Robust Optical Richness Estimation with Reduced Scatter
  Reducing the scatter between cluster mass and optical richness is a key goal
for cluster cosmology from photometric catalogs. We consider various
modifications to the red-sequence matched filter richness estimator of Rozo et
al. (2009), and evaluate their impact on the scatter in X-ray luminosity at
fixed richness. Most significantly, we find that deeper luminosity cuts can
reduce the recovered scatter, finding that sigma_lnLX|lambda=0.63+/-0.02 for
clusters with M_500c >~ 1.6e14 h_70^-1 M_sun. The corresponding scatter in mass
at fixed richness is sigma_lnM|lambda ~ 0.2-0.3 depending on the richness,
comparable to that for total X-ray luminosity. We find that including blue
galaxies in the richness estimate increases the scatter, as does weighting
galaxies by their optical luminosity. We further demonstrate that our richness
estimator is very robust. Specifically, the filter employed when estimating
richness can be calibrated directly from the data, without requiring a-priori
calibrations of the red-sequence. We also demonstrate that the recovered
richness is robust to up to 50% uncertainties in the galaxy background, as well
as to the choice of photometric filter employed, so long as the filters span
the 4000 A break of red-sequence galaxies. Consequently, our richness estimator
can be used to compare richness estimates of different clusters, even if they
do not share the same photometric data. Appendix 1 includes "easy-bake"
instructions for implementing our optimal richness estimator, and we are
releasing an implementation of the code that works with SDSS data, as well as
an augmented maxBCG catalog with the lambda richness measured for each cluster.
