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We measure the logarithmic scatter in mass at fixed richness for clusters inthe maxBCG cluster catalog, an optically selected cluster sample drawn fromSDSS imaging data. Our measurement is achieved by demanding consistency betweenavailable weak lensing and X-ray measurements of the maxBCG clusters, and theX-ray luminosity--mass relation inferred from the 400d X-ray cluster survey, aflux limited X-ray cluster survey. We find \sigma_{\lnM|N_{200}}=0.45^{+0.20}_{-0.18} (95% CL) at N_{200} ~ 40, where N_{200} is thenumber of red sequence galaxies in a cluster. As a byproduct of our analysis,we also obtain a constraint on the correlation coefficient between \ln Lx 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 acorrelation coefficient involving two different cluster mass tracers. We useour results to produce a state of the art estimate of the halo mass function atz=0.23 -- the median redshift of the maxBCG cluster sample -- and find that itis consistent with the WMAP5 cosmology. Both the mass function data and itscovariance matrix are presented.

Constraining the Scatter in the Mass-Richness Relation of maxBCG Clusters With Weak Lensing and X-ray Data