Constraining the nuclear equation of state from terrestrial experiments and neutron star observations using relativistic mean-field models

TL;DR

This study develops a relativistic mean-field framework (the OMEG family) incorporating $\sigma$-$\delta$ and $\omega$-$\rho$ mixing to constrain the nuclear equation of state using terrestrial nuclei data alongside neutron-star observations from NICER and GW170817. The model achieves a soft symmetry-energy regime around $\rho_B\approx 2\rho_0$, yielding small radii and tidal deformabilities while ensuring a stiff high-density EoS that can support $2M_{\odot}$ stars; the curvature parameter $K_{\textrm{sym}}$ is negative and crucial for this soft-to-hard evolution. A tension remains between PREX-2 and CREX neutron-skin measurements, though the OMEG family can accommodate the larger $R_{\rm skin}^{208}$ indicated by PREX-2 without conflicting with astrophysical constraints. Overall, the work provides a unified RMF description linking finite-nucleus properties to neutron-star radii and tidal responses, highlighting the role of $K_{\textrm{sym}}$ in reconciling terrestrial and astrophysical data.

Abstract

We investigate the nuclear equation of state (EoS) for isospin-asymmetric matter using a new set of RMF interactions with the $σ$-$δ$ and $ω$-$ρ$ mixing, referred to as the OMEG family. These interactions are optimized so as to reproduce both terrestrial nuclear measurements and astrophysical constraints extracted from NICER and GW170817. The $σ$-$δ$ mixing softens the nuclear symmetry energy and pressure around twice the saturation density, which enables relatively small neutron-star radii and tidal deformabilities while keeping the nuclear EoS sufficiently stiff at high densities to support $2M_{\odot}$ neutron stars. We find that the curvature parameter, $K_{\textrm{sym}}$, plays an important role in realizing the soft-to-hard behavior of the nuclear EoS, and the astrophysical data favor small or even negative values of $K_{\textrm{sym}}$.

Figures (3)

• Figure 1: Mass–radius relations of neutron stars for the OMEG family. The observational constraints are taken from PSR J0030$+$0451 ($1.40^{+0.13}_{-0.12}$$M_{\odot}$ and $11.71^{+0.88}_{-0.83}$ km) Vinciguerra:2023qxq, PSR J0437$-$4715 ($1.418\pm0.037$$M_{\odot}$ and $11.36^{+0.95}_{-0.63}$ km) Choudhury:2024xbk, PSR J0740$+$6620 ($2.073^{+0.069}_{-0.069}$$M_{\odot}$ and $12.49^{+1.28}_{-0.88}$ km) Salmi:2024aum, and PSR J1231$-$1411 ($1.04^{+0.05}_{-0.03}$$M_{\odot}$ and $12.6\pm0.3$ km) Salmi:2024bss. The other theoretical results are explained in Ref. Miyatsu:2024ioc.
• Figure 2: Pressure, $P$, in pure neutron matter as a function of baryon density ratio, $\rho_{B}/\rho_{0}$. The empirical constraints on the nuclear EoS extracted from the particle-flow analyses in heavy-ion collisions are also provided Danielewicz:2002pu.
• Figure 3: Neutron skin thickness of $^{48}$Ca and $^{208}$Pb, $R_{\rm skin}^{48}$ and $R_{\rm skin}^{208}$. A detailed description of all the interactions used in this figure is provided in Ref. Miyatsu:2024ioc.