  Previous measurements of a quadrupole component of azimuth correlations
denoted by symbol $v_2$ have been interpreted to represent elliptic flow, a
hydrodynamic phenomenon conjectured to play a major role in noncentral
nucleus-nucleus collisions. $v_2$ measurements provide the main support for
conclusions that a ``perfect liquid'' is formed in heavy ion collisions at the
Relativistic Heavy Ion Collider (RHIC). However, conventional $v_2$ methods
based on one-dimensional (1D) azimuth correlations give inconsistent results
and may include a jet contribution. In some cases the data trends appear to be
inconsistent with hydrodynamic interpretations. In this study we distinguish
several components of 2D angular correlations and isolate a nonjet (NJ) azimuth
quadrupole denoted by $v_2\{\text{2D}\}$. We establish systematic variations of
the NJ quadrupole on $y_t$, centrality and collision energy. We adopt
transverse rapidity $y_t$ as both a velocity measure and as a logarithmic
alternative to transverse momentum $p_t$. Based on NJ quadrupole trends we
derive a completely factorized universal parametrization of quantity
$v_2\{\text{2D}\}(y_t,b,\sqrt{s_{NN}})$ which describes the centrality, $y_t$
and energy dependence. From $y_t$-differential $v_2(y_t)$ data we isolate a
quadrupole spectrum and infer a quadrupole source boost having unexpected
properties. NJ quadrupole $v_2$ trends obtained with 2D model fits are
remarkably simple. The centrality trend appear to be uncorrelated with a sharp
transition in jet-related structure that may indicate rapid change of Au-Au
medium properties. The lack of correspondence suggests that the NJ quadrupole
may be insensitive to such a medium. Several quadrupole trends have interesting
implications for hydro interpretations.
