The cosmic epoch dependence of environmental effects on size evolution of red-sequence early-type galaxies

This work aims to observationally investigate the history of size growth of early-type galaxies and how the growth depends on cosmic epoch and the mass of the halo in which they are embedded. We carried out a photometric and structural analysis in the rest-frame V band of a mass-selected (log M/M-circle dot > 10.7) sample of red-sequence early-type galaxies with spectroscopic/grism redshift in the general field up to z = 2 to complement a previous work presenting an identical analysis but in halos 100 times more massive and 1000 times denser. We homogeneously derived sizes (effective radii) fully accounting for the multi-component nature of galaxies and the common presence of isophote twists and ellipticity gradients. By using these mass-selected samples, composed of 170 red-sequence early-type galaxies in the general field and 224 identically selected and analyzed in clusters, we isolate the effect on galaxy sizes of the halo in which galaxies are embedded and its dependence on epoch. We find that the log of the galaxy size at a fixed stellar mass, log M/M-circle dot = 11, has increased with epoch at a rate twice as fast in the field than in cluster in the last 10 Gyr (0.26 +/- 0.03 versus 0.13 +/- 0.02 dex per unit redshift). Red-sequence early-type galaxies in the general field reached the size of their cousins in denser environment by z = 0.25 +/- 0.13 in spite of being three times smaller at z similar to 2. Data point toward a model where size growth is epoch-independent (i.e., partial derivative log r(e)/partial derivative z = c), but with a rate c depending on environment, partial derivative c/partial derivative log M-halo approximate to 0.05. Environment determines the growth rate (d log r(e)/dz) at all redshifts, indicating an external origin for the galaxy growth without any clear epoch where it ceases to have an effect. The larger size of early-type galaxies in massive halos at high redshift indicates that their size grew buildup earlier (at z > 2) at an accelerated rate, slowing down at some still unidentified z > 2 redshift. Instead, the size growth rate of red-sequence early-type galaxies in low-mass halos is reversed: it proceeds at an increased rate at late epochs after an early period (z > 2) of reduced growth, in agreement with the qualitative hierarchical picture of galaxy evolution. We found similar values of scatter around the mass-size relation independently of environment and epoch, indicating that the amount of dissipation in the system forming the observed galaxy does not vary greatly with epoch or environment.