Hierarchical Galaxy Growth and Scatter in the Stellar Mass - Halo Mass
  Relation
  The relation between galaxies and dark matter halos reflects the combined
effects of many distinct physical processes. Observations indicate that the
$z=0$ stellar mass-halo mass (SMHM) relation has remarkably small scatter in
stellar mass at fixed halo mass ($\lesssim$ 0.2 dex) with little dependence on
halo mass. We investigate the origins of this scatter by combining N-body
simulations with observational constraints on the SMHM relation. We find that
at the group and cluster scale ($M_{\rm vir}>10^{14}{M_\odot}$) the scatter due
purely to hierarchical assembly is $\approx0.16$ dex, which is comparable to
recent direct observational estimates. At lower masses, mass buildup since
$z\approx2$ is driven largely by in-situ growth. We include a model for the
in-situ buildup of stellar mass and find that an intrinsic scatter in this
growth channel of $0.2$ dex produces a relation between scatter and halo mass
that is consistent with observations from $10^{12}{M_\odot}<M_{\rm
vir}<10^{14.75}{M_\odot}$. The approximately constant scatter across a wide
range of halo masses at $z=0$ thus appears to be a coincidence as it is
determined largely by in-situ growth at low masses and by hierarchical assembly
at high masses. These results indicate that the scatter in the SMHM relation
can provide unique insight into the regularity of the galaxy formation process.
