Constraining turbulence in protoplanetary discs using the gap contrast: an application to the DSHARP sample

Constraining the strength of gas turbulence in protoplanetary discs is an open problem that has relevant implications for the physics of gas accretion and planet formation. In this work, we gauge the amount of turbulence in 6 of the discs observed in the DSHARP programme by indirectly measuring the vertical distribution of their dust component. We employ the differences in the gap contrasts observed along the major and the minor axes due to projection effects, and build a radiative transfer model to reproduce these features for different values of the dust scale heights. We find that (a) the scale heights that yield a better agreement with data are generally low ($\lesssim 4$ AU at a radial distance of $100$ AU), and in almost all cases we are only able to place upper limits on their exact values; these conclusions imply (assuming an average Stokes number of $\approx10^{-2}$) low turbulence levels of $\alpha_{\rm SS}\lesssim10^{-3}-10^{-4}$; (b) for the 9 other systems we considered out of the DSHARP sample, our method yields no significant constraints on the disc vertical structure; we conclude that this is because these discs have either a low inclination or gaps that are not deep enough. Based on our analysis we provide an empirical criterion to assess whether a given disc is suitable to measure the vertical scale height.