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The relative roles of mergers and star formation in regulating galaxy growth are still a matter of intense debate. We here present our decode , a new Discrete statistical sEmi-empiriCal mODEl specifically designed to predict rapidly and efficiently, in a full cosmological context, galaxy assembly, and merger histories for any given input stellar mass–halo mass (SMHM) relation. decode generates object-by-object dark matter merger trees (hence discrete) from accurate subhalo mass and infall redshift probability functions (hence statistical) for all subhaloes, including those residing within other subhaloes, with virtually no resolution limits on mass or volume. Merger trees are then converted into galaxy assembly histories via an input, redshift-dependent SMHM relation, which is highly sensitive to the significant systematics in the galaxy stellar mass function and on its evolution with cosmic time. decode can accurately reproduce the predicted mean galaxy merger rates and assembly histories of hydrodynamic simulations and semi-analytical models, when adopting in input their SMHM relations. In this work, we use decode to prove that only SMHM relations implied by stellar mass functions characterized by large abundances of massive galaxies and significant redshift evolution, at least at |$M_\star \gtrsim 10^{11} \, \mathrm{M}_\odot$|⁠ , can simultaneously reproduce the local abundances of satellite galaxies, the galaxy (major merger) pairs since z ∼ 3, and the growth of Brightest Cluster Galaxies. The same models can also reproduce the local fraction of elliptical galaxies, on the assumption that these are strictly formed by major mergers, but not the full bulge-to-disc ratio distributions, which require additional processes. [ABSTRACT FROM AUTHOR]

We carry out a systematic investigation of the total mass density profile of massive (logMstar/M☉ ~ 11.5) early-type galaxies and its dependence on redshift, specifically in the range 0 ≳ z ≳ 1. We start from a large sample of Sloan Digital Sky Survey early-type galaxies with stellar masses and effective radii measured assuming two different profiles, de Vaucouleurs and Sérsic. We assign dark matter haloes to galaxies via abundance matching relations with standard ΛCDM profiles and concentrations. We then compute the total, massweighted density slope at the effective radius γ γ, and study its redshift dependence at fixed stellar mass. We find that a necessary condition to induce an increasingly flatter γ γ at higher redshifts, as suggested by current strong lensing data, is to allow the intrinsic stellar profile of massive galaxies to be Sérsic and the input Sérsic index n to vary with redshift as n(z) - (1 + z)δ, with δ ≳ -1. This conclusion holds irrespective of the input Mstar-Mhalo relation, the assumed stellar initialmass function (IMF), or even the chosen level of adiabatic contraction in the model. Secondary contributors to the observed redshift evolution of γ γ may come from an increased contribution at higher redshifts of adiabatic contraction and/or bottom-light stellar IMFs. The strong lensing selection effects we have simulated seem not to contribute tothis effect. A steadily increasing Sérsic index with cosmic time is supported by independent observations, though it is not yet clear whether cosmological hierarchical models (e.g. mergers) are capable of reproducing such a fast and sharp evolution. [ABSTRACT FROM AUTHOR]