tokens: This holds true in particular for CO line emission which is optically thick. A second parameter to explore is , the power-law index of the surface density distribution. Models with different values are presented separately in the lower panels of Fig. A.1 . The line luminosities produced by models with and are almost indistinguishable, while differences can be found comparing these with models with . In particular in the intermediate disk mass regime, models for show three different populations that reflect models with different values. This effect is less clear for models with . Finally, it is interesting to investigate how much the central star influences the CO isotopologues emission in the disk. Models with the same physical disk parameters, but irradiated by a T Tauri-like and a Herbig-like star are presented in Fig. 2 (respectively in the left and in the right panel) and in Fig. 3 . For the Herbig disks, the derived line intensities are higher for more massive disks and lower for less massive disks compared with those obtained for the T Tauri disks. Since Herbig disks are warmer, less material is frozen-out onto grains in the higher mass regime and can contribute to the total emission enhancing the line luminosity. Also, the higher temperatures enhance the moderately optically thick CO lines. On the other hand, the strong UV flux coming from the Herbig star is very efficient in photodissociating CO isotopologue molecules for lower mass disks (, ) where the column densities are not high enough for shielding the photons. This combination of high UV field and low column densities reduces the line luminosities, thus they are lower than those from T Tauri disks. 3.2.4. Dependence on gas-to-dust ratio To test the sensitivity of the results to the gas-to-dust ratio for a fixed gas mass, we ran two T Tauri disk models ( au, , , , , ) with reduced gas-to-dust ratios of ten and one. The ray-traced line intensities for CO isotopologues are presented in Fig. A.3 as functions of the gas-to-dust ratio, normalized to the value at gas-to-dust =100. For the disk the optically thin CO intensities increase by a factor of 3.5 if the gas-to-dust ratio is lowered by a factor of 100. This can be understood by the fact that if the dust mass is enhanced for a fixed gas mass, the FUV flux will be more efficiently attenuated. Accordingly CO and its isotopologues survive more easily and their lines are brighter for low gas-to-dust ratios, especially if their emission is optically thin. In addition, if the dust opacity dominates over the line mutual shielding, isotope-selective processes are minimized. The CO and CO emission on the other hand stay the same within 30% because they are more optically thick. There are also small temperature differences of order 20% between the models in the emitting layer which can affect their line intensities. For the disk the trend is opposite: line intensities decrease if the gas-to-dust ratio is lowered for all three
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