Evolution of mass distribution in cold dark matter 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) proportional to 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 similar to 10(3) to similar to 10(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 similar to 10(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 ACDM cosmology, we have found that the concentration c(vir) = R-vir/r(s) has a log-normal distribution, with 1sigma Delta(log c(vir)) = 0.18 at a given mass, corresponding to a scatter in maximum rotation velocities of DeltaV(max)/V-max = 0.12. The average concentration declines with redshift at fixed mass as c(vir)(z) proportional to (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 ACDM simulations. But we also note that the very limited evolution with redshift of the velocity function predicted by ACDM 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.