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.
