Toward a model-independent constraint of the high-density dependence of the symmetry energy
Neutron-proton elliptic flow difference and ratio have been shown to be promising observables in the attempt to constrain the density dependence of the symmetry energy above the saturation point from heavy-ion collision data. Their dependence on model parameters such as microscopic nucleon-nucleon cross sections, compressibility of nuclear matter, optical potential, and symmetry energy parametrization is thoroughly studied. By using a parametrization of the symmetry energy derived from the momentum-dependent Gogny force in conjunction with the T\"ubingen quantum molecular dynamics (QMD) model and comparing the results with the experimental FOPI-LAND data for ${}^{197}$Au +${}^{197}$Au collisions at 400 MeV/nucleon, a moderately stiff (${L}_{\mathrm{sym}}=122\ifmmode\pm\else\textpm\fi{}57$ MeV and ${K}_{\mathrm{sym}}=229\ifmmode\pm\else\textpm\fi{}363$ MeV) symmetry energy is extracted, a result that agrees with that of a similar study that employed the UrQMD transport model and a power-law parametrization of the symmetry energy. This contrasts with diverging results extracted from the FOPI ${\ensuremath{\pi}}^{\ensuremath{-}}/{\ensuremath{\pi}}^{+}$ ratio available in the literature.