The mass and structural evolution of massive galaxies is one of the hottest topics in galaxy formation. This is because it may reveal invaluable insights into the still debated evolutionary processes governing the growth and assembly of spheroids. Ho
wever, direct comparison between models and observations is usually prevented by the so-called progenitor bias, i.e., new galaxies entering the observational selection at later epochs, thus eluding a precise study of how pre-existing galaxies actually evolve in size. To limit this effect, we here gather data on high-redshift brightest group and cluster galaxies, evolve their (mean) host halo masses down to z=0 along their main progenitors, and assign as their descendants local SDSS central galaxies matched in host halo mass. At face value, the comparison between high redshift and local data suggests a noticeable increase in stellar mass of a factor of >2 since z~1, and of >2.5 in mean effective radius. We then compare the inferred stellar mass and size growth with those predicted by hierarchical models for central galaxies, selected at high redshifts to closely match the halo and stellar mass bins as in the data. Only hierarchical models characterized by very limited satellite stellar stripping and parabolic orbits are capable of broadly reproducing the stellar mass and size increase of a factor ~2-4 observed in cluster galaxies since z ~1. The predicted, average (major) merger rate since z~1 is in good agreement with the latest observational estimates.
The stellar mass-halo mass relation is a key constraint in all semi-analytic, numerical, and semi-empirical models of galaxy formation and evolution. However, its exact shape and redshift dependence remain debated. Several recent works support a rela
tion in the local Universe steeper than previously thought. Based on the comparisons with a variety of data on massive central galaxies, we show that this steepening holds up to z~1, for stellar masses Mstar>2e11 Msun. Specifically, we find significant evidence for a high-mass end slope of beta>0.35-0.70, instead of the usual beta~0.20-0.30 reported by a number of previous results. When including the independent constraints from the recent BOSS clustering measurements, the data, independent of any systematic errors in stellar masses, tend to favor a model with a very small scatter (< 0.15 dex) in stellar mass at fixed halo mass, in the redshift range z < 0.8 and for Mstar>3e11 Msun, suggesting a close connection between massive galaxies and host halos even at relatively recent epochs. We discuss the implications of our results with respect to the evolution of the most massive galaxies since z~1.
We compare state-of-the-art semi-analytic models of galaxy formation as well as advanced sub-halo abundance matching models with a large sample of early-type galaxies from SDSS at z < 0.3. We focus our attention on the dependence of median sizes of c
entral galaxies on host halo mass. The data do not show any difference in the structural properties of early-type galaxies with environment, at fixed stellar mass. All hierarchical models considered in this work instead tend to predict a moderate to strong environmental dependence, with the median size increasing by a factor of about 1.5-3 when moving from low to high mass host haloes. At face value the discrepancy with the data is highly significant, especially at the cluster scale, for haloes above log Mhalo > 14. The convolution with (correlated) observational errors reduces some of the tension. Despite the observational uncertainties, the data tend to disfavour hierarchical models characterized by a relevant contribution of disc instabilities to the formation of spheroids, strong gas dissipation in (major) mergers, short dynamical friction timescales, and very short quenching timescales in infalling satellites. We also discuss a variety of additional related issues, such as the slope and scatter in the local size-stellar mass relation, the fraction of gas in local early-type galaxies, and the general predictions on satellite galaxies.
