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 ρNFW (r) ∝ r (r + rs) −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 ∼ 10 to ∼ 10, we have also shown that rs, the radius where the log-slope is -2, can be determined accurately for halos with as few as ∼ 10 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 ΛCDM cosmology, we have found that the concentration cvir ≡ Rvir/rs has a log-normal distribution, with 1σ ∆(log cvir) = 0.18 at a given mass, corresponding to a scatter in maximum rotation velocities of ∆Vmax/Vmax = 0.12. The average concentration declines with redshift at fixed mass as cvir(z) ∝ (1 + z) . 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 ΛCDM simulations. But we also note that the very limited evolution with redshift of the velocity function predicted by ΛCDM 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.