Effects of incompressibility $K_0$ in heavy-ion collisions at intermediate energies

Within the possible least uncertainty on the nuclear incompressibility $K_0$, we examine effects of $K_0$ in heavy-ion collisions at intermediate energies. Based on simulations of Au + Au collision at 400 MeV/nucleon using an isospin- and momentum-dependent transport model, we find that the incompressibility $K_0$ indeed affects significantly the attainable density in central regions, and thus the particle productions and/or distributions at final states, e.g., nucleon rapidity distributions and yields of charged pions. Nevertheless, through examining the free neutron over proton ratios $n\mathrm{/}p$, the neutron-proton differential transverse and directed flows as well as the charged pion ratio ${\pi }^{-}\mathrm{/}{\pi }^{+}$ and its kinetic energy distribution, we find that these observables are less affected by the uncertainty of $K_0$, but mainly sensitive to the slope of symmetry energy at the saturation density. We also compare and discuss our results with the corresponding data.