A transport calculation with an embedded (3+1)d hydrodynamic evolution: Elliptic flow as a function of transverse momentum at SPS energies

The transverse momentum dependence of elliptic flow of pions calculated in a full (3+1)d Boltzmann approach with an intermediate hydrodynamic stage for heavy ion reactions for CERN-SPS energies is discussed in the context of the experimental data. At higher SPS energies, where the pure transport calculation cannot account for the high elliptic flow values, the smaller mean free path in the hydrodynamic evolution leads to larger elliptic flow. Due to the more realistic initial conditions and the incorporated hadronic rescattering the results are in line with the experimental data. Within this integrated dynamical approach different equations of state are applied without adjusting the initial state and the freeze-out conditions. We employ a hadron gas equation of state to investigate the differences in the dynamics and viscosity effects, a chiral equation of state with a moderate first order phase transition and a critical endpoint and a bag model equation of state with a large latent heat. The elliptic flow results are shown to be rather insensitive to changes in the equation of state.