Extrinsic Sources of Scatter in the Richness-Mass Relation of Galaxy
  Clusters
  Maximizing the utility of upcoming photometric cluster surveys requires a
thorough understanding of the richness-mass relation of galaxy clusters. We use
Monte Carlo simulations to study the impact of various sources of observational
scatter on this relation. Cluster ellipticity, photometric errors, photometric
redshift errors, and cluster-to-cluster variations in the properties of
red-sequence galaxies contribute negligible noise. Miscentering, however, can
be important, and likely contributes to the scatter in the richness-mass
relation of galaxy maxBCG clusters at the low mass end, where centering is more
difficult. We also investigate the impact of projection effects under several
empirically motivated assumptions about cluster environments. Using SDSS data
and the maxBCG cluster catalog, we demonstrate that variations in cluster
environments can rarely (\approx 1% - 5% of the time) result in significant
richness boosts. Due to the steepness of the mass/richness function, the
corresponding fraction of optically selected clusters that suffer from these
projection effects is \approx 5% - 15%. We expect these numbers to be generic
in magnitude, but a precise determination requires detailed, survey-specific
modeling.
