Turbulence in protoplanetary disks: A systematic analysis of dust settling in 33 disks

The level of dust vertical settling and radial dust concentration in protoplanetary disks is of critical importance for understanding the efficiency of planet formation. Here, we present the first uniform analysis of the vertical extent of millimeter dust for a representative sample of 33 protoplanetary disks, covering broad ranges of disk evolutionary stages and stellar masses. We used radiative transfer modeling of archival high-angular-resolution (≲0.1″) ALMA dust observations of inclined and ringed disks to estimate their vertical dust scale height, which was compared to estimated gas scale heights to characterize the level of vertical sedimentation. In all 23 systems for which constraints could be obtained, we find that the outer parts of the disks are vertically settled. Five disks allow for the characterization of the dust scale height both within and outside approximately half the dust disk radius, showing a lower limit on their dust heights at smaller radii. This implies that the ratio between vertical turbulence, α z , and the Stokes number, α z /St, decreases radially in these sources. For 21 rings in 15 disks, we also constrained the level of radial concentration of the dust, finding that about half of the rings are compatible with strong radial trapping. In most of these rings, vertical turbulence is found to be comparable to or weaker than radial turbulence, which is incompatible with the turbulence generated by the vertical shear instability at these locations. We further used our dust settling constraints to estimate the turbulence level under the assumption that the dust size is limited by fragmentation, finding typical upper limits around α frag ≲ 10 −3 . In a few sources, we find that turbulence cannot be the main source of accretion. Finally, in the context of pebble accretion, we identify several disk regions that have upper limits on their dust concentration that would allow core formation to proceed efficiently, even at wide orbital distances outside of 50 au.