Dark matter density profiles from the Jeans equation

We make a simple analytical study of radial profiles of dark matter structures, with special attention to the question of the central radial density profile. We let our theoretical assumptions be guided by results from numerical simulations, and show that at any radius where both the radial density profile, ρ, and the phase-space-like density profile, ρ/σǫ, are exact power laws, the only allowed density slopes in agreement with the spherical symmetric and isotropic Jeans equation are in the range 1 < β < 3, where β ≡ −dlnρ/dlnr. We also allow for a radial variation of these power laws, as well as anisotropy, and show how this allows for more shallow central slopes.