Measurement of the correlation between flow harmonics of different order in lead-lead collisions at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msqrt><mml:msub><mml:mi>s</mml:mi><mml:mi mathvariant="italic">NN</mml:mi></mml:msub></mml:msqrt><mml:mo>=</mml:mo><mml:mn>2.76</mml:mn></mml:mrow></mml:math> TeV with the ATLAS detector

Correlations between the elliptic or triangular flow coefficients ${v}_{m}$ ($m=2$ or 3) and other flow harmonics ${v}_{n}$ ($n=2$ to 5) are measured using $\sqrt{{s}_{{}_{NN}}}=2.76$ TeV $\mathrm{Pb}+\mathrm{Pb}$ collision data collected in 2010 by the ATLAS experiment at the LHC, corresponding to an integrated luminosity of $7 \ensuremath{\mu}{\mathrm{b}}^{\ensuremath{-}1}$. The ${v}_{m}\text{\ensuremath{-}}{v}_{n}$ correlations are measured in midrapidity as a function of centrality, and, for events within the same centrality interval, as a function of event ellipticity or triangularity defined in a forward rapidity region. For events within the same centrality interval, ${v}_{3}$ is found to be anticorrelated with ${v}_{2}$ and this anticorrelation is consistent with similar anticorrelations between the corresponding eccentricities, ${\ensuremath{\epsilon}}_{2}$ and ${\ensuremath{\epsilon}}_{3}$. However, it is observed that ${v}_{4}$ increases strongly with ${v}_{2}$, and ${v}_{5}$ increases strongly with both ${v}_{2}$ and ${v}_{3}$. The trend and strength of the ${v}_{m}\text{\ensuremath{-}}{v}_{n}$ correlations for $n=4$ and 5 are found to disagree with ${\ensuremath{\epsilon}}_{m}\text{\ensuremath{-}}{\ensuremath{\epsilon}}_{n}$ 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 a nonlinear term that is a function of ${v}_{2}^{2}$ or of ${v}_{2}{v}_{3}$, as predicted by hydrodynamic models. A simple two-component fit is used to separate these two contributions. The extracted linear and nonlinear contributions to ${v}_{4}$ and ${v}_{5}$ are found to be consistent with previously measured event-plane correlations.

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