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

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.

arXiv comment12 pages, 6 figures, accepted for publication in Phys. Rev. C

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