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Key factor for determining relation between radius and tidal deformability of neutron stars: Slope of symmetry energy

The constraints on tidal deformability of neutron stars were first extracted from GW170817 by LIGO and Virgo Collaborations. However, the relationship between the radius and tidal deformability is still under debate. Using an isospin-dependent parameterized equation of state (EOS), we study the relation between and and its dependence on parameters of symmetry energy and EOS of symmetric nuclear matter when the mass is fixed at , , and . We find that, although the changes of high order parameters of and can shift individual values of and , the relation remains approximately at the same fitted curve. The slope of the symmetry energy plays the dominant role in determining the relation. By investigating the mass dependence of the relation, we find that the well fitted relation for 1.4 is broken for massive neutron stars.