# Clusters Have Edges: The Projected Phase SpaceStructure of SDSS redMaPPer Clusters

**Authors:** Paxton Tomooka, Eduardo Rozo, Erika L. Wagoner, Han Aung, Daisuke Nagai, Sasha Safonova  
**arXiv:** [2003.11555](https://arxiv.org/abs/2003.11555)  
**Date:** 2020-03-25  
**Summary page:** https://www.summarizepaper.com/en/paper/2003.11555v1/

## Key points

- The study investigates the distribution of line-of-sight velocities of galaxies near SDSS redMaPPer galaxy clusters.
- Galaxies are classified into two groups: those dynamically associated with the cluster and random line-of-sight projections.
- Both the fraction of galaxies associated with the clusters and the velocity dispersion exhibit a distinct feature at a radial scale known as the "edge radius" (R_edge).
- R_edge is approximately 2.2 times the cluster radius assigned by redMaPPer (R_lambda) and represents a true "cluster edge."
- A model is proposed that divides galaxies associated with a cluster into two components: orbiting galaxies within the halo and infalling galaxies.
- This model provides an explanation for the observed sharp feature in both fraction and velocity dispersion profiles.
- The significance of R_edge is supported by a companion paper that investigates three-dimensional phase space distributions of dark matter substructures in numerical simulations.
- R_edge coincides with a suitably defined splashback radius in the companion paper's findings.
- The study sheds light on the projected phase space structure of SDSS redMaPPer galaxy clusters and highlights the absence of orbiting structures beyond R_edge.

## Summary

In this study, the authors investigate the distribution of line-of-sight velocities of galaxies near SDSS redMaPPer galaxy clusters. By analyzing the velocities, they classify galaxies into two groups: those that are dynamically associated with the cluster and those that are random line-of-sight projections. The authors find that both the fraction of galaxies associated with the clusters and the velocity dispersion exhibit a distinct feature as a function of radius. Interestingly, this feature occurs at a radial scale known as the "edge radius," denoted as R_edge, which is approximately 2.2 times the cluster radius assigned by redMaPPer (R_lambda). The edge radius represents a true "cluster edge" because no orbiting structures exist beyond this point. To explain these findings, the authors propose a model that further divides galaxies dynamically associated with a galaxy cluster into two components: one consisting of galaxies orbiting within the halo and another comprising infalling galaxies. This model provides a natural explanation for the observed sharp feature in both the fraction and velocity dispersion profiles. The significance of R_edge is further supported by a companion paper (Aung et al., 2020), which investigates three-dimensional phase space distributions of dark matter substructures in numerical simulations. The companion paper demonstrates that R_edge coincides with a suitably defined splashback radius. Overall, this study sheds light on the projected phase space structure of SDSS redMaPPer galaxy clusters and highlights the existence of an edge radius beyond which no orbiting structures are found. These findings contribute to our understanding of galaxy cluster dynamics and provide valuable insights for future studies in cosmology and astrophysics.