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A large fraction of the protoplanetary disks observed with ALMA displaymultiple well-defined and nearly perfectly circular rings in the continuum, inmany cases with substantial peak-to-valley contrast. The DSHARP campaign showsthat several of these rings are very narrow in radial extent. In this paper wetest the hypothesis that these dust rings are caused by dust trapping in radialpressure bumps, and if confirmed, put constraints on the physics of the dusttrapping mechanism. We model this process analytically in 1D, assumingaxisymmetry. By comparing this model to the data, we find that all rings areconsistent with dust trapping. Based on a plausible model of the dusttemperature we find that several rings are narrower than the pressure scaleheight, providing strong evidence for dust trapping. The rings have peakabsorption optical depth in the range between 0.2 and 0.5. The dust massesstored in each of these rings is of the order of tens of Earth masses, thoughmuch ambiguity remains due to the uncertainty of the dust opacities. The dustrings are dense enough to potentially trigger the streaming instability, butour analysis cannot give proof of this mechanism actually operating. Ourresults show, however, that the combination of very low alpha_turb << 5e-4 andvery large grains a_grain >> 0.1 cm can be excluded by the data for all therings studied in this paper.

The Disk Substructures at High Angular Resolution Project (DSHARP) VI: Dust trapping in thin-ringed protoplanetary disks