Characteristic density profiles corresponding to each relative energy α = ϵ/ϵ_max in a Schuster-Plummer potential (the solid lines; Eq. (16)) and in a NFW potential (the dashed lines; Eq. (23)). The symbol β stands for the normalized radial coordinate r/r_sp. All energies contribute to the innermost regions (β ≪ 1) whereas only the smallest energies contribute to the outer halo (β ≫ 1).