Constraining the scatter in the galaxy-halo connection at Milky Way
  masses
  We develop and implement two new methods for constraining the scatter in the
relationship between galaxies and dark matter halos. These new techniques are
sensitive to the scatter at low halo masses, making them complementary to
previous constraints that are dependent on clustering amplitudes or rich galaxy
groups, both of which are only sensitive to more massive halos. In both of our
methods, we use a galaxy group finder to locate central galaxies in the SDSS
main galaxy sample. Our first technique uses the small-scale cross-correlation
of central galaxies with all lower mass galaxies. This quantity is sensitive to
the satellite fraction of low-mass galaxies, which is in turn driven by the
scatter between halos and galaxies. The second technique uses the kurtosis of
the distribution of line-of-sight velocities between central galaxies and
neighboring galaxies. This quantity is sensitive to the distribution of halo
masses that contain the central galaxies at fixed stellar mass. Theoretical
models are constructed using peak halo circular velocity, $V_{\rm peak}$, as
our property to connect galaxies to halos. The cross-correlation technique
yields a constraint of $\sigma[ M_\ast|V_{\rm peak}]=0.27\pm 0.05$ dex,
corresponding to a scatter in $\log M_\ast$ at fixed $M_h$ of $\sigma[
M_\ast|M_h]=0.38\pm 0.06$ dex at $M_h=10^{11.8}$ Msun. The kurtosis technique
yields $\sigma[ M_\ast|V_{\rm peak}]=0.30\pm0.03$, corresponding to $\sigma[
M_\ast|M_h]=0.34\pm 0.04$ at $M_h=10^{12.2}$ Msun. The values of $\sigma[
M_\ast|M_h]$ are significantly larger than the constraints at higher masses, in
agreement with the results of hydrodynamic simulations. This increase is only
partly due to the scatter between $V_{\rm peak}$ and $M_h$, and it represents
an increase of nearly a factor of two relative to the values inferred from
clustering and group studies at high masses.
