# Accurate Model of the Projected Velocity Distribution of Galaxies in Dark Matter Halos

**Authors:** Han Aung, Daisuke Nagai, Eduardo Rozo, Brandon Wolfe, Susmita Adhikari  
**arXiv:** [2204.13131](https://arxiv.org/abs/2204.13131)  
**Date:** 2022-04-27  
**Summary page:** https://www.summarizepaper.com/en/paper/2204.13131v1/

## Key points

- Aung et al. present a highly accurate model for the line-of-sight velocity distribution of galaxies around dark matter halos.
- The model is developed and tested using synthetic galaxy catalogs generated with the UniverseMachine run on the Multi-Dark Planck 2 N-body simulations.
- The authors focus on understanding the kinematics of galaxies around clusters and decompose them into three distinct classes: orbiting, infalling, and interloping galaxies.
- These three types of galaxies can be statistically distinguished using only projected line-of-sight velocity information.
- The halo edge radius inferred from the line-of-sight velocity dispersion serves as an excellent proxy for the three-dimensional halo edge radius.
- Accurate recovery of the full velocity dispersion profile for each population of galaxies is possible.
- Orbiting and infalling galaxies have five independent parameters in their velocity dispersion profiles, including three radial scales and two velocity dispersion amplitudes, all correlated with mass.
- Redundancies in the velocity dispersion profiles allow for nontrivial systematics checks from a single data set, providing valuable insights into galaxy cluster properties and enabling more robust cosmological and astrophysical constraints.
- Potential applications of this new model include detecting the edge radius of halos and constraining cosmology and astrophysics using upcoming spectroscopic surveys.

## Summary

In their study, Aung et al. present a highly accurate model for the line-of-sight velocity distribution of galaxies around dark matter halos. The model is developed and tested using synthetic galaxy catalogs generated with the UniverseMachine run on the Multi-Dark Planck 2 N-body simulations. The authors focus on understanding the kinematics of galaxies around clusters and decompose them into three distinct classes: orbiting, infalling, and interloping galaxies. They demonstrate that these three types of galaxies can be statistically distinguished using only projected line-of-sight velocity information. One key finding of their study is that the halo edge radius inferred from the line-of-sight velocity dispersion serves as an excellent proxy for the three-dimensional halo edge radius. This has important implications for accurately determining the spatial extent of dark matter halos. Furthermore, Aung et al. show that they can accurately recover the full velocity dispersion profile for each population of galaxies. Specifically, they find that the velocity dispersion profiles of orbiting and infalling galaxies contain five independent parameters, including three distinct radial scales and two velocity dispersion amplitudes, all of which are correlated with mass. Importantly, these redundancies in the velocity dispersion profiles allow for nontrivial systematics checks from a single data set; this provides valuable insights into galaxy cluster properties and enables more robust cosmological and astrophysical constraints. The authors discuss several potential applications of their new model, including detecting the edge radius of halos and constraining cosmology and astrophysics using upcoming spectroscopic surveys. Overall, this study presents a significant advancement in our understanding of galaxy kinematics around dark matter halos by providing accurate modeling techniques with wide-ranging implications for various areas of astrophysics and cosmology research.