Exploring Hyperon Skyrme Forces in Multi-$Λ$ Hypernuclei and Neutron Star Matter

TL;DR

The paper addresses the uncertainty in strangeness-rich dense matter by performing a Bayesian analysis of ΛΛ and ΛΛN interactions within a Skyrme Hartree–Fock framework, constrained by hypernuclear data and multi-messenger neutron star observations. It finds that the local ΛΛ interaction parameter λ0 is tightly constrained and attractive, while momentum-dependent λ1 and λ2 are repulsive at high density; the ΛΛ potential depth U_{ΛΛ} in pure Λ matter strongly shapes the two-body interaction. Repulsive ΛΛ and ΛΛN components reduce hyperon fractions and stiffen the EOS, increasing the maximum neutron-star mass by up to about 22% (and up to ~0.1 M⊙ from ΛΛN), enabling hyperon-rich stars to reach ~2 M⊙ without contradiction to observations. The work demonstrates a promising pathway toward a unified, experimentally grounded description of dense, strange nuclear matter and outlines future extensions to include Σ and Ξ hyperons for a complete neutron-star EOS.

Abstract

A major source of uncertainty in modeling the strangeness-rich interiors of neutron stars arises from the poorly constrained two-body and three-body interactions among hyperons and nucleons. We perform a comprehensive Bayesian analysis of the $ΛΛ$ and $ΛΛN$ interaction parameters within the Skyrme Hartree-Fock framework, constrained by both hypernuclei experimental data and astrophysical observations. Our results show that the parameter space of the $ΛΛ$ interaction is tightly constrained by combining nuclear and astrophysical data, while the parameters of the $ΛΛN$ three-body interaction remain sensitive to astrophysical inputs alone. Specifically, the local, momentum-independent two-body interaction parameter $λ_0$ is tightly constrained and predominantly attractive, while the momentum-dependent parameters $λ_1$ and $λ_2$ contribute repulsive effects at high densities. A key role is played by the $ΛΛ$ potential depth in pure $Λ$ matter, which effectively constrains the two-body $ΛΛ$ interaction and governs the balance between attraction at low densities and repulsion at high densities. The repulsive components of $ΛΛ$ interactions then decrease hyperon fractions and reconcile hyperon-rich equations of state with the observed $\sim2\,M_{\odot}$ neutron stars, increasing the maximum mass by up to 22\%. The inclusion of $ΛΛN$ three-body forces further stiffens the EOS, raising the maximum mass by up to $\sim 0.1\,M_{\odot}$. Our study represents a promising step toward a complete, experimentally grounded description of dense matter across a wide range of densities and strangeness compositions.

Figures (10)

• Figure 1: (Colour online) The $\Lambda\Lambda$ potential depth $U_{\Lambda\Lambda}$ in pure $\Lambda$ matter as a function of the ratio of $\Lambda$ density $\rho_{\Lambda}$ to the nuclear saturation density $\rho_{0}$, calculated using the SLL1, SLL2, SLL3, SLL1$^{\prime}$, and SLL3$^{\prime}$ parameter sets of the $\Lambda\Lambda$ interaction 1998PhRvC..58.3351L2011NuPhA.856...55M, combined with the SLy4+SLL4 parametrization for the $\Lambda N$ sector. The two red squares mark the experimental values extracted from different double-$\Lambda$ hypernuclei 1995NuPhA.585...83F2009NuPhA.828..191A2013PhRvC..88a4003A2015JPhG...42g5202O, highlighting the current uncertainty in the empirical $\Lambda\Lambda$ potential depth.
• Figure 2: (Colour online) Mass–radius relations for neutron stars (dashed lines) and hyperon stars (solid/dotted lines) using different interaction combinations. Pure neutron star matter (SKI3, SGI, SLy4) is shown with black squares marking the maximum mass. Hyperon star sequences include $\Lambda N$ and $\Lambda\Lambda$ interactions, with maximum masses marked by black stars or dots—illustrating the EOS softening and maximum mass reduction that characterizes the hyperon puzzle. Observational constraints from NICER (PSR J0030+0451, PSR J0740+6620, PSR J0437–4715) and LIGO/Virgo (GW170817) are included for comparison.
• Figure 3: Corner plot showing the posterior distributions and correlations for parameters$\lambda_0$, $\lambda_1$, $\lambda_2$, $\lambda_3$, $\alpha$, using the SLy4+SLL4 interaction, constrained by both astrophysical and nuclear data (+Astro+Nucl). The contours represent the 68.3% confidence level. See Table \ref{['tab:Post_NN&NY_combined_para']} for detailed numerical values. The distributions show that $\lambda_0$ is tightly constrained and attractive, while $\lambda_0$, $\lambda_1$, and $\lambda_3$ are repulsive. The constraints exclude parameter space with low values of these parameters (lower left corners of the 2D contours).
• Figure 4: Posterior distributions of $\Lambda\Lambda$ parameters ($\lambda_0$, $\lambda_1$, $\lambda_2$) under different constraints: +Astro, +Nucl, and +Astro+Nucl, based on SLy4+SLL4.
• Figure 5: Posterior probability distributions of $\Lambda\Lambda$ interaction parameters ($\lambda_0$, $\lambda_1$, $\lambda_2$; upper panel) and $\Lambda\Lambda$N interaction parameters ($\lambda_3$, $\alpha$; lower panel) for various $NN$+$\Lambda$ interactions, constrained by combined astrophysical and nuclear data (+Astro+Nucl).