Ideal hydrodynamics and elliptic flow at SPS energies: Importance of the initial conditions

TL;DR

This paper demonstrates that realistic initial conditions and a hybrid approach combining hydrodynamics with transport models are crucial for accurately reproducing elliptic flow data across a wide energy range in heavy ion collisions, challenging previous assumptions about hydrodynamic limits.

Contribution

The study introduces a full (3+1)d hybrid Boltzmann approach with realistic initial conditions, showing improved agreement with experimental elliptic flow data at SPS energies.

Findings

Hydrodynamic evolution with realistic initial conditions matches experimental data.

Viscosity effects and initial conditions significantly influence elliptic flow.

The $v_2/\epsilon$ scaling curve shape differs from previous ideal hydrodynamics results.

Abstract

The elliptic flow excitation function calculated in a full (3+1)d hybrid Boltzmann approach with an intermediate hydrodynamic stage for heavy ion reactions from GSI-SIS to the highest CERN-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 non-equilibrium 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_{\rm lab}=2-160A $GeV. Thus, this new approach leads to a substantially different shape of the $v_2/\epsilon$ scaling curve as a function of $(1/S dN_{ch}/dy)$ in line with the experimental data compared to previous ideal hydrodynamic calculations. This hints to 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 RHIC energies.