Equation of state for neutron stars with hyperons by the variational method

TL;DR

This paper explores how the unknown odd-state part of the $\Lambda ext{-}\Lambda$ interaction influences neutron star structure by constructing various equations of state using the variational method, and finds that repulsive interactions lead to stiffer EOSs and more massive neutron stars.

Contribution

It introduces multiple EOS models for hyperonic matter with different odd-state $\Lambda ext{-}\Lambda$ interactions using the variational method, addressing the impact on neutron star properties.

Findings

Stiffer EOSs with more repulsive odd-state $\Lambda ext{-}\Lambda$ interactions increase maximum neutron star mass.

The onset density of $\Sigma^- ext{-}$ hyperons depends strongly on the $\Lambda ext{-}\Lambda$ interaction.

Including three-baryon repulsive forces aligns results with heavy neutron star observations.

Abstract

We investigate the effects of the odd-state part of bare $\Lambda \Lambda$ interactions on the structure of neutron stars (NSs) by constructing equations of state (EOSs) for uniform nuclear matter containing $\Lambda$ and $\Sigma^-$ hyperons with use of the cluster variational method. The isoscalar part of the Argonne v18 two-nucleon potential and the Urbana IX three-nucleon potential are employed as the interactions between nucleons, whereas, as the bare $\Lambda N$ and even-state $\Lambda \Lambda$ interactions, two-body central potentials that are determined so as to reproduce the experimental data on single- and double-$\Lambda$ hypernuclei are adopted. In addition, the $\Sigma^- N$ interaction is constructed so as to reproduce the empirical single-particle potential of $\Sigma^-$ in symmetric nuclear matter. Since the odd-state part of the $\Lambda \Lambda$ interaction is not known owing to lack of experimental data, we construct four EOSs of hyperonic nuclear matter, each with a different odd-state part of the $\Lambda \Lambda$ interaction. The EOS obtained for NS matter becomes stiffer as the odd-state $\Lambda \Lambda$ interaction becomes more repulsive, and correspondingly the maximum mass of NSs increases. It is interesting that the onset density of $\Sigma^-$ depends strongly on the repulsion of the odd-state $\Lambda \Lambda$ interaction. Furthermore, we take into account the three-baryon repulsive force to obtain results that are consistent with observational data on heavy NSs.