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 the 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 the 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 dependences 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 the highest considered energies to \( \sim 0.5\) at the lowest ones.
Highlights
Observables that are the most sensitive to the dissipation at the expansion stage of the reaction are the elliptic flow and other anisotropic flow coefficients
TSchaena(nBaElySs)isroafntghee√SsTNANR=da7t.a7–in20t0hGe ReVHI[2C],BreeacemntElynepregryformed within a hybrid model [3], indicated that the η/s ratio remains approximately in the same range even at lower BES-Relativistic Heavy Ion Collider (RHIC) energies
This is definitely in contrast to common expectations that at the BES-RHIC energies the viscosity of the matter should rapidly rise because the system spends most of its time in the hadronic phase [4]
Summary
Observables that are the most sensitive to the dissipation at the expansion stage of the reaction are the elliptic flow and other anisotropic flow coefficients. In order to estimate this dissipation in terms of an effective viscosity, we consider the entropy produced in the 3FD simulations as if it is generated within the conventional one-fluid viscous hydrodynamics.
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