Influence of Finite-Nuclei Constraints on High-Density Transitions and Neutron Star Properties

TL;DR

This work investigates how incorporating finite-nuclei constraints affects the high-density neutron-star EoS within a relativistic mean-field framework. It employs a Bayesian approach with three constraint sets—Theoretical, Implicit, and Explicit FN—plus a model-agnostic high-density speed-of-sound extension to connect low- and high-density regimes. Explicit FN constraints dramatically tighten the low-density EoS, reducing the transition density range to about $1$–$4\rho_{\text{ref}}$ and predicting larger radii for low-mass NSs, which can clash with NICER observations for some pulsars; higher-density behavior remains similar across constraint sets, but correlations between nuclear-matter parameters and NS observables become constraint-dependent. Overall, the study underscores the pivotal role of accurate low-density finite-nuclei information in shaping NS properties and highlights possible tensions with observations that warrant further theoretical and observational effort.

Abstract

We construct posterior distributions of the equation of state (EoS) for matter beyond the inner crust of neutron stars by incorporating finite nuclei (FN) constraints within relativistic mean field models. These constraints are implemented in three complementary ways: (i) through theoretical bounds on the EoS, (ii) implicitly via nuclear matter parameters, and (iii) explicitly by enforcing consistency with experimental binding energies and charge radii of selected nuclei. The resulting low-density nucleonic EoSs are subsequently matched to a model-agnostic speed-of-sound parametrization, constrained by astrophysical observations, including NICER mass-radius measurements, tidal deformability limits from GW170817, and lower bounds on the maximum neutron-star mass inferred from radio pulsar observations. We find that the admissible range of the transition density is strongly sensitive to the choice of the low-density EoS. In particular, the inclusion of explicit FN constraints significantly reduces the allowed parameter space of the nucleonic EoS at low densities, narrowing the transition-density range by nearly a factor of two. Consequently, neutron-star properties inferred from EoSs with explicit FN constraints differ substantially, with especially pronounced effects for low-mass neutron stars and their correlations with nuclear matter parameters. A quantitative comparison, using metrics based on Mahalanobis distance, shows consistency of the explicit constraints with PSRs J0740+6620, J0030+0451, and J0437-4715, but suggest a possible tension with PSR J0614-3329. These findings underscore the critical importance of a consistent treatment of finite-nuclei properties for reliably inferring the behavior of high-density matter and the presence of possible phase transitions from astrophysical observations.

Figures (7)

• Figure 1: Posterior distributions of nuclear matter parameters of the RMF model for the three distinct set of constraints: Theoretical, Implicit and Explicit. The 1$\sigma$ intervals are shown as vertical dashed lines in the marginalized posterior distributions. All are in the units of MeV, except $\rho_0$ and $m^*/m$ which are in fm$^{-3}$ and dimensionless respectively.
• Figure 2: Posterior distributions for high density parameters. All are in the units of fm${}^{-3}$, except $h_p$ and $s_p$ which are dimensionless.
• Figure 3: Posterior distributions of the transition density $\rho_{tr}$ for the three sets of distinct constraints. Vertical dashed lines are the median values while the solid lines bound the 99% CI
• Figure 4: 99% confidence regions for pressure $P$, squared speed of sound $(c_s/c)^2$, and the conformality parameter $d_c$ across the low densities (0.8-2.5 $\rho_{\text{ref}}$ in the left panels), and across the density range upto 10$\rho_{\text{ref}}$ in the right panels. Also shown are the 95% credible region from annala2023strongly bounded by thick black lines in (e) and (f), along with the speed of sound in the conformal limit in (c) and (d) shown as horizontal dash-dotted lines. The vertical lines cover the 99% CI of the central density, corresponding to maximum mass stars for each of the case. The threshold conformality parameter $d_c = 0.2$, which indicates the proximity to conformal limit is also shown as dash-dotted lines in (f).
• Figure 5: 99% confidence regions for mass and radius for the three distinct cases. The observed mass-radius of the recent pulsar observations are shown are shown. (inset) The maximum mass distribution for the three cases along with the observational lower limit on the maximum mass coming from PSRs J0740+6620 fonseca2021refined (dotted patch), J0348+0432 doi:10.1126/science.1233232 (left hatched), and J1614--2230 Arzoumanian_2018 (right hatched).