Constraining Scatter in the Stellar Mass--Halo Mass Relation for Haloes
  Less Massive than the Milky Way
  Most galaxies are hosted by massive, invisible dark matter haloes, yet little
is known about the scatter in the stellar mass--halo mass relation for galaxies
with host halo masses $M_{h}\le 10^{11}M_{\odot}$. Using mock catalogues based
on dark matter simulations, we find that two observable signatures are
sensitive to scatter in the stellar mass--halo mass relation even at these mass
scales; i.e., conditional stellar mass functions and velocity distribution
functions for neighbouring galaxies. We compute these observables for 179,373
galaxies in the Sloan Digital Sky Survey (SDSS) with stellar masses $M_{\ast} >
10^9 M_{\odot}$ and redshifts 0.01 $< z <$ 0.307. We then compare to mock
observations generated from the $\textit{Bolshoi-Planck}$ dark matter
simulation for stellar mass--halo mass scatters ranging from 0 to 0.6 dex. The
observed results are consistent with simulated results for most values of
scatter ($<$0.6 dex), and SDSS statistics are insufficient to provide firm
constraints. However, this method could provide much tighter constraints on
stellar mass--halo mass scatter in the future if applied to larger data sets,
especially the anticipated Dark Energy Spectroscopic Instrument Bright Galaxy
Survey. Constraining the value of scatter could have important implications for
galaxy formation and evolution.
