Impact parameter dependence of anisotropic flow: Bayesian reconstruction in ultracentral nucleus-nucleus collisions

Peculiar phenomena have been observed in analyses of anisotropic flow (vn) fluctuations in ultracentral nucleus-nucleus collisions: The fourth-order cumulant of the elliptic flow (v2) distribution changes sign. In addition, the ATLAS Collaboration has shown that cumulants of vn fluctuations of all orders depend significantly on the centrality estimator. We show that these peculiarities are due to the fact that the impact parameter b always spans a finite range for a fixed value of the centrality estimator. We provide a quantitative determination of this range through a simple Bayesian analysis. We obtain excellent fits of STAR and ATLAS data, with a few parameters, by assuming that the probability distribution of vn solely depends on b at a given centrality. This probability distribution is almost Gaussian, and its parameters depend smoothly on b, in a way that is constrained by symmetry and scaling laws. We reconstruct, thus, the impact parameter dependence of the mean elliptic flow in the reaction plane in a model-independent manner, and assess the robustness of the extraction using Monte Carlo simulations of the collisions where the impact parameter is known. We argue that the non-Gaussianity of vn fluctuations gives direct information on the hydrodynamic response to initial anisotropies, ATLAS data being consistent with a smaller response for n=4 than for n=2 and n=3, in agreement with hydrodynamic calculations.