The mass–concentration–redshift relation of cold dark matter haloes

Abstract

We use the Millennium Simulation series to investigate the mass and redshift dependence of the concentration of equilibrium cold dark matter (CDM) halos. We extend earlier work on the relation between halo mass profiles and assembly histories to show how the latter may be used to predict concentrations for halos of all masses and at any redshift. Our results clarify the link between concentration and the "collapse redshift" of a halo as well as why concentration depends on mass and redshift solely through the dimensionless "peak height" mass parameter, ν(M, z) = δ crit (z)/σ(M, z). We combine these results with analytic mass accretion histories to extrapolate the c(M, z) relations to mass regimes difficult to reach through direct simulation. Our model predicts that, at given z, c(M ) should deviate systematically from a simple power law at high masses, where concentrations approach a constant value, and at low masses, where concentrations are substantially lower than expected from extrapolating published empirical fits. This correction may reduce the expected self-annihilation boost factor from substructure by about one order of magnitude. The model also reproduces the c(M, z) dependence on cosmological parameters reported in earlier work, and thus provides a simple and robust account of the relation between cosmology and the massconcentration-redshift relation of CDM halos.

A unified model for the spatial and mass distribution of subhaloes

“…This is calculated from equation (5) for a satellite with an NFW profile at accretion, with a mass of 10 −4 M 200 and a concentration determined from the average mass-concentration relation of Ludlow et al (2014). Overall, the tidal limit approximately delineates the upper envelope of the stripped masses, in agreement with expectation.…”

Exploring the liminality: properties of haloes and subhaloes in borderlinef(R) gravity

“…Recent simulations and modelling have indicated that the mass dependence of the halo concentration can be more complicated and is not a simple power law across the whole halo mass range (e.g. Prada et al 2012;Ludlow et al 2014;Ng et al 2014;Sanchez-Conde & Prada 2014). However, our GR simulation has too small a dynamical range to be affected by this.…”

Structure formation with suppressed small-scale perturbations

“…The concentration-mass relation is a direct consequence of the connection between concentrations and the halo accretion history, as shown explicitly in numerical studies of pure CDM cosmologies (Wechsler et al 2002;Ludlow et al 2014). In a Universe governed by hierarchical clustering, small haloes collapse first while the average density is high what translates into an increased value for the concentration.…”