  A large fraction of the protoplanetary disks observed with ALMA display
multiple well-defined and nearly perfectly circular rings in the continuum, in
many cases with substantial peak-to-valley contrast. The DSHARP campaign shows
that several of these rings are very narrow in radial extent. In this paper we
test the hypothesis that these dust rings are caused by dust trapping in radial
pressure bumps, and if confirmed, put constraints on the physics of the dust
trapping mechanism. We model this process analytically in 1D, assuming
axisymmetry. By comparing this model to the data, we find that all rings are
consistent with dust trapping. Based on a plausible model of the dust
temperature we find that several rings are narrower than the pressure scale
height, providing strong evidence for dust trapping. The rings have peak
absorption optical depth in the range between 0.2 and 0.5. The dust masses
stored in each of these rings is of the order of tens of Earth masses, though
much ambiguity remains due to the uncertainty of the dust opacities. The dust
rings are dense enough to potentially trigger the streaming instability, but
our analysis cannot give proof of this mechanism actually operating. Our
results show, however, that the combination of very low alpha_turb << 5e-4 and
very large grains a_grain >> 0.1 cm can be excluded by the data for all the
rings studied in this paper.
