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 noncentral 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.

• Received 29 November 2011

DOI:https://doi.org/10.1103/PhysRevC.85.024908