Relativistic mean-field model with density- and isospin-density-dependent couplings

TL;DR

The authors develop a density- and isospin-density dependent relativistic mean-field EoS with hyperons (DID/DIDY), calibrated via Bayesian inference to HALQCD+BHF hyperon potentials, χEFT neutron-matter pressures, nuclear saturation data, heavy-ion collisions, and NS observations. A low-density NSE treatment with 8244 nuclei connects the crust to the RMF core, producing a complete general-purpose EoS for astrophysical simulations. The DIDY hyperonic extension yields improved agreement with hyperon potentials across ISM and NM and, crucially, preserves compatibility with NS mass and tidal deformability constraints, offering a viable path to addressing the hyperon puzzle. Finite-temperature results reveal a nonmonotonic speed of sound and rich temperature- and isospin-dependent composition, enhancing the applicability of the EoS to core-collapse supernovae and mergers and enabling future exploration with neutrino transport and cooling calculations.

Abstract

We present a new hadronic EoS with hyperons built within the relativistic mean-field (RMF) formalism with baryon-density- and isospin-density-dependent couplings. Motivated by microscopic calculations showing density- and isospin-asymmetry-dependence of self-energies, we implement a new form for the baryon-meson couplings. The parameters for the couplings are constrained by a Bayesian analysis, which anchors the model to nuclear saturation properties, chiral effective field theory ($χ$EFT) predictions for pure neutron matter, heavy-ion collision data, and HALQCD-based hyperon potential calculations at 3-momentum $|\mathbf{k}|=0$ in both isospin-symmetric and pure neutron matter. The resulting EoS satisfies neutron star mass-radius constraints from NICER and GW170817, providing another way to address the hyperon puzzle. The low-density part of the EoS is described via nuclear statistical equilibrium with modern mass tables (AME20/FRDM12, 8244 nuclei), providing a novel and complete general-purpose EoS for astrophysical simulations.

Figures (10)

• Figure 1: Cartoon representation of the HS model composition as a heterogeneous mixture of unbound nucleons (green) and bound nuclei (blue), and the corresponding fractions of space.
• Figure 2: The table of nuclides used in our HS model; masses from AME20 are shown in blue and masses from FRDM12 are shown in pink; light-yellow nuclei are excluded by the neutron-drip cutoff. The $\beta$-stable nuclei are also shaded in dark colors.
• Figure 3: Plot of meson couplings to nucleons in DID as a function of baryon and isospin density. The solid lines represent ISM ($\beta=0$), the dotted lines are for NM ($\beta = -1$), and the unmarked edge of the shaded zone is the theoretical limit of $\beta = \pm2$. The vertical dashed line corresponds to the saturation density for the DID model.
• Figure 4: Left panel: Hyperon single-particle potentials as functions of baryon density $n_B$ for ISM within DDB (dashed lines) and DID (solid lines) models. Three remaining panels: Hyperon single-particle potentials in NM for DDBY and DIDY, respectively. In all panels, dots with error bars denote the BHF results halqcd2019a for the hyperon potentials at $|\mathbf{k}| = 0$ with their respective uncertainties.
• Figure 5: Baryon fractions as functions of the baryon density $n_B$ in the $\beta$-equilibrium matter with hyperons for DIDY (solid lines), DDBY (dashed lines), and DD2Y (dotted lines) models.