Universal Relation for the Neutron Star Maximum Mass within Relativistic Mean-Field Theories

TL;DR

The paper addresses predicting the neutron-star maximum mass $M_{\max}$ within relativistic mean-field (RMF) theories and identifies which nuclear-matter properties most influence it. It employs an extended RMF Lagrangian with $\sigma$, $\omega$, and $\rho$ fields including an omega self-coupling $\zeta$, and constrains the pure neutron matter EOS at low density with chiral EFT to build 250 parameter sets. The main contribution is an empirical universal formula $M_{\max} = f(\zeta)\, n_0 + g(\zeta)\, m^* + h(\zeta)$, with $f,g,h$ quadratic in $\zeta$, showing that $M_{\max}$ is governed primarily by $n_0$, $m^*$, and $\zeta$, while symmetry-energy details play a smaller role. The results demonstrate high agreement with TOV solutions for $\zeta \lesssim 0.005$ (Pearson $\approx 0.996$), offering a practical RMF-based method to estimate NS maximum mass and highlighting how high-density stiffness controlled by $\zeta$ shapes the mass-radius landscape and future connections to finite-nucleus observables.

Abstract

We obtain a universal relation for the neutron star maximum mass arising from a particular combination of the saturation density ($n_0$), the effective mass ($m^*$), and (when present) the vector meson self-coupling constant ($ζ$) within the relativistic mean-field model framework. Observations of massive neutron stars heavier than $\sim 2M_{\odot}$ have eliminated the softest equation of state from consideration and impose strong constraints on nuclear interactions used to model dense nuclear matter. To date there have been numerous attempts to refine relativistic mean-field models by including the presence of additional mesons, such as the delta meson, and couplings. We show that current RMF models, including our own constructions, exhibit a maximum neutron star mass that is primarily determined by the combination of the saturation density, the effective mass at saturation, and the vector meson self-coupling constant. When constraining the pure neutron matter equation of state using chiral effective field theory (ChEFT) at low densities, 250 parameter sets were generated to derive an empirical formula for the maximum mass of neutron stars and apply the formula with the present relativistic mean field models.

Figures (12)

• Figure 1: Pearson correlation analysis between nuclear matter properties and the maximum mass of a neutron star. The nuclear matter properties include the symmetry energy ($J$), its slope ($L$), incompressibility ($K$), skewness ($Q$), binding energy per nucleon ($B/A$), saturation density ($n_0$), effective mass ($m^*$), and the $\zeta$ coupling constant. The correlation coefficients are computed based on the parameter sets listed in Table \ref{['M2.35 nuclear matter']}.
• Figure 2: Pressure as a function of baryon density for the NL3, IUFSU, and FSU parameter sets. The total pressure of pure neutron matter and the symmetry energy contribution ($n^2\tfrac{S(n)}{dn}$) are shown separately. The central densities of the corresponding maximum-mass neutron stars are indicated with stars.
• Figure 3: Mass–radius relations for the NL3, IUFSU, and FSU parameter sets. For each case, additional curves are shown for varied incompressibility values of $K=200 \rm \, MeV$ and $K=300\,\rm MeV$ to illustrate the sensitivity of the stellar structure to the incompressibility of nuclear matter.
• Figure 4: Energy per particle $E/N$ as a function of baryon number density $n$ for pure neutron matter. The gray band (labeled "RMF") represents a family of relativistic mean field (RMF) equations of state constrained to reproduce the microscopic results shown by the black dashed line ("N2LO500"). For comparison, results from two representative models-SLy4 (blue dot-dashed line) and NL3 (red dotted line)-are also shown.
• Figure 5: Mass-radius relations for neutron stars with varying values of the coupling constant $\zeta$, as indicated in the legend. Each curve corresponds to a different equation of state model. Observational constraints from the massive pulsars PSR J2215+5135 and PSR J0348+0432 are shown as horizontal bands Linares2018Antoniadis2013. Results from the NICER analyses of PSR J0740+6620 by Riley et al. and Miller et al. are shown as dotted yellow and orange contours, respectively Riley2021Miller2021. The enclosed areas indicate the $+1\,\sigma$ confidence regions.