The relative O-mode and X-mode fluxes and polarization spectra for two first-order prescriptions (see Equation (28)) for the scattered-in component, compared with the unscattered case in the simplified model setup. The blue curves show the unweighted first-scattered baseline, while the orange curves apply the ﹩\exp (-{\tau }_{\alpha })﹩ attenuation factor to the scattered-in component. Other parameters are B_p = 5 × 10¹³ G, kT = 0.6 keV, R = 10 km, a hot spot at (θ_s, ϕ_s) = (65°, 30°), viewing angle θ = 25°, and ζ ≡ ξ_τ/β₀ = 7.0 (see Equations (2) and (16)).