Mapping the hydrodynamic response to the initial geometry in heavy-ion collisions
Abstract
We investigate how the initial geometry of a heavy-ion collision is transformed into final flow observables by solving event-by-event ideal hydrodynamics with realistic fluctuating initial conditions. We study quantitatively to what extent anisotropic flow (vn) is determined by the initial eccentricity epsilonn for a set of realistic simulations, and we discuss which definition of epsilonn gives the best estimator of vn. We find that the common practice of using an r2 weight in the definition of varepsilonn in general results in a poorer predictor of vn than when using rn weight, for n > 2. We similarly study the importance of additional properties of the initial state. For example, we show that in order to correctly predict v4 and v5 for non-central collisions, one must take into account nonlinear terms proportional to (epsilon2)2 and (epsilon2)*(epsilon3), respectively. We find that it makes no difference whether one calculates the eccentricities over a range of rapidity, or in a single slice at z=0, nor is it important whether one uses an energy or entropy density weight. This knowledge will be important for making a more direct link between experimental observables and hydrodynamic initial conditions, the latter being poorly constrained at present.