Measuring the mean and scatter of the X-ray luminosity-optical richness relation for maxBCG galaxy clusters

Determining the scaling relations between galaxy cluster observables requires large samples of uniformly observed clusters. We measure the mean X-ray luminosity-optical richness ((L) over bar (X)-(N) over bar (200)) relation for an approximately volume-limited sample of more than 17,000 optically selected clusters from the maxBCG catalog spanning the redshift range 0.1 < z < 0.3. By stacking the X-ray emission from many clusters using ROSAT All-Sky Survey data, we are able to measure mean X-ray luminosities to similar to 10% (including systematic errors) for clusters in nine independent optical richness bins. In addition, we are able to crudely measure individual X-ray emission from similar to 800 of the richest clusters. Assuming a lognormal form for the scatter in the L-X-N-200 relation, we measure sigma(ln L) = 0.86 +/- 0.03 at fixed N-200. This scatter is large enough to significantly bias the mean stacked relation. The corrected median relation can be parameterized by (L) over tilde (X) = e(alpha)((N) over bar (200)/40)(beta) x 10(42) h(-2) ergs s(-1), where alpha = 3.57 +/- 0.08 and beta = 1.82 +/- 0.05. We find that X-ray-selected clusters are significantly brighter than optically selected clusters at a given optical richness. This selection bias explains the apparently X-ray-underluminous nature of optically selected cluster catalogs.