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.
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