Clusters Have Edges: The Projected Phase SpaceStructure of SDSS
  redMaPPer Clusters
  We study the distribution of line-of-sight velocities of galaxies in the
vicinity of SDSS redMaPPer galaxy clusters. Based on their velocities, galaxies
can be split into two categories: galaxies that are dynamically associated with
the cluster, and random line-of-sight projections. Both the fraction of
galaxies associated with the galaxy clusters, and the velocity dispersion of
the same, exhibit a sharp feature as a function of radius. The feature occurs
at a radial scale $R_{\rm edge} \approx 2.2R_{\rm{\lambda}}$, where
$R_{\rm{\lambda}}$ is the cluster radius assigned by redMaPPer. We refer to
$R_{\rm edge}$ as the "edge radius." These results are naturally explained by a
model that further splits the galaxies dynamically associated with a galaxy
cluster into a component of galaxies orbiting the halo and an infalling galaxy
component. The edge radius $R_{\rm edge}$ constitutes a true "cluster edge", in
the sense that no orbiting structures exist past this radius. A companion paper
(Aung et al. 2020) tests whether the "halo edge" hypothesis holds when
investigating the full three-dimensional phase space distribution of dark
matter substructures in numerical simulations, and demonstrates that this
radius coincides with a suitably defined splashback radius.
