81 Chapter 3: v$_{2}$ vs. R$_{AA}$ as a Constraint on sQGP Dynamics expansion of the medium had a negligible effect on the total energy loss. Since the partonic production spectrum observed at Rhic can be approx- imated by a power law, we use the momentum Jacobian ( p f T = (1 − ϵ ) p i $_{T}$) as the survival probability of hard partons; see Appendix B. Following the fac- torization theorem and Glauber approach [366], we distribute partons in the overlap region according to ρ$_{coll}$ = T$_{AA}$ and isotropically in azimuth; hence where 4 ≲ n ≲ 5. The difference between n = 4 and n = 5 is less than 10%, and in this paper we will always use the former. We evaluate R$_{AA}$ ( φ ) at 24 values of φ from 0-2 π and then find the Fourier modes R$_{AA}$ and v$_{2}$ of this distribution. We label the results of this model in the plots as GREL for geometric radiative energy loss. A different method for finding v$_{2}$ , not used here, assumes the final parton distribution is given exactly by R$_{AA}$ and v$_{2}$ , and then determines v$_{2}$ from the ratio of R$_{AA}$ (0) and R$_{AA}$ ( π/ 2); this systematically enhances v$_{2}$ , especially at large centralities. Choosing 40 − 50% centrality as a good representative, we calculate the line in ( R$_{AA}$, p$_{T}$ ) space corresponding to 0 ≤ κ < ∞ , Fig. 3.1. One sees in the figure that the curve does not cross the error ellipse for the relevant Phenix π 0 data. This is despite the simplifying use of hard sphere geometry, where we took R$_{HS}$ = 6 . 78 fm to ensure that 〈 r 2 ⊥ $_{,WS}$〉 = 〈 r 2 ⊥ $_{,HS}$〉 , that amplifies the v$_{2}$ . Since the experimental errors are the most basic estimate—it would R$_{AA}$ ( φ ; b ) = ∫∫ d x d y T$_{AA}$ ( x, y ; b ) (1 − ϵ ( x, y, φ ; b )) n N$_{coll}$ ( b ) , (3.5)