Constraining the scatter in the mass-richness relation of maxbcg clusters with weak lensing and x-ray data

We measure the logarithmic scatter in mass at fixed richness for clusters in the maxBCG cluster catalog, an optically selected cluster sample drawn from Sloan Digital Sky Survey imaging data. Our measurement is achieved by demanding consistency between available weak-lensing and X-ray measurements of the maxBCG clusters, and the X-ray luminosity-mass relation inferred from the 400 days X-ray cluster survey, a flux-limited X-ray cluster survey. We find (95% CL) at N ₂₀₀ 40, where N ₂₀₀ is the number of red sequence galaxies in a cluster. As a byproduct of our analysis, we also obtain a constraint on the correlation coefficient between ln L_X and ln M at fixed richness, which is best expressed as a lower limit, r _L,M|N ≥ 0.85(95% CL). This is the first observational constraint placed on a correlation coefficient involving two different cluster mass tracers. We use our results to produce a state-of-the-art estimate of the halo mass function at z = 0.23 - the median redshift of the maxBCG cluster sample - and find that it is consistent with the WMAP5 cosmology. Both the mass function data and its covariance matrix are presented.