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tokens: was derived as the distance between the two radii, where the normalized intensity profile becomes lower than (1 − 0.66 × (1 − Ī min )) ( Rosotti et al. 2016 ), where the outer of these two radii is defined as the CO wall ( R CO ). We defined the gap radius ( R gap ) as the midpoint between these two radii. Finally, the radius of the sub-mm ring ( R mm ) was defined as the radius of maximum intensity in the radial continuum intensity profile outside the gap radius. The distance of this ring from the gap is R mm − R gap . A visualization of these three radial parameters can be found in Fig. 6 . 4.2.1 Distance of the sub-mm ring from the gap radius The distance of the sub-mm ring from the gap radius (normalized to the gap radius itself) as a function of planet mass is presented in Fig. 11 . The plot shows a clear trend in which the distance of the ring increases with planet mass. The plot contains quantities derived for all eight simulations, and where the analyzed images were produced with three different beam sizes, specifically 0.03 ′′ , 0.08 ′′ , and 0.15 ′′ . The plot shows planet radii as derived from 13 CO. The same result holds for planet radii obtained from 12 CO or C 18 O, since for these three CO isotopologs, and for the beam sizes considered here (up to 0.15 ′′ ), the gap radius is always recovered with an accuracy 1.5 AU. The very small scatter of the ring distance for a given planet mass shows that this diagnostic does not depend on the disk viscosity, at least for the range of viscosities and planet masses analyzed here. Moreover, this diagnostic does not require the gap to be radially resolved; the only requirement is that for a given gap width and depth, the angular resolution is high enough to pick the presence of a gap. This is enforced by the rather small scatter with beam sizes. A linear fitting formula in log-log space can easily be retrieved, using all the points shown in Fig. 11 , leading to the simple relation Fig. 11 Distance of the sub-mm ring R mm from the gapradius R gap as a function of planet mass for all the simulations. The gap radius is estimated from the 13 CO J = 3-2 emission, whereas the ring radius is obtained from the maximum in sub-mm (850 μ m) continuum emission outside the gap radius. The ring distance is defined as the ring radius minus the gap radius. Circles, squares, and diamonds indicate quantities retrieved from images convolved with a 0.03 ′′ , 0.08 ′′ , and 0.15 ′′ beam, respectively, for sources located at a distance of 150 pc. The dashed green line shows a linear fit obtained for this relation in log–log space. The blue dashed-dotted line and brown dashed line indicate the fitting formula by Rosotti et al. (2016) obtained from hydro-simulations with 400 and 3000 planet orbits, respectively, where the gap location was inferred from synthetic scattered light maps. where A = −0.324 and B = 0.428. Interestingly, the relation between ring distance and planet mass is also well resembled by the