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