Symmetry energy at high densities from neutron/proton flow excitation functions

Determination of the high density behavior of the symmetry energy through the simultaneous measurement of elliptic flow excitation functions of neutrons, protons and light clusters is proposed. The elliptic flow developed in relativistic heavy ion collisions has been proven theoretically and experimentally to have a unique sensitivity and robustness in probing the symmetry energy up to around $2 \rho_{o}$. The knowledge of the density dependence of the symmetry energy in a broad range of densities will provide a missing link for astrophysical predictions of the neutron star mass--radius relation. In particular, the data colud provide tighter constraints on the slope parameter L and entirely new limits on $K_{sym}$, the currently poorly constrained symmetry energy curvature parameter.