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.