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 _ { \text { peak } } , as our property to connect galaxies to halos , and all comparisons between theory and observation are made after first passing the model through the group-finding algorithm .
We parameterize scatter as a log-normal distribution in M _ { \ast } at fixed V _ { \text { peak } } , \sigma [ M _ { \ast } |V _ { \text { peak } } ] .
The cross-correlation technique yields a constraint of \sigma [ M _ { \ast } |V _ { \text { peak } } ] = 0.27 \pm 0.05 dex at a mean V _ { \text { peak } } of 168 km s ^ { -1 } , corresponding to a scatter in \log M _ { \ast } at fixed M _ { \text { h } } of \sigma [ M _ { \ast } |M _ { h } ] = 0.38 \pm 0.06 dex at M _ { \text { h } } = 10 ^ { 11.8 } \text { M } _ { \odot } .
The kurtosis technique yields \sigma [ M _ { \ast } |V _ { \text { peak } } ] = 0.30 \pm 0.03 at V _ { \text { peak } } = 209 km s ^ { -1 } , corresponding to \sigma [ M _ { \ast } |M _ { h } ] = 0.34 \pm 0.04 at M _ { \text { h } } = 10 ^ { 12.2 } \text { M } _ { \odot } .
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 _ { \text { 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 .