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 %, 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.Comment: the paper is written version of the talk at Quark Matter 2011, and it will appear in this form in proceedings published in J. Phys. G: Nucl. Part. Phy