The origin of galaxy colour bimodality in the scatter of the
  Stellar-to-Halo Mass Relation
  Recent observations reveal that, at a given stellar mass, blue galaxies tend
to live in haloes with lower mass while red galaxies live in more massive host
haloes. The physical driver behind this is still unclear because theoretical
models predict that, at the same halo mass, galaxies with high stellar masses
tend to live in early-formed haloes which naively leads to an opposite trend.
Here, we show that the {\sc Simba} simulation quantitatively reproduces the
colour bimodality in SHMR and reveals an inverse relationship between halo
formation time and galaxy transition time. It suggests that the origin of this
bimodality is rooted in the intrinsic variations of the cold gas content due to
halo assembly bias. {\sc Simba}'s SHMR bimodality quantitatively relies on two
aspects of its input physics: (1) Jet-mode AGN feedback, which quenches
galaxies and sets the qualitative trend; and (2) X-ray AGN feedback, which
fully quenches galaxies and yields better agreement with observations. The
interplay between the growth of cold gas and the AGN quenching in {\sc Simba}
results in the observed SHMR bimodality.
