Decomposition of sensitivity of the symmetry energy observables

To exactly answer which density region that some frequently used symmetry-energy-sensitive observables probe, for the first time, we make a study of decomposition of the sensitivity of some symmetry-energy-sensitive observables. It is found that for the Au+Au reaction at incident beam energies of 200 and 400 MeV/nucleon, frequently used symmetry-energy-sensitive observables mainly probe the density-dependent symmetry energy around 1.25$\rho_{0}$ (for pionic observables) or 1.5$\rho_{0}$ (for nucleonic observables). Effects of the symmetry energy in the low-density region is in general small but observable. The fact that the symmetry-energy-sensitive observables are not sensitive to the symmetry energy in the maximal baryon-density region increases the difficulty of studying nuclear symmetry energy at super-density.