Going, going, gone dark: Quantifying the scatter in the faintest dwarf
  galaxies
  We predict the stellar mass-halo mass (SMHM) relationship for dwarf galaxies
and their satellites residing in halos down to M$_{halo} =$ 10$^7$ M$_{\odot}$
with 10$^4$ M$_{\odot} <$ M$_{star}$($z=0$) $< 10^8$ M$_{\odot}$, and quantify
the predicted scatter in the relation at the low mass end, using cosmological
simulations. The galaxies were drawn from a cosmological simulation of dwarf
galaxies, run with the N-body + SPH code, ChaNGA, at a high resolution of 60
pc. For M$_{halo} > 10^9$ M$_{\odot}$, the simulated SMHM relationship agrees
with literature determinations, including exhibiting a small scatter. However,
the scatter in the SMHM relation increases dramatically for lower-mass halos.
We find that some of this scatter is due to {\em dark dwarfs}, halos devoid of
stars. However, even when only considering well-resolved halos that contain a
stellar population, the scatter in stellar mass reaches nearly 1 dex for
M$_{halo}$($z=0$) 10$^7$ M$_{\odot}$. Much of this scatter is due to including
satellites of the dwarf galaxies that have had their halo masses reduced
through tidal stripping. The fraction of dark dwarfs (those that contain no
stars) increases substantially with decreasing halo mass. When these dark halos
are considered, the true scatter in the SMHM at low masses is even larger. At
the faintest end of the SMHM relation probed by our simulations, a galaxy
cannot be assigned a unique halo mass based solely on its luminosity. We
provide a formula to stochastically populate low-mass halos following our
results. Our predicted large scatter at low halo masses increases the slope of
the resulting stellar mass function on the ultra-faint dwarf galaxy scales
currently being probed by such surveys as the Dark Energy Survey or the
Hyper-Suprime Cam Subaru Strategic Program, and in the future by the Large
Synoptic Survey Telescope.
