Decomposition of fluctuating initial conditions and flow harmonics

TL;DR

This paper investigates how initial geometric fluctuations in heavy ion collisions influence flow harmonics, revealing non-linear effects and breakdown of linearity in non-Gaussian initial conditions through hydrodynamic simulations.

Contribution

It systematically studies the connection between cumulants and flow harmonics, highlighting non-linear effects in non-Gaussian initial conditions using hydrodynamic modeling.

Findings

Linearity between eccentricities and flow harmonics partially breaks down for non-Gaussian initial conditions.

Coupling between different order cumulants produces higher order flow harmonics.

Non-linear hydrodynamics explains the generation of complex flow patterns.

Abstract

Collective flow observed in heavy ion collisions is largely attributed to initial geometrical fluctuations, and it is the hydrodynamic evolution of the system that transforms those initial spatial irregularities into final state momentum anisotropies. Cumulant analysis provides a mathematical tool to decompose those initial fluctuations in terms of radial and azimuthal components. It is usually thought that a specified order of azimuthal cumulant, for the most part, linearly produces flow harmonic of the same order. In this work, we carry out a systematic study on the connection between cumulants and flow harmonics using a hydrodynamic code called NeXSPheRIO. We conduct three types of calculations, by explicitly decomposing the initial conditions into components corresponding to a given eccentricity and studying the out-coming flow through hydrodynamic evolution. It is found that for initial conditions deviating significantly from Gaussian, such as those from NeXuS, the linearity between eccentricities and flow harmonics partially breaks down. Combining with the effect of coupling between cumulants of different orders, it causes the production of extra flow harmonics of higher orders. We argue that these results can be seen as a natural consequence of the non-linear nature of hydrodynamics, and they can be understood intuitively in terms of the peripheral-tube model.