Resolving the structure of cold dark matter halos

We present results of a convergence study in which we compare the density profiles of cold dark matter halos simulated with varying mass and force resolutions. We show that although increasing the mass and force resolution allows one to probe deeper into the inner halo regions, the halo profiles converge on scales larger than the effective spatial resolution of the simulation. This resolution is defined by both the force softening and 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 increases further. In the simulations presented in this paper, we are able to probe the density profile of a relaxed isolated galaxy-size halo on scales r = (0.005-1)r(vir). We find that the density distribution at resolved scales can be well approximated by the profile suggested by Moore and coworkers: rho proportional to x(-1.5)(1 + x(1.5))(-1), where x = r/r(s) and r(s) is the characteristic radius. The analytical profile proposed by Navarro and coworkers, rho proportional to 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 on scales well below 0.01r(vir). We also find that halos of similar mass may have density profiles with somewhat different parameters (characteristic radius, maximum rotation velocity, etc.) and shapes. We associate this scatter in properties with differences in halo merger histories and with the amount of substructure present in the analyzed halos.