Plane correlations and hydrodynamic simulations of heavy ion collisions

Abstract: We use a nonlinear response formalism to describe the event plane correlations measured by the ATLAS collaboration. With one exception ($\left\langle \cos(2\Psi_2 - 6\Psi_3 + 4 \Psi_4) \right\rangle$), the event plane correlations are qualitatively reproduced by considering the linear and quadratic response to the lowest cumulants. For the lowest harmonics such as $\left\langle \cos(2\Psi_2+3\Psi_3 - 5\Psi_5) \right\rangle$, the correlations are quantitatively reproduced, even when the naive Glauber model prediction has the wrong sign relative to experiment. The quantitative agreement for the higher plane correlations (especially those involving $\Psi_6$) is not as good. The centrality dependence of the correlations is naturally explained as an average of the linear and quadratic response.