The parameters of relaxation during the dark matter halo formation: how to fit observational data?

We show that moderate energy relaxation in the formation of dark matter haloes invariably leads to density profiles that match those observed in the central regions of galaxies. The density profile of the central region turns out to be universal and insensitive neither to the seed perturbation shape nor to the details of the relaxation process. The profile has a central core; multiplication of the central density on the core radius is almost independent of the halo mass, in accordance with observations. In the core area the density distribution behaves as an Einasto profile with small index ($n\sim 0.5$); at larger distances it has an extensive region with $\rho\propto r^{-2}$. This is exactly the shape that observations suggest for the central region of galaxies. On the other hand, this shape does not fit the galaxy cluster profiles. A possible explanation of this fact is that the relaxation is violent in the case of galaxy clusters; however, it is not violent enough when galaxies or smaller dark matter structures are considered. We discuss the reasons why it could be so.