On a unified theory of cold dark matter halos based on collisionless Boltzmann–Poisson polytropes

Collisionless particles in dark matter halos constitute ideal systems for applying the theory of collisionless Boltzmann–Poisson (BP) polytropes. This analysis provides a powerful complementary method for studying galactic halos. A comparison of the results obtained here and the Navarro, Frenk and White (NFW), Isothermal and Burkert profiles is shown. We obtain very good agreement with NFW profiles with errors of the order of 3%. The best polytropic profile for a finite mass halo is close to the Plummer/Schuster profile. We can explore in detail the central region and find the inner profile that complements the NFW profile. A simple formula for the inner region to which the NFW should converge for R→0 could be ρ=ρ0(1−(R/C)2)4.7, ρ0 and C being constants. Boltzmann–Poisson polytropes provide a theoretical approach fully compatible with the universal NFW profiles at intermediate radii and complementing them at low radii: they permit the determination of the density profile in the inner kiloparsec inaccessible to N-body simulations because of resolution limits.