Constraining the $ΛΛ$ interaction with terrestrial and astronomical data

Abstract

Terrestrial double-$Λ$ hypernuclear data and astronomical observations of neutron stars provide complementary constraints on the $ΛΛ$ interaction. In this work, we investigate the $ΛΛ$ interaction within a Skyrme energy density functional framework based on the KIDS (Korea-IBS-Daegu-SKKU) models. We employ a Skyrme-type $ΛΛ$ interaction that includes the standard $s$- and $p$-wave terms, as well as a density-dependent term that effectively represents an $NΛΛ$ three-body force. The $s$-wave terms are constrained using data on double-$Λ$ hypernuclei supplemented by pseudodata obtained from core + $2Λ$ three-body model calculations including heavier hypernuclei. We show that the data on heavier systems are essential to simultaneously constrain the two $s$-wave parameters. We further explore the impact of the $p$-wave and $NΛΛ$ components on the neutron-star properties and find that appropriate repulsive contributions of these terms yield consistency with current neutron-star mass-radius observations. These results indicate that the present framework provides phenomenologically acceptable equations of state for dense $(N,Λ)$ matter over a wide range of densities and highlight the importance of future experimental data on heavier double-$Λ$ hypernuclei.

Figures (6)

• Figure 1: MD values defined in Eq. \ref{['eq:MD']} as functions of the $\Lambda\Lambda$ interaction parameters $\lambda_0$ and $\lambda_1$ for (a) the restricted dataset consisting of $^{11}_{\Lambda\Lambda}$Be, $^{~9}_{\Lambda\Lambda}$Li, and $^{~9}_{\Lambda\Lambda}$Be, and (b) the full dataset listed in Table \ref{['tb:dataset']}. The remaining parameters are fixed at $\lambda_2=0$ and $\lambda_3=0$. KIDS0 and KIDS0-Y4 parameter sets are used for $NN$ and $N\Lambda$ interactions, respectively.
• Figure 2: Values of $(\lambda_0,\lambda_1)$ determined by fittings to hypernuclear data with $\lambda_3$ fixed at $0,\ 100,\ 200,\ \dots$ MeV fm$^6$. The squares and circles represent the results for KIDS-A and -D, respectively, and the color indicates the value of $\lambda_3$. The upper bounds of $\lambda_3$ is determined by the MD values. See main texts for detail.
• Figure 3: (a) Mass-radius (M-R) relations of neutron stars calculated with different EoSs. The black-dashed curve corresponds to nucleonic matter (KIDS-A), while the colored curves show the results for hyperonic matter based on the KIDS-A + KIDS-A-Y4 + KIDS-A-Y4-LL4($\lambda_2,0$) models. Each curve is terminated at the central density where the causality condition is violated anywhere inside the star. Filled circles indicate the maximum-mass configurations when they are reached before the causality limit. The light-blue regions enclosed by solid and dashed lines indicate the $1\sigma$ and $2\sigma$ credible regions, respectively, of NICER data for PSR J0740+6620 Salmi24Salmi24-data. (b) Speed of sound as a function of the baryon density for the corresponding EoSs. (c) Fraction of $\Lambda$ hyperons at the centers of neutron stars as a function of stellar mass.
• Figure 4: Same as Fig. \ref{['fig:MR-cs-YL_KIDSA-LL4-a2-0']} but for KIDS-D model.
• Figure 5: Summary of the neutron-star properties in the $(\lambda_2,\lambda_3)$ plane for (a) KIDS-A-Y4-LL4($\lambda_2,\lambda_3$) and (b) KIDS-D-Y4-LL4($\lambda_2,\lambda_3$) parameter sets. Closed and open symbols indicate whether or not the maximum neutron-star mass exceeds $2M_\odot$. The consistency of the M-R curves with the NICER data for PSR J0740+6620 Salmi24Salmi24-data is distinguished by colors (blue: consistent within $1\sigma$; green: consistent within $2\sigma$; gray: outside the $2\sigma$ region).