Cold dark matter haloes in the Planck era: evolution of structural parameters for Einasto and NFW profiles

We present the evolution of the structure of relaxed cold dark matter (CDM) haloes in the cosmology from the Planck satellite. Our simulations cover five decades in halo mass, from dwarf galaxies to galaxy clusters. Because of the increased matter density and power spectrum normalization the concentration-mass relation in the Planck cosmology has a similar to 20 per cent higher normalization at redshift z = 0 compared to Wilkinson Microwave Anisotropy Probe cosmology. We confirm that CDM haloes are better described by the Einasto profile; for example, at scales near galaxy half-light radii CDM haloes have significantly steeper density profiles than implied by Navarro-Frenk-White (NFW) fits. There is a scatter of similar to 0.2 dex in the Einasto shape parameter at fixed halo mass, adding further to the diversity of CDM halo profiles. The evolution of the concentration-mass relation in our simulations is not reproduced by any of the analytic models in the literature. We thus provide a simple fitting formula that accurately describes the evolution between redshifts z = 5 and 0 for both NFW and Einasto fits. Finally, the observed concentrations and halo masses of spiral galaxies, groups and clusters of galaxies at low redshifts are in good agreement with our simulations, suggesting only mild halo response to galaxy formation on these scales.