The second act of hydro: small perturbations

Abstract

Hydrodynamical description of the ‘Little Bang’ in heavy ion collisions is surprisingly successful: here we systematically study propagation of small perturbations 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 m = 7 and maximum at m = 9, which remarkably have some evidence for both in the data. We estimate effective viscosity and the size of the perturbation from the fit to power spectrum. The shape of the two-point correlator is also reproduced remarkably well. At the end, we argue that independent perturbations are local, and thus harmonics phases are correlated.