shows that matched crust–core constructions introduce systematic radius differences of a few percent, underscoring the importance of a unified treatment. These results enhance the reliability of NS inferences from NICER and GW observations and clarify how sub-saturation nuclear physics feeds into macroscopic crustal observables.

Abstract

We study the properties of neutron-star crust within a Bayesian framework based on a unified relativistic mean-field (RMF) description of dense matter. The analysis focuses on the posterior distributions of crust properties, constrained by nuclear experimental data, chiral effective field theory, and multimessenger neutron-star observations. In the inference, the outer crust is fixed using the AME2020 nuclear mass table, supplemented by Hartree--Fock--Bogoliubov mass models, while the inner crust is described using a compressible liquid-drop model consistently coupled to the RMF interaction. The same RMF framework is used to describe the uniform core, ensuring a unified treatment across all density regimes. From the resulting posteriors, we extract key crustal observables, including the crust--core transition density and pressure, crust thickness, crust mass, and the fractional crustal moment of inertia. We find that the transition density is primarily governed by the symmetry-energy slope $L$ and curvature $K_{\rm sym}$ evaluated at sub-saturation densities, while the transition pressure plays a central role in determining global crustal properties. The inner-crust equation of state reflects a collective interplay between isovector nuclear-matter properties rather than a dependence on any single parameter. We also assess the impact of using matched crust--core constructions and show that they can introduce systematic differences in predicted neutron-star properties when compared with fully unified treatments.

Figures (13)

• Figure 1: Marginalized posterior distributions of the nuclear--matter parameters $K_0$, $J$, $L$, and $K_{\mathrm{sym}}$, and the NS properties $M_{\max}$, $R_{1.4}$, $\Lambda_{1.4}$, and $I_{1.4}$. The diagonal panels show the one--dimensional marginalized posteriors, with vertical lines marking the 68% confidence intervals (CIs). The off--diagonal panels display the two--dimensional joint posteriors, where the filled contour ellipses correspond to the 1$\sigma$, 2$\sigma$, and 3$\sigma$ CIs. Darker shades indicate regions of higher probability, while lighter shades represent the broader, lower--probability extensions of the posterior distribution.
• Figure 2: Left panel: Pressure as a function of baryon density for the ensemble of EOS consistent with all applied constraints. The shaded green band shows the 95% credible interval obtained from our Bayesian analysis. For comparison, we also display the constraints of Huth et al.Huth2022 and the multi-physics constrained band reported by Tsang et al.Tsang2024, together with the pressure constraints inferred from GW170817 Abbott2017. Right panel: Mass--radius relations corresponding to the same EOS ensemble. The green band denotes the 95% credible region obtained from the TOV solutions. Shaded elliptical regions show the mass--radius constraints from NICER pulse-profile modeling for PSR J0030+0451 and PSR J0740+6620, with darker and lighter regions indicating the 68% and 95% credibility intervals, respectively, while PSR J0437--4715 is shown as an additional low-mass constraint. The contours correspond to the GW170817 mass--radius posterior.
• Figure 3: Properties of nuclear clusters in the inner crust as a function of baryon density $\rho$ inside the crust. Shown are the cluster mass number $A$ (upper left), atomic number $Z$ (upper right), density of the cluster $n_0$ (middle left), neutron gas density $n_g$ (middle right), the WS cell radius $R_{\mathrm{WS}}$ (lower left), and the cluster isospin asymmetry $\alpha$ (lower right). The quantum calculations of Negele and Vautherin NEGELE1973298 and Onsi et al.Onsi_2008 are also shown.
• Figure 4: Posterior distributions of the surface–friction parameters and their correlations with NM properties.
• Figure 5: Pressure as a function of energy density for the unified crust--core EOS obtained from our Bayesian analysis, shown on logarithmic axes to span the full density range from the outer crust to the core. The shaded region denotes the $95\%$ credible interval of the posterior distribution. For comparison, we include the upper and lower bounds from Klausner et al.klausner2025neutronstarcrustinformed and the microscopic crust calculations of Burrello et al.Burrello_2025, both converted to consistent units. The inset shows the pressure as a function of baryon density in the crust region, where our results are compared with the constraints of Huth et al.Huth2022 and the band of Tsang et al.Tsang2024. The magenta band show the CC transition uncertainty.