Toward Accurate Modeling of Galaxy Clustering on Small Scales:
  Constraining the Galaxy-Halo Connection with Optimal Statistics
  Applying halo models to analyze the small-scale clustering of galaxies is a
proven method for characterizing the connection between galaxies and their host
halos. Such works are often plagued by systematic errors or are limited to
clustering statistics which can be predicted analytically. In this work, we
employ a numerical mock-based modeling procedure to examine the clustering of
SDSS DR7 galaxies. We apply a standard halo occupation distribution (HOD) model
to dark-matter-only simulations with a LCDM cosmology. To constrain the
theoretical models, we utilize a combination of galaxy number density and
selected scales of the projected correlation function, redshift-space
correlation function, group multiplicity function, average group velocity
dispersion, mark correlation function, and counts-in-cells statistics. We
design an algorithm to choose an optimal combination of measurements that
yields tight and accurate constraints on our model parameters. Compared to
previous work using fewer clustering statistics, we find significant
improvement in the constraints on all parameters of our halo model for two
different luminosity-threshold galaxy samples. Most interestingly, we obtain
unprecedented high-precision constraints on the scatter in the relationship
between galaxy luminosity and halo mass. However, our best-fit model results in
significant tension (>4 sigma) for both samples, indicating the need to add
second-order features to the standard HOD model. To guarantee the robustness of
these results, we perform an extensive analysis of the systematic and
statistical errors in our modeling procedure, including a first-of-its-kind
study of the sensitivity of our constraints to changes in the halo mass
function due to baryonic physics.
