Linear and cubic response to the initial eccentricity in heavy-ion collisions

We study the relation between elliptic flow, v₂, and the initial eccentricity, ε₂, in heavy-ion collisions, using hydrodynamic simulations. Significant deviations from linear eccentricity scaling are seen in more peripheral collisions. We identify the mechanism responsible for these deviations as a cubic response, which we argue is a generic property of the hydrodynamic response to the initial density profile. The cubic response increases elliptic flow fluctuations, thereby improving agreement of initial condition models with experimental data.