Elliptic Flow and Dissipation in Heavy-Ion Collisions at E_{lab} = (1--160)A GeV

Abstract

Elliptic flow in heavy-ion collisions at incident energies $E_{lab}\simeq$ (1--160)A GeV is analyzed within the model of 3-fluid dynamics (3FD). We show that a simple correction factor, taking into account dissipative affects, allows us to adjust the 3FD results to experimental data. This single-parameter fit results in a good reproduction of the elliptic flow as a function of the incident energy, centrality of the collision and rapidity. The experimental scaling of pion eccentricity-scaled elliptic flow versus charged-hadron-multiplicity density per unit transverse area turns out to be also reasonably described. Proceeding from values of the Knudsen number, deduced from this fit, we estimate the upper limit the shear viscosity-to-entropy ratio as $η/s \sim 1-2$ at the SPS incident energies. This value is of the order of minimal $η/s$ observed in water and liquid nitrogen.