We use two very large cosmological simulations to study how the density profiles of relaxed \Lambda CDM 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 \sim 0.16 for present-day galaxy halos to \alpha \sim 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 \sim 3 the average concentration of relaxed halos does not vary appreciably over the mass range accessible to our simulations ( M \lower 3.225 pt \hbox { $ \sim$ } \hbox to 0.0 pt { \raise 1.161 pt \hbox { $ > $ } } 3 % \times 10 ^ { 11 } h ^ { -1 } M _ { \odot } ) .
Furthermore , in our biggest simulation , the average concentration of the most massive , relaxed halos is constant at \langle c _ { 200 } \rangle \sim 3.5 to 4 for 0 \leq z \leq 3 .
These results agree well with those of Zhao et al ( 2003b ) and support the idea that halo densities reflect the density of the universe at the time they formed , as proposed by Navarro , Frenk & White ( 1997 ) .
With their original parameters , the NFW prescription overpredicts halo concentrations at high redshift .
This shortcoming can be reduced by modifying the definition of halo formation time , although the evolution of the concentrations of Milky Way mass halos is still not reproduced well .
In contrast , the much-used revisions of the NFW prescription by Bullock et al .
( 2001 ) and Eke , Navarro & Steinmetz ( 2001 ) predict a steeper drop in concentration at the highest masses and stronger evolution with redshift than are compatible with our numerical data .
Modifying the parameters of these models can reduce the discrepancy at high masses , but the overly rapid redshift evolution remains .
These results have important implications for currently planned surveys of distant clusters .