Heat map of the characteristic resonant optical depth in the full model. The parameters are as follows: B_p = 5 × 10¹³ G, R = 10 km, kT_e = 10 keV, kT_s = 0.6 keV, a hot spot at (θ_s, ϕ_s) = (53°, 37°), and viewing angle θ = 35°. Contours for τ₀ = 1.0, 0.4, and 0.1 delineate the validity regime of the single-scattering/first-order approximation.