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 (NN), nucleon-Lambda hyperon (N Lambda) and Lambda-Lambda (Lambda Lambda) interactions. A phenomenological finite-range force (FRF) 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 (TOV) 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 similar or equal to 2 M-circle dot) 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-circle dot NSs, and at the same time satisfy observationally constrained mass-radius relations.