17 Chapter 2: Motivation (a) (b) Figure 2.2: (a) v$_{2}$ scaled to the initial spacial eccentricity, ϵ , as a function of the charge particle density per unit transverse area. low- p$_{T}$ flow at previous colliders fell far short of the hydrodnamic limit, which is reached for the first time at $_{Rhic}$. Figure adapted from [107]. (b) Early azimuthal asymmetry, v$_{2}$ ( p$_{T}$ ) , predictions from [106] compared to Rhic data [108] as adapted from [77]. ditions statements drawn from hydrodynamical modeling will be inconclusive at best. There are two additional major complications in interpreting hydrodynam- ics results. The first comes from evolution beyond a thermalized medium into a viscous gas of hadronic particles. As the system expands with time it neces- sarily becomes too dilute for equilibrium to be maintained and hydrodynamics can no longer be a valid description. Often taken to occur at the same time is the breakup of the quark gluon plasma into ordinary hadronic matter. But the transition from quark and gluon degrees of freedom to baryons and mesons is not well understood. Unlike high- p$_{T}$ fragmentation—discussed later—this