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 (L̄_X-N̄₂₀₀) 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 lognormal form for the scatter in the L_X-N₂₀₀ relation, we measure σ_{ln 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 L̃_X = e ^α(N̄₂₀₀/40)^β × 10 ⁴² h^-2 ergs s^-1, where α = 3.57 ± 0.08 and β = 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.