We analyze 40 cosmological re-simulations of individual massive galaxies with present-day stellar masses of M _ { * } > 6.3 \times 10 ^ { 10 } M _ { \odot } in order to investigate the physical origin of the observed strong increase in galaxy sizes and the decrease of the stellar velocity dispersions since redshift z \approx 2 .
At present 25 out of 40 galaxies are quiescent with structural parameters ( sizes and velocity dispersions ) in agreement with local early type galaxies .
At z=2 all simulated galaxies with M _ { * } \gtrsim 10 ^ { 11 } M _ { \odot } ( 11 out of 40 ) at z=2 are compact with projected half-mass radii of \approx 0.77 ( \pm 0.24 ) kpc and line-of-sight velocity dispersions within the projected half-mass radius of \approx 262 ( \pm 28 ) kms ^ { -1 } ( 3 out of 11 are already quiescent ) .
Similar to observed compact early-type galaxies at high redshift the simulated galaxies are clearly offset from the local mass-size and mass-velocity dispersion relations .
Towards redshift zero the sizes increase by a factor of \sim 5 - 6 , following R _ { 1 / 2 } \propto ( 1 + z ) ^ { \alpha } with \alpha = -1.44 for quiescent galaxies ( \alpha = -1.12 for all galaxies ) .
The velocity dispersions drop by about one-third since z \approx 2 , following \sigma _ { 1 / 2 } \propto ( 1 + z ) ^ { \beta } with \beta = 0.44 for the quiescent galaxies ( \beta = 0.37 for all galaxies ) .
The simulated size and dispersion evolution is in good agreement with observations and results from the subsequent accretion and merging of stellar systems at z \lesssim 2 which is a natural consequence of the hierarchical structure formation .
A significant number of the simulated massive galaxies ( 7 out of 40 ) experience no merger more massive than 1:4 ( usually considered as major mergers ) .
On average , the dominant accretion mode is stellar minor mergers with a mass-weighted mass-ratio of 1:5 .
We therefore conclude that the evolution of massive early-type galaxies since z \approx 2 and their present-day properties are predominantly determined by frequent ’ minor ’ mergers of moderate mass-ratios and not by major mergers alone .