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 (LX--N₂00) 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 ~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 ~800 of the richest clusters. Assuming a log-normal form for the scatter in the LX--N₂00 relation, we measure L=0. 86+/-0. 03 at fixed N₂00. This scatter is large enough to significantly bias the mean stacked relation. The corrected median relation can be parameterized by LX = (e^) (N₂00/40) ^ 10⁴2 h^-2 ergs/s, where = 3. 57+/-0. 08 and = 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.