Table C.1.
Results of our simulation validating our method to derive mean luminosities and ratios (see Appendix C).
| Observable | ⟨Xtrue⟩ | ⟨Xmes⟩ |
 |
 |
 |
|---|---|---|---|---|---|
| Line fluxes in Jy km s−1 | |||||
| I13CO(4-3) | 0.148 | 0.157 | 1.063 | 0.016 | 0.183 |
| IHCN(5-4) | 0.142 | 0.146 | 1.030 | 0.015 | 0.177 |
| IHCO+(5-4) | 0.149 | 0.155 | 1.038 | 0.016 | 0.158 |
| IHNC(5-4) | 0.149 | 0.152 | 1.017 | 0.017 | 0.172 |
| ICN(4-3) | 0.093 | 0.091 | 0.974 | 0.026 | 0.263 |
| Line flux ratios | |||||
|
1.050 | 1.059 | 1.008 | 0.020 | 0.326 |
|
1.596 | 1.672 | 1.047 | 0.116 | 1.559 |
|
1.055 | 1.042 | 0.988 | 0.031 | 0.452 |
Notes. For line fluxes, the true sample mean value ⟨Xtrue⟩ is the mean of the 500 injected fluxes of our simulated sample. As justified in Sect. 2.5, the mean line flux ratios are derived by dividing the mean flux of a given line by the mean flux of another line. The fluxes measured using our line extraction tool are used to derive ⟨Xmes⟩. 
must be close to unity if the method is not biased. 
is the uncertainty on this ratio caused by the instrumental noise. Finally, by drawing 1000 subsamples of five sources from our 500 objects without withdrawal, we estimated the mean uncertainty on the measured-versus-true ratio for a subsample of five objects 
as is the case for our real observations.
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