Mass density ρ_b(r) = M_bp_b(r) of a marginally stable BH population given by the solution of the system (25) and (26). The average individual BH mass is assumed to be m_b = 10 M_⊙ and the Spitzer parameter equals the marginal value of the onset of the instability S = 0.25. The BH population is embedded in a globular cluster with average individual mass density m_⋆ = 0.5 M_⊙ and half-mass radius r_hm = 1 pc. The black dotted line represents the Plummer mass density profile of the host globular cluster.