The X-ray Properties of Optically-Selected Galaxy Clusters
  We stacked the X-ray data from the ROSAT All Sky Survey for over 4,000 clusters selected from the 2MASS catalog and divided into five richness classes. We detected excess X-ray emission over background at the center of the stacked images in all five richness bins. The interrelationships between the mass, X-ray temperature and X-ray luminosity of the stacked clusters agree well with those derived from catalogs of X-ray clusters. Poisson variance in the number of galaxies occupying halos of a given mass leads to significant differences between the average richness at fixed mass and the average mass at fixed richness that we can model relatively easily using a simple model of the halo occupation distribution. These statistical effects probably explain recent results in which optically-selected clusters lie on the same X-ray luminosity-temperature relations as local clusters but have lower optical richnesses than observed for local clusters with the same X-ray properties. When we further binned the clusters by redshift, we did not find significant redshift-dependent biases in the sense that the X-ray luminosities for massive clusters of fixed optical richness show little dependence on redshift beyond that expected from the effects of Poisson fluctuations. Our results demonstrate that stacking of RASS data from optically selected clusters can be a powerful test for biases in cluster selection algorithms. 
Xinyu Dai, Christopher S. Kochanek, and Nicholas D. Morgan (The Ohio   State University)