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 (Nλ) and Lambda-Lambda (λλ) interactions. A phenomenological finite-range force (FRF) 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 (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 ≃ 2M_⊙) 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 2M_⊙ NSs, and at the same time satisfy observationally constrained mass-radius relations.