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tokens: flux were fit simultaneously by varying and the gas-to-dust ratio. The outer radius was set by fitting the CO spectrum (the maxima in the spectra or double peaks that arise from the Keplerian motion) and provides outer boundaries for computing the gas masses. Using this surface density profile, the emission inside the cavity is constrained by the parameters (Fig. 4 ). The near-infrared excess determines the dust density in the inner disk through . The gas cavity radius and drop were fit to the CO emission. In some cases, an additional drop in gas surface density is required between and the dust cavity radius . This drop is indicated by . The main parameters that are varied are the gas cavity radius and the drop in gas density between and . The CO isotopologs provide better constraints on the density than the CO because they are less optically thick (CO) or even optically thin (CO). The effects of isotope-selective photodissociation are properly considered in the modeling and are discussed in Sect. 4.3 . 4. Results Table 3 Results for the gas density profile of each transition disk. Notes. (a) HD13 = HD 135344B. (b) The masses are only constrained within for the detected surface brightness. (c) The drop inside 7 AU could not be constrained by the ALMA data; we adopt the value from CO rovibrational spectroastrometry by Pontoppidan et al. (2008) . (d) The uncertainties on the gas cavity size are typically 5 AU and lower than one order of magnitude on the depth of the drop. Fig. 5 Modeling results and observations of the CO and CO emission for the best-fitting models in derotated images and spectra. The left panels show the direct image comparison of the zero-moment map: derotated observations, model, convolved model, and residual. In the residual map the overlaid contours indicate the 3 levels, where dashed lines are negative. The central panels show the gas density profiles with different drops as solid lines and the dust density profile as dashed lines. The right panels show the resulting intensity cuts for the major and minor axis for both CO and CO. The best-fitting model is indicated in red, other values in blue. The drop in density can be constrained to within an order of magnitude. Data and models are compared through the spectra and the zero-moment 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