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

TL;DR

This paper investigates how elliptic flow in heavy-ion collisions relates to initial eccentricity, revealing a cubic response mechanism that enhances model-data agreement and varies with collision centrality.

Contribution

It introduces the concept of cubic response as a key factor in the hydrodynamic response, extending the linear eccentricity scaling model.

Findings

Deviations from linear scaling are prominent in peripheral collisions.

Cubic response accounts for these deviations.

Inclusion of cubic response improves agreement with experimental data.

Abstract

We study the relation between elliptic flow, $v_2$ and the initial eccentricity, $\varepsilon_2$, 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.