The second act of hydro: small perturbations

TL;DR

This paper develops an analytical hydrodynamic model for small perturbations in heavy ion collision fireballs, revealing acoustic features and estimating viscosity, with results aligning well with experimental data.

Contribution

It provides a semi-analytical solution for propagating small perturbations in the Gubser flow, including viscous effects, and connects harmonic analysis to experimental observations.

Findings

Identified acoustic minima at harmonic number m=7 and maxima at m=9.

Estimated effective viscosity and perturbation size from power spectrum fits.

Reproduced the shape of the two-point correlator accurately.

Abstract

Hydrodynamical description of the "Little Bang" in heavy ion collisions is surprisingly successful: here we systematically study propagation of small perturbations %, also treated hydrodynamically. Using analytic description of the expanding fireball known as the "Gubser flow", we proceed to linearized equations for perturbations. As all variables are separated and all equations solved (semi)analytically, we can collect all the harmonics and reconstruct the complete Green function of the problem, even in the viscous case. Applying it to the power spectrum we found acoustic minimum at the $m=7$ and maximum at $m=9$, which remarkably have some evidence for both in the data. We estimate effective viscosity and size of the perturbation from a fit to power spectrum. The shape of the two-point correlator is also reproduced remarcably well. At the end we argue that independent perturbations are local, and thus harmonics phases are correlated.