Estimation of the Shear Viscosity from 3FD Simulations of Au+Au Collisions at $\sqrt{s_{NN}}=$ 3.3--39 GeV

TL;DR

This study estimates the effective shear viscosity in central Au+Au collisions across a range of energies using 3FD simulations, revealing its dependence on temperature and density, and providing insights into the medium's fluidity.

Contribution

It introduces a method to estimate effective shear viscosity from 3FD simulations by relating entropy production to viscous hydrodynamics, considering different equations of state.

Findings

Effective viscosity-to-entropy ratio $\rac{\eta}{s}$ scales as $1/T^4$ with temperature.

$\rac{\eta}{s}$ is mainly determined by entropy density dependence on net-baryon density.

Range of $\rac{\eta}{s}$ values from 0.05 to 0.5 across collision energies.

Abstract

An effective shear viscosity in central Au+Au collisions is estimated in the range of incident energies 3.3 GeV $\le \sqrt{s_{NN}}\le$ 39 GeV. The simulations are performed within a three-fluid model employing three different equations of state with and without the deconfinement transition. In order to estimate this effective viscosity, we consider the entropy produced in the 3FD simulations as if it is generated within the conventional one-fluid viscous hydrodynamics. It is found that the effective viscosity within different considered scenarios is very similar at the expansion stage of the collision: as a function of temperature ($T$) the viscosity-to-entropy ratio behaves as $\eta/s \sim 1/T^4$; as a function of net-baryon density ($n_B$), $\eta/s \sim 1/s$, i.e. it is mainly determined by the density dependence of the entropy density. The above dependencies take place along the dynamical trajectories of Au+Au collisions. At the final stages of the expansion the $\eta/s$ values are ranged from $\sim$0.05 at highest considered energies to $\sim$0.5 at the lowest ones.