The XMM Cluster Survey analysis of the SDSS DR8 redMaPPer Catalogue:
  Implications for scatter, selection bias, and isotropy in cluster scaling
  relations
  In this paper we present the X-ray analysis of SDSS DR8 redMaPPer (SDSSRM)
clusters using data products from the $XMM$ Cluster Survey (XCS). In total,
1189 SDSSRM clusters fall within the $XMM$-Newton footprint. This has yielded
456 confirmed detections accompanied by X-ray luminosity ($L_{X}$)
measurements. Of the detected clusters, 382 have an associated X-ray
temperature measurement ($T_{X}$). This represents one of the largest samples
of coherently derived cluster $T_{X}$ values to date. Our analysis of the X-ray
observable to richness ($\lambda$) scaling relations has demonstrated that
scatter in the $T_{X}-\lambda$ relation is roughly a third of that in the
$L_{X}-\lambda$ relation, and that the $L_{X}-\lambda$ scatter is intrinsic,
i.e. will not be significantly reduced with larger sample sizes. Our analysis
of the scaling relation between $L_{X}$ and $T_{X}$ has shown that the fits are
sensitive to the selection method of the sample, i.e. whether the sample is
made up of clusters detected "serendipitously" compared to those deliberately
targeted by $XMM$. These differences are also seen in the $L_{X}-\lambda$
relation and, to a lesser extent, in the $T_{X}-\lambda$ relation. Exclusion of
the emission from the cluster core does not make a significant impact to the
findings. A combination of selection biases is a likely, but as yet unproven,
reason for these differences. Finally, we have also used our data to probe
recent claims of anisotropy in the $L_{X}-T_{X}$ relation across the sky. We
find no evidence of anistropy, but stress that this may be masked in our
analysis by the incomplete declination coverage of the SDSS DR8 sample.
