In order to investigate the structure and dynamics of the recently discovered massive ( M _ { * } \gtrsim 10 ^ { 11 } M _ { \odot } ) compact z \sim 2 galaxies , cosmological hydrodynamical/N-body simulations of a \sim 50000 Mpc ^ { 3 } co-moving ( lagrangian ) , proto-cluster region have been undertaken .
At z = 2 , the highest resolution simulation contains \sim 5800 resolved galaxies , of which 509 , 27 and 5 have M _ { * } > 10 ^ { 10 } M _ { \odot } , M _ { * } > 10 ^ { 11 } M _ { \odot } and M _ { * } > 4 \times 10 ^ { 11 } M _ { \odot } , respectively .
Total stellar masses , effective radii and characteristic stellar densities have been determined for all galaxies .
At z = 2 , for the definitely well resolved mass range of M _ { * } \gtrsim 10 ^ { 11 } M _ { \odot } , we fit the relation R _ { eff } = R _ { eff, 12 } M _ { *, 12 } ^ { 1 / 3 } to the data , where M _ { *, 12 } is the total stellar mass in units of 10 ^ { 12 } M _ { \odot } .
This yields R _ { eff, 12 } = ( 1.20 \pm 0.04 ) kpc , in line with observational findings for compact z \sim 2 galaxies , though somewhat more compact than the observed average .
The only line-of-sight velocity dispersion measured for a z \sim 2 compact galaxy is very large , \sigma _ { *,p } = 510 ^ { +165 } _ { -95 } km/s ( 45 ) .
This value can be matched at about the 1- \sigma level , although a somewhat larger mass than the estimated M _ { * } \simeq 2 \times 10 ^ { 11 } M _ { \odot } is indicated .
For the above mass range , the galaxies have an average axial ratio < b / a > = 0.64 \pm 0.02 with a dispersion of 0.1 , and an average rotation to 1D velocity dispersion ratio < v / \sigma > = 0.46 \pm 0.06 with a dispersion of 0.3 , and a maximum value of v / \sigma \simeq 1.1 .
Rotation and velocity anisotropy both contribute significantly 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 = 2 R _ { eff } .