Anisotropies in momentum space at finite shear viscosity in ultrarelativistic heavy-ion collisions

Within a parton cascade we investigate the dependence of anisotropies in momentum space, namely the elliptic flow v 2 = 〈 cos ( 2 ϕ ) 〉 and the v 4 = 〈 cos ( 4 ϕ ) 〉 , on both the finite shear viscosity η and the freeze-out (f.o.) dynamics at the RHIC energy of 200 GeV. In particular the impact of the f.o. dynamics is discussed looking at two different procedures: switching-off the collisions when the energy density goes below a fixed value or reducing the cross section according to the increase in η / s from a QGP phase to a hadronic one. We address the relation between the scaling of v 2 ( p T ) with the eccentricity ϵ x and with the integrated elliptic flow. We show that the breaking of the v 2 ( p T ) / ϵ x scaling is not coming mainly from the finite η / s but from the f.o. dynamics and that the v 2 ( p T ) is weakly dependent on the f.o. scheme. On the other hand the v 4 ( p T ) is found to be much more sensitive to both the η / s and the f.o. dynamics and hence is indicated to put better constraints on the properties of the QGP. A first semi-quantitative analysis shows that both v 2 and v 4 (with the smooth f.o.) consistently indicate a plasma with 4 π η / s ∼ 1 − 2 .