Mapping the hydrodynamic response to the initial geometry in heavy-ion collisions

TL;DR

This study uses event-by-event ideal hydrodynamics to analyze how initial geometric fluctuations influence final flow observables in heavy-ion collisions, identifying optimal eccentricity definitions and nonlinear effects for better predictive accuracy.

Contribution

It demonstrates the importance of specific eccentricity definitions and nonlinear terms in accurately predicting anisotropic flow from initial geometry in heavy-ion collisions.

Findings

r^n weighting improves flow prediction for n > 2

Nonlinear terms are essential for v_4 and v_5 predictions

Initial eccentricity calculations are robust across different methods

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 (v_n) is determined by the initial eccentricity epsilon_n for a set of realistic simulations, and we discuss which definition of epsilon_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 (epsilon_2)^2 and (epsilon_2)*(epsilon_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.