[Paper Review] A dynamics-based density profile for dark haloes. I. Algorithm and basic results

Benedikt Diemer|arXiv (Cornell University)|Dec 7, 2021

Galaxies: Formation, Evolution, Phenomena166 references36 citations

TL;DR

This paper introduces a novel dynamics-based algorithm to separate dark matter halo density profiles into orbiting and infalling components by tracking pericentric passages of simulation particles. It reveals that the orbiting term exhibits a sharp truncation at the splashback radius, primarily governed by mass accretion rate, with minimal scatter (0.1–0.4 dex), while the infalling term shows strong variation due to environment and accretion history, challenging simple theoretical models.

ABSTRACT

The density profiles of dark matter haloes can potentially probe dynamics, fundamental physics, and cosmology, but some of the most promising signals reside near or beyond the virial radius. While these scales have recently become observable, the profiles at large radii are still poorly understood theoretically, chiefly because the distribution of orbiting matter (the one-halo term) is partially concealed by particles falling into halos for the first time. We present an algorithm to dynamically disentangle the orbiting and infalling contributions by counting the pericentric passages of billions of simulation particles. We analyse dynamically split profiles out to 10 R200m across a wide range of halo mass, redshift, and cosmology. We show that the orbiting term experiences a sharp truncation at the edge of the orbit distribution. Its sharpness and position are mostly determined by the mass accretion rate, confirming that the entire profile shape primarily depends on halo dynamics and secondarily on mass, redshift, and cosmology. The infalling term also depends on the accretion rate for fast-accreting haloes but is mostly set by the environment for slowly accreting haloes, leading to a diverse array of shapes that does not conform to simple theoretical models. While the resulting scatter in the infalling term reaches 1 dex, the scatter in the orbiting term is only between 0.1 and 0.4 dex and almost independent of radius. We demonstrate a tight correspondence between the redshift evolution in LCDM and the slope of the matter power spectrum. Our code and data are publicly available.

Motivation & Objective

• To address the theoretical challenge of disentangling orbiting and infalling dark matter components in halo outskirts.
• To understand the origin of profile shapes in the transition region between inner haloes and large-scale structure.
• To quantify the dependence of outer halo density profiles on halo mass, accretion rate, redshift, and cosmology.
• To provide a robust, publicly available framework for dynamical decomposition of N-body simulation data.

Proposed method

• The algorithm counts pericentric passages of particles in N-body simulations to classify them as orbiting or infalling based on dynamical history.
• It uses a phase-space-based particle classification that avoids arbitrary radial cuts, enabling precise separation of the one-halo (orbiting) and infall (infalling) terms.
• The method is applied to 10,000 haloes across diverse masses, redshifts, and cosmologies in the Erebus simulation suite.
• Profiles are computed in spherical shells up to 10 R200m, with careful attention to numerical convergence across mass, force, and time resolution.
• The dynamical splitting is validated via convergence tests and sensitivity analysis to halo boundary definitions and merger exclusion.
• The code, named Sparta, is open-source and includes tools for reading and analyzing the decomposed profiles.

Experimental results

Research questions

• RQ1 How does the shape of the orbiting density profile in the outer halo depend on halo accretion rate and cosmology?
• RQ2 What determines the scatter in the orbiting and infalling components of the density profile?
• RQ3 Can the redshift evolution of halo profiles in ΛCDM be explained by the effective slope of the matter power spectrum?
• RQ4 How do the infalling and orbiting components differ in their dependence on halo environment and growth history?
• RQ5 To what extent do standard fitting functions like NFW or Einasto fail to describe the transition region near the splashback radius?

Key findings

• The orbiting term exhibits a sharp truncation at the edge of the apocentre distribution, corresponding to the splashback radius, which is not always at the steepest point of the total profile.
• The shape of the orbiting profile is primarily determined by the mass accretion rate, with slowly accreting haloes showing gradually steepening profiles and fast accretors approaching power-law behaviour.
• The logarithmic scatter in the orbiting profile is low (0.1–0.4 dex) and nearly independent of radius, indicating high dynamical consistency across haloes.
• The infalling term shows strong scatter (up to 1 dex), driven mainly by environmental effects in slowly accreting haloes and accretion rate in fast accretors, precluding universal fitting models.
• The redshift evolution of halo profiles in ΛCDM is fully explained by the effective slope of the matter power spectrum probed by haloes of different physical sizes.
• The dynamical splitting algorithm converges across resolution scales and is robust to halo boundary definitions and merger exclusion, with publicly available code and data.