Constraints on the Symmetry Energy from PREX-II in the Multimessenger Era

Abstract

The neutron skin thickness $Δr_{\rm{np}}$ of heavy nuclei is essentially determined by the symmetry energy density slope $L({ρ})$ at $ρ_c = 0.11~{\rm {fm}^{-3}}\approx 2/3ρ_0$ ($ρ_0$ is nuclear saturation density), roughly corresponding to the average density of finite nuclei. The PREX collaboration recently reported a model-independent extraction of $Δr^{208}_{\rm{np}} = 0.283 \pm 0.071$ fm for the $Δr_{\rm{np}}$ of $^{208}$Pb, suggesting a rather stiff symmetry energy $E_{\rm{sym}}({ρ})$ with $L({ρ_c }) \ge 52$ MeV. We show that the $E_{\rm{sym}}({ρ})$ cannot be too stiff and $L({ρ_c }) \le 73$ MeV is necessary to be compatible with (1) the ground-state properties and giant monopole resonances of finite nuclei, (2) the constraints on the equation of state of symmetric nuclear matter at suprasaturation densities from flow data in heavy-ion collisions, (3) the largest neutron star (NS) mass reported so far for PSR J0740+6620, (4) the NS tidal deformability extracted from gravitational wave signal GW170817 and (5) the mass-radius of PSR J0030+045 measured simultaneously by NICER. This allows us to obtain $52 \le L({ρ_c }) \le 73$ MeV and $0.212 \le Δr^{208}_{\rm{np}} \le 0.271$ fm, and further $E_{\rm{sym}}({ρ_0 }) = 34.3 \pm 1.7$ MeV, $L({ρ_0 }) = 83.1 \pm 24.7$ MeV, and $E_{\rm{sym}}({2ρ_0 }) = 62.8 \pm 15.9$ MeV. A number of critical implications on nuclear physics and astrophysics are discussed.