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We consider the behavior of spherically symmetric Einasto halos composed of gravitating particles in the Fokker-Planck approximation. This approach allows us to consider the undesirable influence of close encounters in the N-body simulations more adequately than the generally accepted criteria. The Einasto profile with index n approximate to 6 is a stationary solution of the Fokker-Planck equation in the halo center. There are some reasons to believe that the solution is an attractor. Then the Fokker-Planck diffusion tends to transform a density profile to the equilibrium one with the Einasto index n approximate to 6. We suggest this effect as a possible reason why the Einasto index n approximate to 6 occurs so frequently in the interpretation of N-body simulation results. The results obtained cast doubt on generally accepted criteria of N-body simulation convergence.
Dwarf spheroidal galaxies are among the most promising targets for detecting signals of Dark Matter (DM) annihilations. The H.E.S.S. experiment has observed five of these systems for a total of about 130 hours. The data are re-analyzed here, and, in the absence of any detected signals, are interpreted in terms of limits on the DM annihilation cross section. Two scenarios are considered: i) DM annihilation into mono-energetic gamma-rays and ii) DM in the form of pure WIMP multiplets that, annihilating into all electroweak bosons, produce a distinctive gamma-ray spectral shape with a high-energy peak at the DM mass and a lower-energy continuum. For case i), upper limits at 95% confidence level of about <sigma upsilon > less than or similar to 3 x 10(-25) cm(3) s(-1) are obtained in the mass range of 400 GeV to 1TeV. For case ii), the full spectral shape of the models is used and several excluded regions are identified, but the thermal masses of the candidates are not robustly ruled out.