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.