In order to investigate the structure and dynamics of the recently discovered massive (M_* > 10^11 M_sun) compact z~2 galaxies, cosmological hydrodynamical/N-body simulations of a proto-cluster region have been undertaken. At z=2, the highest resolution simulation contains ~5800 resolved galaxies, of which 509, 27 and 5 have M_* > 10^10 M_sun, > 10^11 M_sun and > 4x10^11 M_sun, respectively. Effective radii and characteristic stellar densities have been determined for all galaxies. At z=2, for the definitely well resolved mass range of M_* > 10^11 Msun, the mass-size relation is consistent with observational findings for the most compact z~2 galaxies. The very high velocity dispersion recently measured for a compact z~2 galaxy (~510 km/s; van Dokkum et al 2009) can be matched at about the 1-sigma level, although a somewhat larger mass than the estimated M_* ~ 2 x 10^11 M_sun is indicated. For the above mass range, the galaxies have an average axial ratio <b/a> = 0.64 +/- 0.02 with a dispersion of 0.1, an average rotation to 1D velocity dispersion ratio <v/sigma> = 0.46 +/- 0.06 with a dispersion of 0.3, and a maximum value of v/sigma ~ 1.1. Rotation and velocity anisotropy both contribute in flattening the compact galaxies. Some of the observed compact galaxies appear flatter than any of the simulated galaxies. Finally, it is found that the massive compact galaxies are strongly baryon dominated in their inner parts, with typical dark matter mass fractions of order only 20% inside of r=2R_eff.
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