Mode-by-mode fluid dynamics for relativistic heavy ion collisions

TL;DR

This paper introduces a mode-by-mode fluid dynamic approach to analyze fluctuations in relativistic heavy ion collisions, highlighting how different wavelength modes influence harmonic flow and the role of dissipation and geometry in smoothing out short wavelength fluctuations.

Contribution

It develops a novel mode-by-mode fluid dynamic framework for heavy ion collisions, enabling detailed analysis of fluctuation propagation and their impact on flow observables.

Findings

Short wavelength fluctuations are suppressed by dissipation and geometric averaging.

Large wavelength fluctuations significantly contribute to harmonic flow coefficients.

The approach supports the coarse-grained interpretation of initial conditions in heavy ion collisions.

Abstract

We propose to study the fluid dynamic propagation of fluctuations in relativistic heavy ion collisions differentially with respect to their azimuthal, radial and longitudinal wavelength. To this end, we introduce a background-fluctuation splitting and a Bessel-Fourier decomposition of the fluctuating modes. We demonstrate how the fluid dynamic evolution of realistic events can be build up from the propagation of individual modes. We describe the main elements of this mode-by-mode fluid dynamics, and we discuss its use in the fluid dynamic analysis of heavy ion collisions. As a first illustration, we quantify to what extent only fluctuations of sufficiently large radial wave length contribute to harmonic flow coefficients. We find that fluctuations of short wave length are suppressed not only due to larger dissipative effects, but also due to a geometrical averaging over the freeze-out hyper surface. In this way, our study further substantiates the picture that harmonic flow coefficients give access to a coarse-grained version of the initial conditions for heavy ion collisions, only.