Detection of the Splashback Radius and Halo Assembly bias of Massive
  Galaxy Clusters
  We show that the projected number density profiles of SDSS photometric
galaxies around galaxy clusters displays strong evidence for the splashback
radius, a sharp halo edge corresponding to the location of the first orbital
apocenter of satellite galaxies after their infall. We split the clusters into
two subsamples with different mean projected radial distances of their members,
$\langle R_{\rm mem}\rangle$, at fixed richness and redshift, and show that the
sample with smaller $\langle R_{\rm mem}\rangle$ has a smaller ratio of the
splashback radius to the traditional halo boundary $R_{\rm 200m}$, than the
subsample with larger $\langle R_{\rm mem}\rangle$, indicative of different
mass accretion rates for the two subsamples. The same cluster samples were
recently used by Miyatake et al. to show that their large-scale clustering
differs despite their similar weak lensing masses, demonstrating strong
evidence for halo assembly bias. We expand on this result by presenting a
6.6-$\sigma$ detection of halo assembly bias using the cluster-photometric
galaxy cross-correlations. Our measured splashback radii are smaller, while the
strength of the assembly bias signal is stronger, than expectations from N-body
simulations based on the $\Lambda$-dominated, cold dark matter structure
formation model. Dynamical friction or cluster-finding systematics such as
miscentering or projection effects are not likely to be the sole source of
these discrepancies.
