Comparison between the input value Ṁ_input (ordinate) and Ṁ_D resulting from using a formula analogous to Eq. (9) (abscissa) for different rotational CO line transitions, but omitting the dependence of the mass-loss rate on R_inner and β (left panel), and on R_inner , β, T _⋆   , and R _⋆  (right panel). Estimates for the non-saturated regime are plotted in black, for the saturated regime in grey. δ,σ,μ,π(3) and π(10) are as in Fig. 6. The dotted line represents equality of the input and estimated mass-loss rates, the dashed lines show a factor 3 difference w.r.t. this relation. The histogram on the right of each panel shows the peak-normalised distribution of log (Ṁ_D/Ṁ_input). The vertical dashed lines in these histograms again show a factor three difference between Ṁ_D and Ṁ_input.