The cosmological size and velocity dispersion evolution of massive early-type galaxies

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. (abridged)