Non linearities in the harmonic spectrum of heavy ion collisions with ideal and viscous hydrodynamics

TL;DR

This paper investigates how non-linear hydrodynamic responses to initial geometric fluctuations influence flow harmonics in heavy ion collisions, highlighting the damping effects of viscosity and the significance of non-linear contributions.

Contribution

It introduces a set of non-linear response coefficients in hydrodynamics to quantify harmonic generation and analyzes viscosity's impact on these responses in heavy ion collisions.

Findings

Viscosity damps both linear and non-linear response coefficients.

Non-linear response dominates for higher harmonics like v4 and v5.

Non-linear effects are significant for v1, contributing about 25% in mid-central collisions.

Abstract

We determine the non-linear hydrodynamic response to geometrical fluctuations in heavy ion collisions using ideal and viscous hydrodynamics. This response is characterized with a set of non-linear response coefficients that determine, for example, the $v_5$ that is produced by an $\epsilon_2$ and an $\epsilon_3$. We analyze how viscosity damps both the linear and non-linear response coefficients, and provide an analytical estimate that qualitatively explains most of the trends observed in more complete simulations. Subsequently, we use these nonlinear response coefficients to determine the linear and non-linear contributions to $v_1$, $v_4$ and $v_5$. For viscous hydrodynamics the nonlinear contribution is dominant for $v_4$, $v_5$ and higher harmonics. For $v_1$, the nonlinear response constitutes an important $\sim 25%$ correction in mid-central collisions. The nonlinear response is also analyzed as a function of transverse momentum for $v_1$, $v_4$ and $v_5$. Finally, recent measurements of correlations between event-planes of different harmonic orders are discussed in the context of non-linear response.