Resolving the structure of cold dark matter halos

We present results of a convergence study in which we compare the density p rofiles of cold dark matter halos simulated with varying mass and force res olutions. We show that although increasing the mass and force resolution al lows one to probe deeper into the inner halo regions, the halo profiles con verge on scales larger than the "effective" spatial resolution of the simul ation. This resolution is defined by both the force softening and the mass resolution. On radii larger than the "effective" spatial resolution, densit y profiles do not experience any systematical trends when the number of par ticles or the force resolution increases further. In the simulations presen ted in this paper, we are able to probe the density profile of a relaxed is olated galaxy-size halo on scales r = (0.005-1)r(vir). We find that the den sity distribution at resolved scales can be well approximated by the profil e 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 analytica l 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 analy tical profiles fit well because for high-concentration galaxy-size halos, t he differences between these profiles become significant only on scales wel l below 0.01r(vir). We also find that halos of similar mass may have densit y profiles with somewhat different parameters (characteristic radius, maxim um rotation velocity, etc.) and shapes. We associate this scatter in proper ties with differences in halo merger histories and with the amount of subst ructure present in the analyzed halos.