tokens: in two galaxies (A and C), while velocity dispersion (third row) is unusually low in C for an elliptical galaxy. We present the rotation parameter as a function of radial distance from the galaxy center (bottom) defined as Equation ( 1 ). Galaxies A and C have a fast rotator profile, whereas B shows a typical profile of a slow rotator. Figure 1. Three examples of model galaxies at z = 0. First row: projected stellar density within 4 R eff in log scale. Second row: mass-weighted radial velocity map of the stellar component with projected stellar density contour. Third row: mass-weighted radial velocity dispersion of the stellar component with projected stellar density contour. Last row: radial profile of rotation parameter. Most of the model galaxies in our clusters are early type in morphology, yet their kinematic properties vary significantly, as found in recent IFU spectroscopic observations. Figure 2 shows the model galaxies in comparison with the ATLAS observational data in the rotation parameter versus ellipticity plane. In a simplistic case of circular symmetry, 0.1 if and if , while (dashed curve) has been suggested as a demarcation line between slow and fast rotators. The observational data and models consistently suggest a positive correlation between ellipticity and spin, in the sense that rounder galaxies tend to rotate more slowly. They present a similar sequence in the diagram, but the ATLAS data span a larger area in the parameter space. Our models are rounder and more slowly rotating than the ATLAS sample. This may be partly due to the fact that our galaxies are exclusively in clusters where environmental effects are more dramatic. Of the 1726 model galaxies, 138 (8%) are classified as slow rotators, which is in rough agreement with the observations. The early SAURON data appeared to suggest a separated distribution between slow and fast rotators (Emsellem et al. 2007 ), but our data do not present such a dichotomy. Figure 2. Rotation parameter vs. ellipticity. The model galaxies in our clusters at z = 0 (blue dots and contours) are presented in comparison to the ATLAS data (red dots). All measurements were performed at 1 R eff . The black dashed line shows the empirical demarcation between slow (below) and fast (above) rotators (Emsellem et al. 2011 ). We present the evolution of the galaxy rotation parameter starting from z = 3, because it is nontrivial to extract the galaxy merger history accurately from a cosmological simulation at higher redshifts where galaxy interactions and mergers occurred in a more chaotic manner. At z = 3, most of the model galaxies were fast rotators (Figure 3 ). It seems that galaxies are indeed born generally as rotating disks, as tidal torque theory suggests. Galaxy mass growth was quick in early high-density peaks that later evolve to be galaxy clusters, and thus the cluster galaxies reached a stage where dispersion is more important than rotation () already at z = 3. The peak in the rotation
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