A UNIVERSAL MODEL FOR HALO CONCENTRATIONS

We present a numerical study of dark matter halo concentrations in Lambda CDM and self-similar cosmologies. We show that the relation between concentration, c, and peak height, nu, exhibits the smallest deviations from universality if halo masses are defined with respect to the critical density of the universe. These deviations can be explained by the residual dependence of concentration on the local slope of the matter power spectrum, n, which affects both the normalization and shape of the c-nu relation. In particular, there is no well-defined floor in the concentration values. Instead, the minimum concentration depends on redshift: at fixed nu, halos at higher z experience steeper slopes n, and thus have lower minimum concentrations. We show that the concentrations in our simulations can be accurately described by a universal seven-parameter function of only. and n. This model matches our Lambda CDM results to less than or similar to 5% accuracy up to z approximate to 6, and matches scale-free Omega(m) = 1 models to less than or similar to 15%. The model also reproduces the low concentration values of Earth-mass halos at z approximate to 30, and thus correctly extrapolates over 16 orders of magnitude in halo mass. The predictions of our model differ significantly from all models previously proposed in the literature at high masses and redshifts. Our model is in excellent agreement with recent lensing measurements of cluster concentrations.