Hydrodynamization in systems with detailed transverse profiles

TL;DR

This paper introduces numerical methods to solve the ultra-relativistic Boltzmann equation for systems with complex transverse profiles, analyzing how azimuthal flow coefficients evolve from free streaming to fluid behavior.

Contribution

It presents a novel numerical approach to study azimuthal flow coefficients with realistic fluctuations, revealing differences in response coefficients away from the fluid-dynamic limit.

Findings

Response coefficients vary non-uniformly with opacity.

Hierarchy of linear and non-linear responses shows characteristic differences.

Signal strength does not diminish uniformly away from fluid limit.

Abstract

The observation of fluid-like behavior in nucleus-nucleus, proton-nucleus and high-multiplicity proton-proton collisions motivates systematic studies of how different measurements approach their fluid-dynamic limit. We have developed numerical methods to solve the ultra-relativistic Boltzmann equation for systems of arbitrary size and transverse geometry. Here, we apply these techniques for the first time to the study of azimuthal flow coefficients $v_n$ including non-linear mode-mode coupling and to an initial condition with realistic event-by-event fluctuations. We show how both linear and non-linear response coefficients extracted from $v_n$ develop as a function of opacity from free streaming to perfect fluidity. We note in particular that away from the fluid-dynamic limit, the signal strength of linear and non-linear response coefficients does not reduce uniformly, but that their hierarchy and relative size shows characteristic differences.