The redshift dependence of the structure of massive LCDM halos

We use two very large cosmological simulations to study how the density profiles of relaxed LCDM dark halos depend on redshift and on halo mass. We confirm that these profiles deviate slightly but systematically from the NFW form and are better approximated by the empirical formula, $d\log\rho/d\log r \propto r^{\alpha}$, first used by Einasto to fit star counts in the Milky Way. The best-fit value of the additional shape parameter, alpha, increases gradually with mass, from alpha~0.16 for present-day galaxy halos to alpha~0.3 for the rarest and most massive clusters. Halo concentrations depend only weakly on mass at z=0, and this dependence weakens further at earlier times. At z~3 the average concentration of relaxed halos does not vary appreciably over the mass range accessible to our simulations (M > 3e11Msun/h). Furthermore, in our biggest simulation the average concentration of the most massive, relaxed halos is constant at c_200 ~3.5 to 4 for 0<=z<=3. These results support the idea that halo densities reflect the density of the universe at the time they formed. They agree surprisingly well with the model originally proposed by Navarro, Frenk & White (1997) and they contradict the much-used revisions of this model by Bullock et al. (2001) and Eke, Navarro & Steinmetz (2001). The latter predict a much steeper drop in concentration at the highest masses and much stronger evolution of concentration with redshift than are compatible with our numerical data. These results have important implications for currently planned surveys of distant clusters.