tokens: reversals are also sometimes seen in other regions of the disk, potentially complicating the extraction of the planet position. The rotation maps presented in Figure 3 were generated with a perfect knowledge of the velocity field and taking into account the radiative transfer effects at the emitting surface. For actual data, the velocity field and altitude of the emitting layers have to be estimated. Uncertainties in the Keplerian velocity model that is subtracted may limit the detectability of Doppler flips to high signal-to-noise cases. In particular, the predicted Doppler flip for the orientation of HD 163296 (labeled panel in Figure 3 ) shows an amplitude twice smaller (≈150 m s −1 ) than the residuals in the differential rotation map presented in Casassus Pérez ( 2019 ) (≈300 m s −1 ). This explains why they did not detect the counterparts of the kink as a Doppler flip in the first moment map. The absence of visible Doppler flip corresponding to the kink in HD 97048 is also not surprising given the residuals in the differential rotation maps presented by Casassus Pérez ( 2019 ). Because of the tentative nature of the detections and the need for higher-resolution observations, we are not yet confident enough to estimate planet masses from the candidate kinks seen in the DSHARP data. Detailed hydrodynamical and radiative transfer modeling of the kink candidates is currently the only way to determine planet masses from velocity deviations in a quantitative manner but would result in poorly constrained estimates given the low signal-to-noise ratio and poor velocity resolution of the data. We estimated the velocity deviations from the number of channels in which the kinks are detected. The limited spectral resolution prevents us from measuring velocity deviations smaller than 640 m s −1 . By comparing with the expected location of the isovelocity curves if the disks were in Keplerian rotation, we estimate the observed perturbations to be of the order of 10%–15% of the local Keplerian velocity (Table 1 ). From our previous modeling of velocity kinks, we expect masses of the order of 1–3 M Jup . In HD 143006, the velocity deviation appears significantly larger, pointing toward a more massive planet. With the exception of HD 143006, such masses are larger by a factor of 4–10 than the masses derived from the continuum gaps by Zhang et al. ( 2018 ) or Lodato et al. ( 2019 ). We found a similar discrepancy for HD 97048 (Pinte et al. 2019 ), where to get a coherent match to both the continuum and line data, our models required the dust grains dominating the emission to have a Stokes number of a few 10 −2 , suggesting very porous and/or fluffy aggregates. The high detection rate of velocity kinks at several tens of astronomical units in the DSHARP data set may appear in contradiction with the occurrence rate of known giant extrasolar planets at large distance from their host stars: in the range of a few up to 5% for massive planets ( M > 2 M Jup )
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