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

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 $\sqrts_{nn} = 5.02$~TeV per nucleon pair, if the second, $v_2$, and third, $v_3$, harmonics of the anisotropic flow are simply implied to be linearly proportional to the eccentricities $\varepsilon_2$ and $\varepsilon_3$ as a reasonable approximation. We show that the eccentricity $\varepsilon_3$ has a pure fluctuation origin and is substantially dependent on the size of the overlap area only, while the eccentricity $\varepsilon_2$ is mainly related to the 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, $v_n \propto A^{-1/3}$, is predicted for this centrality interval.