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The relative roles of mergers and star formation in regulating galaxy growthare still a matter of intense debate. We here present our DECODE, a newDiscrete statistical sEmi-empiriCal mODEl specifically designed to predictrapidly and efficiently, in a full cosmological context, galaxy assembly andmerger 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 (hencestatistical) for all subhaloes, including those residing within othersubhaloes, with virtually no resolution limits on mass or volume. Merger treesare then converted into galaxy assembly histories via an input, redshiftdependent SMHM relation, which is highly sensitive to the significantsystematics in the galaxy stellar mass function and on its evolution withcosmic time. DECODE can accurately reproduce the predicted mean galaxy mergerrates and assembly histories of hydrodynamic simulations and semi-analyticmodels, when adopting in input their SMHM relations. In the present work we useDECODE to prove that only SMHM relations implied by stellar mass functionscharacterized by large abundances of massive galaxies and significant redshiftevolution, at least at $M_\star \gtrsim 10^{11} \, M_\odot$, can simultaneouslyreproduce the local abundances of satellite galaxies, the galaxy (major merger)pairs since $z \sim 3$, and the growth of Brightest Cluster Galaxies. The samemodels can also reproduce the local fraction of elliptical galaxies, on theassumption that these are strictly formed by major mergers, but not the fullbulge-to-disc ratio distributions, which require additional processes.

monthly notices of the royal astronomical society

Testing the key role of the stellar mass-halo mass relation in galaxy  merger rates and morphologies via DECODE, a novel Discrete statistical  sEmi-empiriCal mODEl