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. (2016) and More et al. (2016). We mimic the optical cluster
detection algorithm and apply it to two different mock catalogs generated from
the Millennium simulation galaxy catalog, 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 catalog 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 shows similar signatures. Furthermore, we also show that projection
effects in optical galaxy clusters can bias the inference of the 3-dimensional
edges of galaxy clusters (splashback radius), so appropriate care should be
taken while interpreting the splashback radius of optical clusters.
