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We critically examine the methodology behind the claimed observationaldetection of halo assembly bias using optically selected galaxy clusters byMiyatake et al. (2016) and More et al. (2016). We mimic the optical clusterdetection algorithm and apply it to two different mock catalogs generated fromthe Millennium simulation galaxy catalog, one in which halo assembly biassignal is present, while the other in which the assembly bias signal has beenexpressly erased. We split each of these cluster samples into two using theaverage cluster-centric distance of the member galaxies to measure thedifference in the clustering strength of the subsamples with respect to eachother. We observe that the subsamples split by cluster-centric radii showdifferences in clustering strength, even in the catalog where the true assemblybias signal was erased. We show that this is a result of contamination of themember galaxy sample from interlopers along the line-of-sight. This undoubtedlyshows that the particular methodology adopted in the previous studies cannot beused to claim a detection of the assembly bias signal. We figure out thetell-tale signatures of such contamination, and show that the observationaldata also shows similar signatures. Furthermore, we also show that projectioneffects in optical galaxy clusters can bias the inference of the 3-dimensionaledges of galaxy clusters (splashback radius), so appropriate care should betaken while interpreting the splashback radius of optical clusters.

On the measurements of assembly bias and splashback radius using optically selected galaxy clusters