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

Abstract

We consider the reasons why a cuspy NFW-like profile persistently occurs in N-body simulations, in contradiction to some astronomical observations. 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 the shape of the 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 NFW, even if the simulation time significantly exceeds the collisional relaxation time ${\tau }_r$. We analyze the test body distribution in the halo center with help of the Fokker-Planck equation. It turns out that the Fokker-Planck diffusion transforms any reasonable initial distribution into NFW-like profile $\rho \propto r^{-1}$ in a time shorter than ${\tau }_r$. On the contrary, profile $\rho \propto r^{-1}$ should survive much longer, being a sort of attractor: the Fokker-Planck diffusion is self-compensated in this case. Thus the test body scattering may create a stable NFW-like pseudosolution that can be mixed up with the real convergence. This fact might help to eliminate the well-known 'cusp vs. core' problem.

7 pages, 1 figure

References in corpus (1)

• NGC 3741: dark halo profile from the most extended rotation curve

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