[Paper Review] Concentrations and Assembly Histories of Dark Matter Halos

Risa H. Wechsler, James S. Bullock+3 more|arXiv (Cornell University)|Nov 5, 2001

Dark Matter and Cosmic Phenomena3 citations

TL;DR

This paper establishes a tight, universal correlation between dark matter halo concentration and its mass assembly history, showing that halo concentration at any epoch is primarily determined by its formation time, with $ c_{\text{vir}} = c_1 a_o / a_c $. The relation explains both the mass and redshift dependence of halo concentrations and accounts for most of the observed scatter in concentration for halos of equal mass.

ABSTRACT

We study the relation between the density profiles of dark matter halos and their mass assembly histories, using a statistical sample of halos in a high-resolution N-body simulation of the LCDM cosmology. For each halo at z=0, we identify its merger-history tree, and determine concentration parameters c_vir for all progenitors, thus providing a structural merger tree for each halo. We fit the mass accretion histories by a universal function with one parameter, the formation epoch a_c, defined when the log mass accretion rate dlog M/doga falls below a critical value. We find that late forming galaxies tend to be less concentrated, such that c_vir ``observed'' at any epoch a_obs is strongly correlated with a_c via c_vir=c_1 a_obs/a_c. Scatter about this relation is mostly due to measurement errors in c_vir and a_c, implying that the actual spread in c_vir for halos of a given mass can be mostly attributed to scatter in a_c. Because of the direct connection between halo concentration and velocity rotation curves, and because of probable connections between halo mass assembly history and star formation history, the tight correlation between these properties provides an essential new ingredient for galaxy formation modeling.

Motivation & Objective

• To understand the physical origin of the scatter in dark matter halo concentration for halos of equal mass.
• To investigate the connection between halo density profiles and their mass accretion histories in a ΛCDM cosmology.
• To quantify how halo formation time, defined via the accretion rate slope, determines concentration.
• To develop a universal functional form linking concentration to formation epoch for use in galaxy formation modeling.

Proposed method

• Conducted a high-resolution N-body simulation of a flat ΛCDM universe with $ \Omega_m = 0.3 $, $ h = 0.7 $, and $ \sigma_8 = 1.0 $, using the ART code.
• Tracked $ 256^3 $ cold dark matter particles from $ z = 40 $ to $ z = 0 $ in a 60 $ h^{-1} $ Mpc box, generating halo catalogs at 36 redshift snapshots.
• Measured NFW density profiles for halos with >200 particles ($ M > 2.2 \times 10^{11} h^{-1} M_\odot $) and computed $ c_{\text{vir}} = R_{\text{vir}} / R_s $ for each.
• Constructed full structural merger trees for ~3000 halos by tracing progenitors backward in time and determining $ c_{\text{vir}} $ at each epoch.
• Fitted mass accretion histories using the functional form $ M(a) = M_o \exp\left[ -a_c S (a_o/a - 1) \right] $, defining $ a_c $ as the scale factor where $ d\log M / d\log a < S $.
• Derived the universal relation $ c_{\text{vir}} = c_1 a_o / a_c $, where $ c_1 \approx 4.1 $, and tested its validity across redshifts and masses.

Experimental results

Research questions

• RQ1 How does the mass assembly history of a dark matter halo influence its concentration parameter?
• RQ2 Can the scatter in halo concentration at fixed mass be explained by variations in formation time?
• RQ3 Is there a universal functional form that links halo concentration to its formation epoch across different redshifts and masses?
• RQ4 To what extent does the concentration at a given epoch depend on the halo's accretion history?
• RQ5 How does the formation time $ a_c $, defined by the accretion rate slope, correlate with observable concentration $ c_{\text{vir}} $?

Key findings

• The concentration parameter $ c_{\text{vir}} $ at any epoch $ a_o $ is tightly correlated with the formation epoch $ a_c $, following $ c_{\text{vir}} = c_1 a_o / a_c $, with $ c_1 \approx 4.1 $.
• The scatter in $ c_{\text{vir}} $ for halos of fixed mass is primarily due to scatter in $ a_c $, not intrinsic scatter in concentration for a given formation time.
• The relation $ c_{\text{vir}} = c_1 a_o / a_c $ accurately describes the dependence of concentration on mass and redshift across the full range of halo masses and redshifts studied.
• Late-forming halos are systematically less concentrated, with $ c_{\text{vir}} $ decreasing as $ a_c $ increases.
• The functional form $ M(a) = M_o \exp\left[ -a_c S (a_o/a - 1) \right] $ provides an excellent fit to individual halo mass accretion histories.
• The characteristic formation time $ a_c $ is invariant under redshift rescaling, making it a robust, universal halo property.