Eccentricities, fluctuations and A-dependence of elliptic and triangular flows in heavy-ion collisions

Abstract

A simple geometrical model with event-by-event fluctuations is suggested to study elliptical and triangular eccentricities in the initial state of relativistic heavy-ion collisions. This model describes rather well the ALICE and ATLAS data for Pb + Pb collisions at center-of-mass energy TeV per nucleon pair, assuming that the second, v 2, and third, v 3, harmonics of the anisotropic flow are simply linearly proportional to the eccentricities ɛ 2 and ɛ 3, respectively. We show that the eccentricity ɛ 3 has a pure fluctuation origin and is substantially dependent on the size of the overlap area only, while the eccentricity ɛ 2 is mainly related to the average collision geometry. Elliptic flow, therefore, is weakly dependent on the event-by-event fluctuations everywhere except of the very central collisions 0%–2%, whereas triangular flow is mostly determined by the fluctuations. The scaling dependence of the magnitude of the flow harmonics on atomic number, v n ∝ A −1/3, is predicted for this centrality interval.