Centrality dependence of mapping the hydrodynamic response to the initial geometry in heavy-ion collisions

Event-by-event correlations between vₙ and εm,n for different collision centralities are studied with hydrodynamics. For the more central collisions vₙ is better correlated with εm,n defined with relatively larger radial weight power m, like $m=n+1$. For the more peripheral collisions, vₙ prefers εm,n with relatively smaller m, like m=n-1. When the fluid viscosity is large, vₙ is better correlated with εm,n with large m. For the most central collisions and for odd harmonics, since anisotropy is solely due to fluctuations, the scaled probability distributions of εm,n are universal. For noncentral collisions, the scaled probability distributions of εm,2 with different radial weight power m deviate from one another. εm,2 defined with smaller m has a wider scaled distribution and a larger scaled standard deviation, and is more consistent with the scaled v₂ distribution after hydrodynamic evolution in peripheral collisions. Hadronic rescattering widens the v₂ distribution in noncentral collisions, which contributes to the observed inconsistency between p(v₂) and p(ε₂) distributions.