# A dynamics-based density profile for dark haloes -- II. Fitting function

**Authors:** Benedikt Diemer  
**arXiv:** [2205.03420](https://arxiv.org/abs/2205.03420)  
**Date:** 2022-05-06  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2205.03420v1/

## Key points

- Authors aim to design a more physically motivated fitting function for describing dark matter halo density profiles
- Utilize profiles that have been dynamically split into orbiting and infalling particles
- Approach captures shapes of orbiting and infalling terms separately
- Fitting function should accurately describe profiles in transition region, be flexible, work across all halo masses, redshifts, cosmologies, and accretion rates
- Propose a five-parameter fitting function based on truncated Einasto profile for orbiting term
- Infalling profile modeled as power law in overdensity transitioning to constant at halo center
- Proposed fitting functions fit averaged total profiles in simulations with about 5% accuracy across wide range of parameter space
- When specific values fixed for α and β (0.18 and 3 respectively), formula becomes three-parameter model that fits individual halos better than Einasto profile on average
- Simulations used are part of Erebos suite of dissipationless N-body simulations with different box sizes and resolutions covering two ΛCDM cosmologies and four self-similar Einstein-de Sitter universes with power-law initial spectra
- Simulations run using Gadget2 code, halo identification performed using Rockstar halo finder
- Paper presents more physically motivated fitting function applicable across various properties such as mass, redshift, cosmology, or accretion rate

## Summary

In this paper, the authors aim to design a more physically motivated fitting function for describing the density profiles of dark matter haloes. They utilize profiles that have been dynamically split into orbiting and infalling particles, using an algorithm presented in a previous paper (referred to as Paper I). This approach allows them to capture the shapes of the orbiting and infalling terms separately. The authors require that their fitting function accurately describes the profiles even in the transition region, is flexible enough to apply to individual halos and different selection criteria, works across all halo masses, redshifts, cosmologies, and accretion rates, relies on as few free parameters as possible with clear physical interpretations, and exhibits minimal parameter degeneracies. To meet these requirements, the authors propose a five-parameter fitting function based on a truncated Einasto profile for the orbiting term. This profile includes normalization parameters, physically distinct scale and truncation radii, and α and β parameters that control how rapidly the profiles steepen. The infalling profile is modeled as a power law in overdensity that smoothly transitions to a constant at the halo center. The authors demonstrate that their proposed fitting functions fit averaged total profiles in simulations with about 5% accuracy across a wide range of parameter space including halo mass, redshift, cosmology, and accretion rate. When specific values are fixed for α and β (0.18 and 3 respectively), their formula becomes a three-parameter model for the orbiting term that fits individual halos better than the Einasto profile on average. The simulations used in this study are part of the Erebos suite of dissipationless N-body simulations. These simulations consist of 14 runs with different box sizes and resolutions covering two ΛCDM cosmologies (consistent with WMAP7 and Planck) as well as four self-similar Einstein-de Sitter universes with power-law initial spectra. The simulations were run using the Gadget2 code, and halo identification was performed using the Rockstar halo finder. Overall, this paper presents a more physically motivated fitting function for describing dark matter halo density profiles which accurately captures both orbiting and infalling terms while being applicable across various properties such as mass or redshift or cosmology or accretion rate. This work provides an invaluable tool for analyzing observed or simulated density profiles in future studies.