Impact of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi mathvariant="normal">Ξ</mml:mi> </mml:math> -hypernuclear constraints on relativistic equation of states and properties of hyperon stars

Significant uncertainties persist in describing the internal structure and equation of state 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 $\mathrm{\ensuremath{\Xi}}$ hypernuclear physics on top of $\mathrm{\ensuremath{\Lambda}}$ hyperons considered in [Astrophys. J. 942, 55 (2023)]. Specifically, based on updated measurements of hyperon separation energies from $\mathrm{\ensuremath{\Xi}}$ hypernuclear experiments, three sets of $\mathrm{\ensuremath{\Xi}}N$ effective interactions are constructed and a linear correlation between their scalar ($\ensuremath{\sigma}$) and vector ($\ensuremath{\omega}$) coupling strength ratios is proposed as a constraint derived from $\mathrm{\ensuremath{\Xi}}$ 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 $\mathrm{\ensuremath{\Lambda}}$ hyperons, the shallower potential and larger rest mass of $\mathrm{\ensuremath{\Xi}}$ hyperons lead to a higher threshold for their appearance in hyperon stars. As a result, the parameter space for the hyperon-nucleon interaction of $\mathrm{\ensuremath{\Xi}}$ hyperons remains more loosely constrained. In particular, compared to the vector $\ensuremath{\omega}$ meson-hyperon coupling, the introduction of linear correlations in hypernuclear physics imposes a more substantial constraint on the scalar $\ensuremath{\sigma}$ meson-hyperon coupling, significantly enhancing its coupling strength and ensuring the stiffness of the equation of state, highlighting the crucial role of hypernuclear studies in solving the hyperon puzzle. Consequently, a maximum mass of around $2{M}_{\ensuremath{\bigodot}}$ can be achieved with all four interactions considered in this study under the combined constraints from astronomical observations and nuclear physics. Moreover, 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. The corresponding uncertainties associated with hyperon-nucleon contributions and the impact on structural properties of hypernuclei are also reliably estimated.