Measurement of the correlation between elliptic flow and higher-order flow harmonics in Pb+Pb collisions at $\sqrt{s_{_{\mathrm{NN}}}}$=2.76 TeV

Correlations between the elliptic flow coefficient, $v_2$, and higher-order flow harmonics, $v_3$, $v_4$ and $v_5$ are measured using 7 $\mu$b$^{-1}$ of Pb+Pb collision data at $\sqrt{s_{_{\mathrm{NN}}}}=2.76$ TeV collected by the ATLAS experiment at the LHC. The $v_2$-$v_n$ correlations are measured as a function of centrality, and, for events within the same centrality interval, also as a function of event ellipticity. The results are compared to initial-state eccentricities calculated from initial geometry models. The $v_2$-$v_n$ correlations within a given centrality interval are very different from the $v_2$-$v_n$ correlations as a function of centrality. For events within the same centrality interval, $v_3$ is found to be anti-correlated with $v_2$ and this anti-correlation is compatible with similar anti-correlations between the corresponding eccentricities $\epsilon_2$ and $\epsilon_3$. On the other hand, the $v_4$ and $v_5$ are found to increase strongly with $v_2$. The trend and strength of the $v_2$-$v_n$ correlations for $n=4$ and 5 are found to disagree with $\epsilon_2$-$\epsilon_n$ correlations predicted by initial geometry models. Instead, these correlations are found to be consistent with the combined effects of a linear contribution to $v_n$ and non-linear term that is a function of $v_2^2$ or of $v_2v_3$, as predicted by hydrodynamic models. A simple two-component fit is used to separate these two contributions. The magnitudes of the linear and non-linear contributions to the $v_2$-$v_4$ and $v_2$-$v_5$ correlations are found to be consistent with previously measured event-plane correlations.