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We have measured the $p_t$-integrated quadrupole component of two-particleazimuth correlations (related to quantity $v_2$, denoted in this case by $v_2\{2D\}$) via two-dimensional (2D) angular autocorrelations on $(\eta, \phi)$for unidentified hadrons in Au-Au collisions at 62 and 200 GeV. The 2Dautocorrelation provides a method to remove non-quadrupole contributions to$v_2$ (conventionally termed ``nonflow'') under the assumption that suchprocesses produce significant dependence on pair-wise relative $\eta$ withinthe detector acceptance. We hypothesize, based on empirical observations, thatnon-quadrupole contributions are dominated by minijets or minimum-bias jets.Using the optical Glauber eccentricity model for initial-state geometry we findsimple and accurate universal energy and centrality trends for the quadrupolecomponent. Centrality trends are determined only by the initial state (impactparameter $b$ and center-of-mass energy $\sqrt{s_{NN}}$). There is no apparentdependence on evolving system dynamics (e.g., equation of state or number ofsecondary collisions). Our measurements of the quadrupole and non-quadrupolecomponents have implications for the contributions to $v_2$. They suggest thatthe main source of the difference between $v_2 \{2\}$ and $v_2 \{4\}$ (or $v_2\{2D\}$) is measured properties of minijets.

Universal Centrality and Collision Energy Trends for $v_2$ Measurements From 2D Angular Correlations