Plot illustrating different DM spike profiles for a SMBH with mass M_BH = 10⁹ M_⊙. The corresponding host halo has a mass of M_vir ≈ 3 × 10¹³ M_⊙. The solid lines correspond to spike profiles with indices γ = (3 + a)/4, where a is related to the nature of the velocity dependence of the cross-section characterised via σ ∝ v^−a. The dashed line corresponds to the SIDM halo of the host halo outside the spike radius. Dotted lines at the end mark a NFW profile of the host halo in the outer parts. Dash-dotted lines correspond to the CDM spike with γ = 7/3.