  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.
