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

We have measured the $p_t$-integrated quadrupole component of two-particle azimuth 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 2D autocorrelation provides a method to remove non-quadrupole contributions to $v_2$ (conventionally termed ``nonflow'') under the assumption that such processes produce significant dependence on pair-wise relative $\eta$ within the detector acceptance. We hypothesize, based on empirical observations, that non-quadrupole contributions are dominated by minijets or minimum-bias jets. Using the optical Glauber eccentricity model for initial-state geometry we find simple and accurate universal energy and centrality trends for the quadrupole component. Centrality trends are determined only by the initial state (impact parameter $b$ and center-of-mass energy $\sqrt{s_{NN}}$). There is no apparent dependence on evolving system dynamics (e.g., equation of state or number of secondary collisions). Our measurements of the quadrupole and non-quadrupole components have implications for the contributions to $v_2$. They suggest that the main source of the difference between $v_2 \{2\}$ and $v_2 \{4\}$ (or $v_2 \{2D\}$) is measured properties of minijets.