Constraining the high-density nuclear symmetry energy with the transverse-momentum-dependent elliptic flow

Within the newly updated version of the ultrarelativistic quantum molecular dynamics (UrQMD) model, the transverse-velocity dependence of the elliptic flow of free nucleons from Au197+Au197 collisions at the incident energy 400 MeV/nucleon is studied within different windows of the normalized c.m. rapidity y₀. It is found that the elliptic flow difference v2n-v2p and ratio v2n/v2p of neutrons versus protons are sensitive to the density dependence of the symmetry energy, especially the ratio v2n/v2p at small transverse velocity in the intermediate rapidity intervals 0.4<|y₀|<0.6. By comparing either transverse-momentum-dependent or integrated FOPI/LAND elliptic flow data of nucleons and hydrogen isotopes with calculations using various Skyrme interactions, all exhibiting similar values of isoscalar incompressibility but very different density dependences of the symmetry energy, a moderately soft to linear symmetry energy is extracted, in good agreement with previous UrQMD or Tübingen QMD model calculations but contrast with results obtained with π^-/π⁺ yield ratios in the literature.