Opacity (top) and cumulative optical depth (bottom) as a function of r/r_S for M_BH = 10⁻¹⁶, 10⁻¹³, and 10⁻¹¹ M_⊙. Thick translucent lines show the total opacity; dashed lines show Klein–Nishina-corrected scattering; and dotted lines show Kramers free–free absorption. The vertical dotted line marks the θ_e = 1 boundary separating the Klein–Nishina-suppressed and Thomson regimes. The horizontal dashed line in the lower panel marks τ = 1.