The efficiency of dust trapping in ringed protoplanetary discs

When imaged at high resolution, many protoplanetary discs show gaps and rings in their dust sub-mm continuum emission profile. These structures are widely considered to originate from local maxima in the gas pressure profile. The properties of the underlying gas structures are however unknown. In this paper, we present a method to measure the dust-gas coupling alpha/St and the width of the gas pressure bumps affecting the dust distribution, applying high-precision techniques to extract the gas rotation curve from emission line data cubes. As a proof of concept, we then apply the method to two discs with prominent substructure, HD 163296 and AS 209. We find that in all cases the gas structures are larger than in the dust, confirming that the rings are pressure traps. Although the grains are sufficiently decoupled from the gas to be radially concentrated, we find that the degree of coupling of the dust is relatively good (alpha/St similar to 0.1). We can therefore reject scenarios in which the disc turbulence is very low and the dust has grown significantly. If we further assume that the dust grain sizes are set by turbulent fragmentation, we find high values of the alpha turbulent parameter (alpha similar to 10(-2)). Alternatively, solutions with smaller turbulence are still compatible with our analysis if another process is limiting grain growth. For HD 163296, recent measurements of the disc mass suggest that this is the case if the grain size is 1 mm. Future constraints on the dust spectral indices will help to discriminate between the two alternatives.