Event-by-event hydrodynamics and elliptic flow from fluctuating initial states

We develop a framework for event-by-event ideal hydrodynamics to study the differential elliptic flow, which is measured at different centralities in Au $+$ Au collisions at the Relativistic Heavy Ion Collider (RHIC). Fluctuating initial energy density profiles, which here are the event-by-event analogs of the wounded nucleon profiles, are created using a Monte Carlo Glauber model. Using the same event plane method for obtaining v₂ as in the data analysis, we can reproduce both the measured centrality dependence and the pT shape of charged-particle elliptic flow up to pT~2 GeV. We also consider the relation of elliptic flow to the initial-state eccentricity using different reference planes and discuss the correlation between the physical event plane and the initial participant plane. Our results demonstrate that event-by-event hydrodynamics with initial-state fluctuations must be accounted for before a meaningful lower limit for viscosity can be obtained from elliptic flow data.