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We analyze the spectrum of harmonic flow, $v_n(p_T)$ for $n=0\text{--}5$, inevent-by-event hydrodynamic simulations of Pb+Pb collisions at the CERN LargeHadron Collider ($\sqrt{s_{NN}}=2.76\,{\text{TeV}}$) with principal componentanalysis (PCA). The PCA procedure finds two dominant contributions to thetwo-particle correlation function. The leading component is identified with theevent plane $v_n(p_T)$, while the subleading component is responsible forfactorization breaking in hydrodynamics. For $v_0$, $v_1$, and $v_3$ thesubleading flow is a response to the radial excitation of the correspondingeccentricity. By contrast, for $v_2$ the subleading flow in \emph{peripheralcollisions} is dominated by the nonlinear mixing between the leading ellipticflow and radial flow fluctuations. In the $v_2$ case, the sub-sub-leading modemore closely reflects the response to the radial excitation of $\varepsilon_2$.A consequence of this picture is that the elliptic flow fluctuations andfactorization breaking change rapidly with centrality, and in centralcollisions (where the leading $v_2$ is small and nonlinear effects can beneglected) the subsub-leading mode becomes important. Radial flow fluctuationsand nonlinear mixing also play a significant role in the factorization breakingof $v_4$ and $v_5$. We construct good geometric predictors for the orientationand magnitudes of the leading and subleading flows based on a linear responseto the geometry, and a quadratic mixing between the leading principalcomponents. Finally, we suggest a set of measurements involving three pointcorrelations which can experimentally corroborate the nonlinear mixing ofradial and elliptic flow and its important contribution to factorizationbreaking as a function of centrality.

Fluctuations of harmonic and radial flow in heavy ion collisions with principal components