Longitudinal flow and onset of deconfinement

Abstract

The effects of the onset of deconfinement on longitudinal and transverse flow are studied. First, we analyze longitudinal pion spectra from $E_{\rm lab}= 2A$ GeV to $\sqrt{s_{\rm NN}}=200$ GeV within Landau's hydrodynamical model and the UrQMD transport approach. From the measured data on the widths of the pion rapidity spectra, we extract the sound velocity $c_s^2$ in the early stage of the reactions. It is found that the sound velocity has a local minimum (indicating a softest point in the equation of state, EoS) at $E_{\rm beam}=30A$ GeV. This softening of the EoS is compatible with the assumption of the formation of a mixed phase at the onset of deconfinement. Furthermore, the energy excitation function of elliptic flow ($v_2$) from $E_{\rm beam}=90A$ MeV to $\sqrt{s_{\rm NN}}=200$ GeV is explored within the UrQMD framework and discussed in the context of the available data. The transverse flow should also be sensitive to changes in the equation of state. Therefore, the underestimation of elliptic flow by the UrQMD model calculation above $E_{\rm lab}= 30A$ GeV might also be explained by assuming a phase transition from a hadron gas to the quark gluon plasma around this energy. This would be consistent with the model calculations, indicating a transition from hadronic matter to ``string matter'' in this energy range.