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Hyperon Puzzle of Neutron Stars with Skyrme Force Models

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 ($NΛ$), and Lambda-Lambda ($ΛΛ$) interactions. A phenomenological finite-range force for the $ΛΛ$ 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, $NΛ$ interactions reduce the maximum mass of NS by about 30~\%, while $ΛΛ$ 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.