Collision energy dependence of viscous hydrodynamic flow in relativistic heavy-ion collisions

Using a (2 + 1)-dimensional viscous hydrodynamical model, we study the dependence of flow observables on the collision energy ranging from root s = 7.7A GeV at the Relativistic Heavy Ion Collider (RHIC) to root s = 2760A GeV at the Large Hadron Collider (LHC). With a realistic equation of state, Glauber model initial conditions, and a small specific shear viscosity eta/s = 0.08, the differential charged hadron elliptic flow v(2)(ch) (pT, root s) is found to exhibit a very broad maximum as a function of root s around top RHIC energy, rendering it almost independent of collision energy for 39 <= root s <= 2760A GeV. Compared to ideal fluid dynamical simulations, this "saturation" of elliptic flow is shifted to higher collision energies by shear viscous effects. For color-glass-motivated Monte Carlo-Kharzeev-Levin-Nardi initial conditions, which require a larger shear viscosity eta/s = 0.2 to reproduce the measured elliptic flow, a similar saturation is not observed up to LHC energies, except for very low p(T). We emphasize that this saturation of the elliptic flow is not associated with the QCD phase transition, but arises from the interplay between radial and elliptic flow, which shifts with root s depending on the fluid's viscosity and leads to a subtle cancellation between increasing contributions from light particles and decreasing contributions from heavy particles to v(2) in the root s range, where v(2)(ch) (p(T), root s) at fixed p(T) is maximal. By generalizing the definition of spatial eccentricity epsilon(x) to isothermal hypersurfaces, we calculate epsilon(x) on the kinetic freeze-out surface at different collision energies. Up to top RHIC energy, root s = 200A GeV, the fireball is still out-of-plane deformed at freeze-out, while at LHC energy the final spatial eccentricity is predicted to approach zero.