$ΛΛ$ Interaction and Neutron Stars

We investigate the effect of the $\Lambda\Lambda$ interactions on the bulk properties of neutron star (NS). We employ a few Skyrme-type models and a finite-range force model in order to describe the $\Lambda \Lambda$ interactions for the nuclear matter of NS. With the model parameters that reproduce the binding energies of the double-$\Lambda$ hypernuclei, we calculate the equation of state (EoS) for the matter of NS self-consistently. By solving the Tolman-Oppenheimer-Volkoff equation with the new EoS, we find that the bulk properties of NS, such as mass and radius, strongly depend on the $\Lambda \Lambda$ interactions. It has been generally known (as "hyperonization puzzle") that the existence of hyperons in NS matter is not well supported by the recent discovery of the high mass NS ($M_{NS} \approx 2 M_\odot$) because hyperons make the EoS soft. However, we find that some of our NS models can predict both the existence of the $\sim 2 M_\odot$ NS and the observationally constrained mass-radius relations. Our results indicate that the $\Lambda \Lambda$ interactions could provide a clue to this puzzle.