Full solution to the radiative transfer approximation (Equation (11)) including the emission term (see Equation (A.2)) compared with the approximate, absorption-only solution (Equation (14c)). We show the flux leaving the planet (dashed black line), the solution taking only absorption into account (dark red dashed line with dots), and the full solution (pale red full line), as well as the source function (blackbody intensity) at the location where τ_λ = 1 radially inwards (grey line), for those wavelengths where τ_λ = 1 is reached. The temperature of the blackbody there is shown against the right axis (blue dotted line). Left panel: Case of Figure 4. The strong preshock absorption at the Doppler-shifted H α resonance near the planet is filled in somewhat by the emission in the accretion flow, almost to the level of the blackbody at τ_λ = 1, roughly according to the Milne–Barbier–Unsöld relationship. Right panel: Case of polar accretion for Ṁ = 3 × 10⁻⁴ M_J yr⁻¹, M_p = 20 M_J for the cold-population radius fit (R_p = 3.4 R_J). Outside of the line centre, the outcoming intensity is much higher than the source function at τ_λ = 1 and thus the full solution is not roughly the sum of the absorption-only curve and the source function at τ_λ = 1.