Is $v_3$ necessary or even informative in describing angular correlation data from RHIC and the LHC?*

One of the more interesting observations from the heavy-ion program at RHIC and now at the LHC are long-range correlations on relative pseudorapidity at small azimuth opening angles. In 2010 Alver and Roland [1] suggested that this so-called same-side ridge could be explained in terms of higher-order, azimuth cosine distributions generated by event-wise energy density fluctuations in the initial-state plus hydrodynamic flow. Applications of third- and higher-order harmonics in analysis of angular correlations from heavy-ion collisions have become ubiquitous in the literature. However, we question the introduction of ``higher harmonics'' to the 2D data description. Extending previous work we examine the necessity and utility of $v_3$. We find that the net effect of $v_3$ is to accommodate minor non-Gaussian structure in the same-side 2D peak for $p_t$-integral correlations from RHIC. A single Gaussian hypothesis for those data is not falsified within statistics. Model ambiguities and instabilities resulting from $v_3$ are discussed and resolved. Lastly, we demonstrate that the 0-1\% angular correlation data for 2.76 TeV Pb-Pb collisions from ATLAS [2] do not require a $v_3$ component.\\[4pt] [1] Phys. Rev. C81, 054905 (2010).\\[0pt] [2] ATLAS, Phys. Rev. C86, 014907 (2012).