  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.
