Resolving the Structure of Cold Dark Matter Halos

We present results of a convergence study in which we compare the density profiles of CDM dark matter halos simulated with varying mass and force resolution. We show that although increasing the mass and force resolution allows one to probe deeper into the inner halo regions, the halo profiles converge at scales larger than the “effective ” spatial resolution of the simulation. This resolution is defined both by the force softening and by the mass resolution. On radii larger than the “effective ” spatial resolution, density profiles do not experience any systematical trends when the number of particles or the force resolution increase further. In the simulations presented in this paper, we are able to probe density profile of a relaxed isolated galaxy-size halo at scales r = (0.005 − 1)rvir. We find that the density distribution at resolved scales can be well approximated by the profile suggested by Moore et al.(1998): ρ ∝ x −1.5 (1 + x 1.5) −1, where x = r/rs and rs is the characteristic radius. The analytical profile proposed by Navarro et al. (1996) ρ ∝ x −1 (1 + x) −2, also provides a good fit, with the same relative errors of about 10 % for radii larger than 1 % of the virial radius. For this limit both analytical profiles fit well because for high-concentration galaxy-size halos the differences between these profiles become significant only at scales well below 0.01rvir. We also find that halos of similar mass may have somewhat different parameters (characteristic radius, maximum rotation velocity, etc.) and shapes of their density profiles. We associate this scatter in properties with differences in halo merger histories and the amount of substructure present in the analyzed halos. Subject headings: cosmology:theory – galaxy structure – methods: numerical 1.