Directed, elliptic and triangular flow of protons in Au+Au reactions at 1.23 AGeV: A theoretical analysis of the recent HADES data

Recently, the HADES experiment at GSI has provided preliminary data on the directed flow, $v_1$ elliptic flow, $v_2$ and triangular flow, $v_3$ of protons in Au+Au reactions at a beam energy of 1.23 A GeV. Here we present a theoretical discussion of these flow harmonics within the UrQMD transport approach. We show that all flow harmonics, including the triangular flow, provide a consistent picture of the expansion of the system, if potential interactions are taken into account. Investigating the dependence of the flow harmonics on the nuclear interaction potentials it is shown that especially $v_3$ can serve as a sensitive probe for the nuclear equation of state at such low energies. The triangular flow and its excitation function with respect to the reaction-plane were calculated for the first time and indicate a complex interplay of the time-evolution of the system and the initial conditions at low beam-energies. Our study also indicates a significant softening of the equation of state at beam energies above $E_{\mathrm{lab}}> 7$A GeV which can be explored by at the future FAIR facility.