Impact of $Ξ$-Hypernuclear Constraints on Relativistic Equation of State and Properties of Hyperon Stars

TL;DR

The paper addresses the hyperon puzzle by integrating NS observations with hypernuclear data, extending Λ-only analyses to include $Ξ$ hypernuclei. It uses density-dependent RMF theory and Bayesian inference to constrain hyperon–nucleon couplings, finding that joint Λ and Ξ nuclear constraints stiffen the EOS and enable NS masses near $2M_{ m solar}$ while reducing hyperon onset uncertainties. A linear correlation between $R_{ ext{σΞ}}$ and $R_{ ext{ωΞ}}$ is established and embedded in the nuclear likelihood, tightening posterior distributions for both Λ and Ξ couplings and demonstrating a stronger constraint when both hyperon species are included. The results show that the combination of hypernuclear data and multimessenger observations yields a maximum hyperon-star mass around $2.18^{+0.14}_{-0.34}\,M_\odot$ for the stiffest model considered, with markedly reduced uncertainties in composition and mass–radius predictions, offering a path toward resolving the hyperon puzzle with future measurements.

Abstract

Significant uncertainties persist in describing the equation of state and internal structure of hyperon stars due to the limited understanding of the mechanisms underlying hyperon interactions. Constraining the interaction parameter space through a combination of the latest astronomical observations and hypernuclear physics experiments is therefore essential. In this study, we incorporate experimental constraints from $Ξ$ hypernuclear physics on top of $Λ$ hyperons considered in \citet{Sun2023APJ942.55}. Specifically, based on updated measurements of hyperon separation energies from $Ξ$ hypernuclear experiments, sets of $ΞN$ effective interactions are constructed and a linear correlation between their scalar ($σ$) and vector ($ω$) coupling strength ratios is proposed as a constraint derived from $Ξ$ hypernuclear physics. Together with experimental correlations and astronomical observational data, four types of analyses are performed to constrain hyperon-nucleon interactions and the properties of hyperon stars. Compared to the vector $ω$ meson-hyperon coupling, the introduction of linear correlations in hypernuclear physics imposes a more substantial constraint on the scalar $σ$ meson-hyperon coupling, significantly enhancing its coupling strength and thereby ensuring the stiffness of the equation of state, highlighting the crucial role of hypernuclear studies in solving the hyperon puzzle problem. Consequently, a maximum mass of around $2M_{\odot}$ can be achieved with all five interactions considered in this study under the combined constraints from astronomical observations and nuclear physics. With more reliably estimated hyperon-nucleon contributions, the uncertainties in both the fractions and the threshold densities at which hyperons appear inside neutron stars are notably reduced, along with those in the mass-radius predictions.

Figures (9)

• Figure 1: Using the six RMF effective Lagrangians listed in Table \ref{['Tab:CouplingStrengthX']}, we calculate the uncertainties of the hyperon potentials in $^{15}_{\Xi^{-}}$C and $^{13}_{\Xi^{-}}$B hypernuclei with the $\Xi^{-}$ hyperon in the $1s$ or $1p$ state, respectively. In the three panels, the light color meshed regions represent the results obtained by adopting only one kind of $\Xi N$ interaction (denoted as Free $\Xi$C$s$, Free $\Xi$C$p$, and Free $\Xi$B$p$) within the range $R_{\omega\Xi}=0.200\text{--}1.000$, while the dark color areas show the constrained distribution after considering the joint +ASTRO+NUCL$\Lambda$+NUCL$\Xi$ analysis (see Table \ref{['Tab:CouplingStrength']} in Sec. \ref{['sec:result']} for details). The pink dotted filled areas indicate the theoretical uncertainty ranges estimated by combining the three fitting strategies of $\Xi N$ interactions (denoted as Free $\Xi N$).
• Figure 2: The hyperon separation energies $B_{\Xi^{-}}$ of $^{15}_{\Xi^{-}}$C and $^{13}_{\Xi^{-}}$B are calculated using four RMF effective Lagrangians PKDD, DD-ME2, DD-MEX, and DD-LZ1, assuming that the $\Xi^{-}$ in either the $1s$ or $1p$ state. The red bars indicate the maximum uncertainties of the separation energies resulting from the combination of the three fitting strategies of $\Xi N$ interactions (denoted as Free $\Xi$C$s$, Free $\Xi$C$p$, and Free $\Xi$B$p$) as $R_{\omega\Xi}$ varies from 0.200 to 1.000, while blue bars denote the maximum uncertainties predicted after considering the joint +ASTRO+NUCL$\Lambda$+NUCL$\Xi$ analysis (see Table \ref{['Tab:CouplingStrength']} in Sec. \ref{['sec:result']} for details). The black error bars correspond to the experimentally measured $\Xi^{-}$ hypernuclear data.
• Figure 3: The correlation between $R_{\sigma\Xi}$ and $R_{\omega\Xi}$ for the effective interactions listed in Table \ref{['Tab:CouplingStrengthX']} is presented. A linear fit to the data yields the relation $R_{\omega\Xi}=1.243R_{\sigma\Xi}-0.064$, which is illustrated by the red line. Results from $\Lambda$ hypernuclei (from Ref. Rong2021PRC104.054321) are also shown as a gray dashed line.
• Figure 4: The mass–radius relations of NSs are calculated using various RMF effective interactions. For comparison, we include the mass–radius measurements from the NICER for PSR J0030+0451 (from PDT-U) Vinciguerra2024APJ961.62 and PSR J0740+6620 Salmi2024APJ974.294, both shown at the 68% and 95% confidence levels, as well as the binary tidal deformability constraints from GW170817 reported by LIGO/Virgo Abbott2017PRL119.161101.
• Figure 5: Posterior PDFs of $R_{\sigma\Lambda}$ (top-left panel), $R_{\omega\Lambda}$ (top-right panel), $R_{\sigma\Xi}$ (bottom-left panel), and $R_{\omega\Xi}$ (bottom-right panel) for the scalar and vector couplings between $\Lambda N$ and $NN$, or $\Xi N$ and $NN$ interactions, based on the RMF models adopted in this work. This analysis incorporates constraints from GW170817 and NICER (PSR J0030+0451 and PSR J0740+6620). Results are shown under different conditions: considering only astrophysical observational constraints (green curves), adding the empirical $R_{\sigma\Lambda}$-$R_{\omega\Lambda}$ relation constrained by single-$\Lambda$ hypernuclear data (orange curves), adding the empirical $R_{\sigma\Xi}$-$R_{\omega\Xi}$ relation constrained by single-$\Xi$ hypernuclear data (red curves), and incorporating both empirical relations from single-$\Lambda$ and single-$\Xi$ hypernuclear data (blue curves).