Ideal hydrodynamics and elliptic flow at CERN Super Proton Synchrotron (SPS) energies: Importance of the initial conditions

Abstract

The elliptic flow excitation function calculated in a full ($3+1$) dimensional hybrid Boltzmann approach with an intermediate hydrodynamic stage for heavy ion reactions from GSI Schwerionen Synchrotron to the highest CERN Super Proton Synchrotron (SPS) energies is discussed in the context of the experimental data. In this study, we employ a hadron gas equation of state to investigate the differences in the dynamics and viscosity effects. The specific event-by-event setup with initial conditions and freeze-out from a nonequilibrium transport model allows for a direct comparison between ideal fluid dynamics and transport simulations. 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 higher elliptic flow values. In contrast to previous studies within pure hydrodynamics, the more realistic initial conditions employed here and the inclusion of a sequential final state hadronic decoupling provides results that are in line with the experimental data almost over the whole energy range from ${E}_{\mathrm{lab}}=2\text{\ensuremath{-}}160A$ GeV. Thus, this new approach leads to a substantially different shape of the ${v}_{2}/\ensuremath{\epsilon}$ scaling curve as a function of $(1/S{\mathit{dN}}_{\mathrm{ch}}/\mathit{dy})$ in line with the experimental data compared to previous ideal hydrodynamic calculations. This hints at a strong influence of the initial conditions for the hydrodynamic evolution on the finally observed ${v}_{2}$ values, thus questioning the standard interpretation that the hydrodynamic limit is only reached at BNL Relativistic Heavy Ion Collider energies.