A simple model linking galaxy and dark matter evolution

We construct a simple phenomenological model for the evolving galaxy population by incorporating pre-defined baryonic prescriptions into a dark matter hierarchical merger tree. Specifically the model is based on the simple gas-regulator model introduced by Lilly et al. 2013 coupled with the empirical quenching rules of Peng et al. 2010/12. The simplest model already does quite well in reproducing, without re-adjusting the input parameters, many observables including the Main Sequence sSFR-mass relation, the faint end slope of the galaxy mass function and the shape of the star-forming and passive mass functions. Compared with observations and/or the recent phenomenological model of Behroozi et al. 2013 based on epoch-dependent abundance-matching, our model also qualitatively reproduces the evolution of the Main Sequence sSFR(z) and SFRD(z) star formation rate density relations, the $M_s - M_h$ stellar-to-halo mass relation and also the $SFR - M_h$ relation. Quantitatively the evolution of sSFR(z) and SFRD(z) is not steep enough, the $M_s - M_h$ relation is not quite peaked enough and, surprisingly, the ratio of quenched to star-forming galaxies around M* is not quite high enough. We show that these deficiencies can simultaneously be solved by ad hoc allowing galaxies to re-ingest some of the gas previously expelled in winds, provided that this is done in a mass-dependent and epoch-dependent way. These allow the model galaxies to reduce an inherent tendency to saturate their star-formation efficiency. This emphasizes how efficient galaxies around M* are in converting baryons into stars and highlights the fact that quenching occurs just at the point when galaxies are rapidly approaching the maximum possible efficiency of converting baryons into stars.