Evolution of Mass Distribution in CDM Halos

On the basis of a new convergence study of high-resolution N-body simulations, my colleagues and I now agree that the Navarro, Frenk, & White (1996) density profile $\rho_{NFW}(r) \propto r^{-1} (r+r_s)^{-2}$ is a good representation of typical dark matter halos of galactic mass. Comparing simulations of the same halo with numbers of particles ranging from $\sim10^3$ to $\sim10^6$, we have also shown that $r_s$, the radius where the log-slope is -2, can be determined accurately for halos with as few as $\sim10^3$ particles. Based on a study of thousands of halos at many redshifts in an Adaptive Refinement Tree (ART) simulation of a cosmological volume in a $\Lambda$CDM cosmology, we have found that the concentration $\cvir \equiv \Rvir/\rs$ has a log-normal distribution, with $1\sigma$ $\Delta (\log \cvir) = 0.18$ at a given mass, corresponding to a scatter in maximum rotation velocities of $\Delta \Vmax/\Vmax = 0.12$. The average concentration declines with redshift at fixed mass as $\cvir(z) \propto (1+z)^{-1}$. This may have important implications for galaxy rotation curves. Finally, we have found that the velocity function determined from galaxy luminosity functions plus luminosity-velocity relations agrees with the predictions from our $\Lambda$CDM simulations. But we also note that the very limited evolution with redshift of the velocity function predicted by $\Lambda$CDM conflicts with the data that is becoming available on the number density of bright galaxies unless there is significant evolution of the luminosity-velocity relation at $z>1$.