Studying the energy dependence of elliptic and directed flow within a relativistic transport approach

The energy excitation functions of directed flow (v₁) and elliptic flow (v₂) from E_beam=90 A MeV to E_cm=200 A GeV are explored within the UrQMD framework and discussed in the context of the available data. The radial and the elliptic flow of the particles produced in a relativistic heavy-ion collision are intimately connected to the pressure and its gradients in the early stage of the reaction. Therefore, these observables should also be sensitive to changes in the equation of state. To prove this connection, the temporal evolution of the pressure, pressure gradients and elliptic flow are shown. For the flow excitation functions it is found that, in the energy regime below E_beam≤10 A GeV, the inclusion of nuclear potentials is necessary to describe the data. Above 40 A GeV beam energy, the UrQMD model starts to underestimate the elliptic flow. Around the same energy the slope of the rapidity spectra of the proton directed flow develops negative values. This effect is known as the third flow component (“antiflow”) and cannot be reproduced by the transport model. The difference between the data and the UrQMD model can possibly be explained by assuming a phase transition from hadron gas to quark–gluon plasma around E_lab=40 A GeV. This would be consistent with the model calculations, indicating a transition from hadronic matter to “string matter” in this energy range. Thus, we speculate that the missing pressure might be generated by strong interactions in the early pre-hadronic/partonic phase of central Au + Au (Pb + Pb) collisions already at lower SPS energies. PACS 25.75.-q; 25.75.Ld; 25.75.Dw; 25.75.Gz; 24.10.Lx