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tokens: profiles (azimuthally averaged) for the dust continuum and line images. Shown are profiles derived from images convolved with representative beam sizes for SPHERE (blue, FWHM = 0.031′′), ALMA (black, FWHM = 0.012′′), and ngVLA (red, FWHM = 0.004′′). The continuum non-detections of wide-orbit CPDs with ALMA indicate low dust masses or very compact optically thick disks ( r out ≲ 0.5 au, Wu et al. 2017a ). Compared to those non-detections, the 860 μ m disk in our reference model seems to be too large. We discuss this further in Sects 3.2 and 3.3 . In contrast to the dust emission the 12 CO J = 3 − 2 emission traces mostly the outer disk and can, in principle, be spatially resolved with ALMA even with larger beams. In the reference model the line is optically thick throughout the disk (see Fig. 4 ) and traces only the upper layers of the disk. Because of the high optical depths 12 CO J = 3 − 2 is very sensitive to the disk size (i.e. emitting area) and the temperature. The different apparent extents of the dust and line emission in our model is similar to observations of T Tauri disks (e.g. de Gregorio-Monsalvo et al. 2013 ; Ansdell et al. 2018 ). It is still unclear if this difference is only caused by optical depth effects or if radial dust migration also plays a role ( Woitke et al. 2016 ; Facchini et al. 2017 ). In our models the cause is solely the different dust and line optical depths. For ngVLA observations at 3 mm the situation is similar to the ALMA Band 7 at 860 μ m. The main difference is the possible higher spatial resolution of the ngVLA (0.004′′, 0.6 au at d = 150 au), which might allow us to also resolve the dust disk (see right panel of Fig. 3 ). Compared to the 860 μ m emission, the emission at 3 mm is weaker and the optically thick region of the dust and the gas are slightly smaller (see Fig. 4 ). 3.2 Exploring disk mass and size In Fig. 5 we compare the modelled fluxes for the dust continuum and gas lines to the 5 σ detection limits of ngVLA and ALMA (6 h on-source observing time, see Appendix C ). We report the peak(maximum) fluxes determined from the synthetic beam convolved continuum images and line cubes (see Appendix D ). If the peak flux of the model is above the reported sensitivity limit a 5 σ detection is possible in the case of the lines in at least one channel. Figure 5 shows the reference model and models with varying R tap (i.e. changing the radial extent of the disk) and with a factor of 10 lower disk mass. Indicated in Fig. 5 are also the 3 σ rms values reported by Wu et al. (2017a , Table 1 ) for their observations of five potential CPDs with ALMA in Band 6. The average on-source integration time for their sample is around 12 min. Fig. 4 Vertical optical depth τ for the dust and for 12 CO lines as a function of radius in the reference model (see also Fig. 3 ). The horizontal dark grey line indicates τ = 1. As Fig. 5 shows our reference model is easily detectable in the dust, also with significantly shorter