The real and apparent convergence of N-body simulations of the dark matter structures: Is the Navarro-Frenk-White profile real?

While N-body simulations suggest a cuspy profile in the centra of the dark matter halos of galaxies, the majority of astronomical observations favor a relatively soft cored density distribution of these regions. The routine method of testing the convergence of N-body simulations (in particular, the negligibility of two-body scattering effect) is to find the conditions under which formed structures is insensitive to numerical parameters. The results obtained with this approach suggest a surprisingly minor role of the particle collisions: the central density profile remains untouched and close to the Navarro-Frenk-White shape, even if the simulation time significantly exceeds the collisional relaxation time τr. In order to check the influence of the unphysical test body collisions we use the Fokker-Planck equation. It turns out that a profile ρ∝r-β where β≃1 is an attractor: the Fokker-Planck diffusion transforms any reasonable initial distribution into it in a time shorter than τr, and then the cuspy profile should survive much longer than τr, since the Fokker-Planck diffusion is self-compensated if β≃1. Thus the purely numerical effect of test body scattering may create a stable NFW-like pseudosolution. Moreover, its stability may be mistaken for the simulation convergence. We present analytical estimations for this potential bias effect and call for numerical tests. For that purpose, we suggest a simple test that can be performed as the simulation progresses and would indicate the magnitude of the collisional influence and the veracity of the simulation results.