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

We critically examine the methodology behind the claimed observational detection of halo assembly bias using optically selected galaxy clusters by Miyatake et al. and More et al. We mimic the optical cluster detection algorithm and apply it to two different mock catalogues generated from the Millennium simulation galaxy catalogue, one in which halo assembly bias signal is present, while the other in which the assembly bias signal has been expressly erased. We split each of these cluster samples into two using the average cluster-centric distance of the member galaxies to measure the difference in the clustering strength of the subsamples with respect to each other. We observe that the subsamples split by cluster-centric radii show differences in clustering strength, even in the catalogue where the true assembly bias signal was erased. We show that this is a result of contamination of the member galaxy sample from interlopers along the line of sight. This undoubtedly shows that the particular methodology adopted in the previous studies cannot be used to claim a detection of the assembly bias signal. We figure out the tell-tale signatures of such contamination, and show that the observational data also show similar signatures. Furthermore, we also show that projection effects in optical galaxy clusters can bias the inference of the 3D edges of galaxy clusters (splashback radius), so appropriate care should be taken while interpreting the splashback radius of optical clusters.