Assembly bias and splashback in galaxy clusters

We use publicly available data for the Millennium Simulation to explore the implications of the recent detection of assembly bias and splashback signatures in a large sample of galaxy clusters. These were identified in the Sloan Digital Sky Survey/Data Release 8 (SDSS/DR8) photometric data by the redMaPPer algorithm and split into high- and low-concentration subsamples based on the projected positions of cluster members. We use simplified versions of these procedures to build cluster samples of similar size from the simulation data. These match the observed samples quite well and show similar assembly bias and splashback signals. Previous theoretical work has found the logarithmic slope of halo density profiles to have a well-defined minimum whose depth decreases and whose radius increases with halo concentration. Projected profiles for the observed and simulated cluster samples show trends with concentration which are opposite to these predictions. In addition, for high-concentration clusters the minimum slope occurs at significantly smaller radius than predicted. We show that these discrepancies all reflect confusion between splashback features and features imposed on the profiles by the cluster identification and concentration estimation procedures. The strong apparent assembly bias is not reflected in the three-dimensional distribution of matter around clusters. Rather it is a consequence of the preferential contamination of low-concentration clusters by foreground or background groups.