Fernando Gardim (USP)
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 ($v_n$) is determined by the initial eccentricity $\varepsilon_n$ for a set of realistic simulations, and we discuss which definition of $\varepsilon_n$ gives the best estimator of $v_n$. We find that the common practice of using an $r^2$ weight in the definition of $\varepsilon_n$ in general results in a poorer predictor of $v_n$ than when using $r^n$ 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 $v_4$ and $v_5$ for non-central collisions, one must take into account nonlinear terms proportional to $\varepsilon_2^2$ and $\varepsilon_2\varepsilon_3$, 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.