Deviations of the Energy-Momentum Tensor from Equilibrium in the Initial State for Hydrodynamics from Transport Approaches

TL;DR

This study investigates how the energy-momentum tensor deviates from equilibrium in heavy ion collisions across various energies and conditions, revealing the importance of pressure anisotropy and the concept of isotropization time for hydrodynamic initialization.

Contribution

It provides a detailed analysis of $T^{}$ deviations from equilibrium in transport-based initial states, introducing the isotropization time and its dependence on collision energy and centrality.

Findings

Pressure anisotropy dominates deviations at high statistics.

Isotropization time decreases with increasing collision energy.

Off-diagonal components of $T^{}$ are generally small.

Abstract

Many hybrid models of heavy ion collisions construct the initial state for hydrodynamics from transport models. Hydrodynamics requires that the energy-momentum tensor $T^{\mu\nu}$ and four-currents $j^{\mu}$ do not deviate considerably from the equilibrium ideal-fluid form, but the ones constructed from transport do not necessarily possess this property. In this work we investigate the space-time picture of $T^{\mu\nu}$ deviations from equilibrium in Au+Au collisions using a coarse-grained transport approach. The collision energy is varied in the range $E_{lab} = 5-160A$ GeV. The sensitivity of $T^{\mu\nu}$ deviations from equilibrium to collision centrality, and other parameters such as the switching criterion, the amount of statistics used to construct the initial state, and the smearing parameter $\sigma$ is investigated. For low statistics deviations of $T^{\mu\nu}$ from equilibrium are large and dominated by the effect of finite sampling. For large statistics the pressure anisotropy plays the most significant role, while the off-diagonal components of $T^{\mu\nu}$ are small in a large volume during the whole evolution. For all considered energies and centralities the pressure anisotropy exhibits a similar feature: there is a narrow interval of time, when it rapidly drops in a considerable volume. This allows us to introduce an "isotropization time," which is found to decrease with energy and slightly increase with centrality. The isotropization times are larger than times typically used for initializing hydrodynamics.