a) Stationary radial density ρ(r) ∝ dN/ dr from the Kepler map at J = 0.005 with u = 17 at time t_S (red curve) and u = 0.035 at time t_u ≈ 4 × 10⁸T_p (black curve); data from the dark map at m_p/M = 10^-3 are shown by the blue curve at u = 17 and time t_S for the Sun-Jupiter case, and by the green curve at u = 0.035 and t_S for the SMBH; the normalization is fixed as , r_p = 1. b) Volume density ρ_v = ρ/r² from the data of panel a), the dashed line shows the slope −2.