# A dynamics-based density profile for dark haloes. I. Algorithm and basic results

**Authors:** Benedikt Diemer  
**arXiv:** [2112.03921](https://arxiv.org/abs/2112.03921)  
**Date:** 2021-12-07  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2112.03921v1/

## Key points

- Dynamics-based density profile for dark matter haloes
- Potential insights into dynamics, fundamental physics, and cosmology
- Promising signals near or beyond the virial radius
- Distribution of orbiting matter partially hidden by infalling particles
- Algorithm to separate contributions from orbiting and infalling matter
- Analysis of dynamically split profiles up to 10 times the R200m across various parameters
- Truncation in orbiting term determined by halo mass accretion rate
- Factors like mass, redshift, and cosmology have some influence on profile shape but are secondary to halo dynamics
- Infalling term influenced by accretion rate for fast-accreting haloes and environmental factors for slow-accreting ones
- Diverse array of shapes not conforming to simple theoretical models with scatter reaching up to 1 dex
- Smaller scatter in orbiting term ranging between 0.1 - 0.4 dex independent from radius
- Close correspondence between redshift evolution in LCDM model and slope of matter power spectrum supporting validity of LCDM as cosmological model

## Summary

This paper presents a dynamics-based density profile for dark matter haloes, focusing on the algorithm and basic results. The density profiles of dark matter haloes have the potential to provide insights into dynamics, fundamental physics, and cosmology. However, the most promising signals are often found near or beyond the virial radius, which has only recently become observable. One of the main challenges in understanding the density profiles at large radii is that the distribution of orbiting matter (known as the one-halo term) is partially hidden by particles falling into haloes for the first time. To address this issue, the authors propose an algorithm that dynamically separates the contributions from orbiting and infalling matter by counting pericentric passages of billions of simulation particles. Using this algorithm, they analyze dynamically split profiles up to 10 times the R200m (the radius within which a halo has an average density 200 times higher than the critical density) across a wide range of halo mass, redshift, and cosmology. The results reveal important insights into both orbiting and infalling profiles. The study finds that the orbiting term experiences a sharp truncation at the edge of its orbit distribution. The sharpness and position of this truncation are primarily determined by halo mass accretion rate, indicating that halo dynamics play a crucial role in shaping its entire profile. Additionally, while factors such as mass, redshift and cosmology have some influence on profile shape; they are secondary compared to halo dynamics. The infalling term also depends on accretion rate for fast-accreting haloes but is mostly influenced by environmental factors for slowly accreting ones; leading to diverse array of shapes not conforming to simple theoretical models with scatter reaching up to 1 dex (an order of magnitude). In contrast; scatter in orbiting term is much smaller ranging between 0.1 - 0.4 dex remaining almost independent from radius. The authors demonstrate close correspondence between redshift evolution in LCDM model and slope of matter power spectrum further supporting validity of LCDM as cosmological model.