Hyperon Puzzle of Neutron Stars with Skyrme Force Models

Abstract

We consider the so called hyperon puzzle of neutron star (NS). We employ Skyrme force models for the description of in-medium nucleon-nucleon, nucleon-Lambda hyperon ($N\Lambda$), and Lambda-Lambda ($\Lambda\Lambda$) interactions. A phenomenological finite-range force for the $\Lambda\Lambda$ interaction is considered as well. Equation of state (EoS) of NS matter is obtained in the framework of density functional theory, and Tolman-Oppenheimer-Volkoff equations are solved to obtain the mass-radius relations of NSs. It has been generally known that the existence of hyperons in the NS matter is not well supported by the recent discovery of large-mass NSs ($M \simeq 2 M_\odot$) since hyperons make the EoS softer than the one without them. For the selected interaction models, $N\Lambda$ interactions reduce the maximum mass of NS by about 30~\%, while $\Lambda\Lambda$ interactions can give about 10~\% enhancement. Consequently, we find that some Skyrme force models predict the maximum mass of NS consistent with the observation of $2 M_\odot$ NSs, and at the same time satisfy observationally constrained mass-radius relations.