X-ray scaling relations from a complete sample of the richest maxBCG clusters

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We use a complete sample of 38 richest maxBCG clusters to study the ICM-galaxy scaling relations and the halo mass selection properties of the maxBCG algorithm, based on X-ray and optical observations. The clusters are selected from the two largest bins of optical richness in the Planck stacking work with the maxBCG richness $N_{200} \geq 78$. We analyze their Chandra and XMM-Newton data to derive the X-ray properties of the ICM. We then use the distribution of $P(X|N)$, $X=T_X,\ L_X,\ Y_X$, to study the mass selection $P(M|N)$ of maxBCG. Compared with previous works based on the whole richness sample, a significant fraction of blended systems with boosted richness is skewed into this richest sample. Parts of the blended halos are picked apart by the redMaPPer, an updated red-sequence cluster finding algorithm with lower mass scatter. Moreover, all the optical blended halos are resolved as individual X-ray halos, following the established $L_X-T_X$ and $L_X-Y_X$ relations. We further discuss that the discrepancy between ICM-galaxy scaling relations, especially for future blind stacking, can come from several factors, including miscentering, projection, contamination of low mass systems, mass bias and covariance bias. We also evaluate the fractions of relaxed and cool core clusters in our sample. Both are smaller than those from SZ or X-ray selected samples. Moreover, disturbed clusters show a higher level of mass bias than relaxed clusters.