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tokens: maps (intensity maps) of both CO and CO. For each target we show the direct comparison of the images of the intensity map of the best-fit model and the constraint on both and through spectra and intensity cuts through the major and minor axis of the zero-moment map. In three of the four targets an inner gas cavity (smaller than the dust cavity) was required to fit the data. In SR21 the 7 AU cavity previously derived from rovibrational emission was adopted, but no gas cavity is resolved at the spatial resolution of (24 AU) in our observations. In all disks, the depth is constrained to within an order of magnitude and the cavity size to within 5 AU, mainly through the comparison of the spatially resolved emission, but further confirmed by the line wings in the spectra. In the intensity cuts in Fig. 5 the parameter is varied. The comparison shows that the uncertainty on the density drop is lower than an order of magnitude. In Appendix C we show the intensity cuts for larger and smaller gas cavity radii, respectively. These plots show that the uncertainty on the gas cavity radius is typically 5 AU and the uncertainty on the depth is lower than one order of magnitude. Furthermore, in both SR21 and DoAr44 an additional drop between and is required to fit the data. The models of the CO fits of van der Marel et al. (2015b) match the isotopolog data in the outer disk remarkably well. Only minor corrections in surface density and gas-to-dust ratio were required to fit the new data. However, inside the cavity the previously derived results for the gas surface density were found to be inconsistent. A modest drop in the gas density inside the dust cavity radius was sufficient to explain the CO data, but no gas cavity was seen. Since the gas cavity becomes visible in the isotopolog data and turns out to be smaller than the dust cavity radius, the gas cavity radius could be fit independently of the depth. 4.1. Results for individual targets HD 135344B HD 135344B shows a clear gas cavity, both in CO and CO images, which is significantly smaller than the dust cavity (see top two panels of Fig. 1 ). The modeling constrains the gas cavity radius to 30 AU (dust cavity radius is 40 AU), and the drop is (top right panels in Fig. 5 ). Previously, the model based on the CO data required of for a cavity radius of 40 AU. A 30 AU gas cavity was also derived in van der Marel et al. (2015b) considering the inner radius of the small dust grains derived from the scattered-light emission ( Garufi et al. 2013 ), but a value as low as underproduces the CO emission inside the cavity. As the CO is optically thick and mainly traces the temperature at the surface, this new result suggests that the temperature structure is somewhat higher than in our model, perhaps because of some residual dust in the cavity (increasing the CO abundance by its shielding and changing the heating-cooling balance) or the vertical structure (shadowing on the outer disk; see Bruderer 2013 , for a