Roles of isoscalar hyperons in probing the density dependence of the nuclear symmetry energy

The role of the isoscalar hyperon Λ in probing the density dependence of the nuclear symmetry energy is studied in multi-Λ hypernuclei, hyperon-rich matter and neutron stars in relativistic models. Relationships between the properties of three types of objects and the neutron thickness in 208Pb are established with respect to the isoscalar-isovector coupling that modifies the density dependence of the symmetry energy. The exotic isotopes far from the neutron drip line can be stabilized by filling in considerable Λ hyperons. The difference of the binding energy of multi-Λ hypernuclei from different models is attributed to different symmetry energies. The isovector potential together with the neutron thickness in multi-Λ hypernuclei investigated is very sensitive to the isoscalar-isovector coupling. The large sensitivity of the Λ hyperon fraction to the isoscalar-isovector coupling occurs at about 2-3ρ0 in beta equilibrated hyperon-rich matter. In neutron stars with hyperonization, an on-off effect with respect to the isoscalar-isovector coupling exists for the neutron star radius.