The mass-concentration-redshift relation of cold and warm dark matter haloes

We use a suite of cosmological simulations to study the mass-concentration-redshift relation, c(M,z), of dark matter halos. Our simulations include standard Λ-cold dark matter (CDM) models, and additional runs with truncated power spectra, consistent with a thermal warm dark matter (WDM) scenario. We find that the mass profiles of CDM and WDM halos are self-similar and well approximated by the Einasto profile. The c(M,z) relation of CDM halos is monotonic: concentrations decrease with increasing virial mass at fixed redshift, and decrease with increasing redshift at fixed mass. The mass accretion histories (MAHs) of CDM halos are also scale-free, and can be used to infer concentrations directly. These results do not apply to WDM halos: their MAHs are not scale-free because of the characteristic scale imposed by the power-spectrum suppression. Further, the WDM c(M,z) relation is non-monotonic: concentrations peak at a mass scale dictated by the truncation scale, and decrease at higher and lower masses. We show that the assembly history of a halo can still be used to infer its concentration, provided that the total mass of its progenitors is considered (the "collapsed mass history"; CMH), rather than just that of its main ancestor. This exploits the scale-free nature of CMHs to derive a simple scaling that reproduces the mass-concentration-redshift relation of both CDM and WDM halos over a vast range of halo masses and redshifts. Our model therefore provides a robust account of the mass, redshift, cosmology and power spectrum dependence of dark matter halo concentrations.