Ratio of the velocity change, Δv = v(0)−v(t), due to dynamical friction acting on the BH for a velocity-dependent and a velocity-independent (constant) cross-section. All cross-sections were matched using the effective cross-section (Eq. 11), i.e. all cross-sections correspond to σ_eff/m = 3 × 10⁻⁸ cm² g⁻¹. The upper panel displays runs with frequent self-interactions, and the lower panel is for isotropic scattering.