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Published May 2025 | Version Published
Journal Article Open

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

Creators

  • 1. ROR icon University of Milan
  • 2. ROR icon University of Copenhagen
  • 3. ROR icon Queen Mary University of London
  • 4. ROR icon Ludwig-Maximilians-Universität München
  • 5. ROR icon Institut de Planétologie et d'Astrophysique de Grenoble
  • 6. ROR icon Jet Propulsion Lab
  • 7. ROR icon University of California, Berkeley
  • 8. ROR icon California Institute of Technology
  • 9. ROR icon Max Planck Institute for Astronomy

Abstract

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, αz, and the Stokes number, αz/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 αfrag ≲ 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.

Copyright and License

© The Authors 2025.

Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Acknowledgement

We thank the referee for their review of the manuscript, and Fabiola Gerosa for spotting a major typo in a final stage of the manuscript. The authors thank the DSHARP team and Jane Huang for making their calibrated visibilities and imaging scripts publicly available. We also thank Feng Long, Myriam Benisty, Jun Hashimoto, and Álvaro Ribas for sharing some of the calibrated visibilities used in this work, and the NRAO SRDP and ESO ARI-L (Massardi et al. 2021) for providing calibrated visibility files. We thank Giuseppe Lodato for very useful discussions. MV and GR acknowledge support from the European Union (grant No. 101039651, project DiscEvol) and from Fondazione Cariplo (grant No. 2022-1217). FMe and GD acknowledge funding from the European Research Council (ERC) under the European Union’s Horizon Europe research and innovation program (grant agreement No. 101053020, project Dust2Planets). AZ acknowledges funding by the STFC (grant ST/P000592/1), and from the European Union under the European Union’s Horizon Europe Research and Innovation Programme 101124282 (EARLYBIRD). ML acknowledges ERC starting grant 101041466-EXODOSS. Views and opinions expressed are, however, those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them. This paper makes use of the following ALMA data: 2013.1.00498.S, 2015.1.00888.S, 2016.1.00484.L, 2016.1.00460.S, 2016.1.00545.S, 2016.1.00771.S, 2016.1.01164.S, 2016.1.01205.S, 2016.1.01239.S, 2016.1.01370.S, 2017.A.00006.S, 2017.1.01151.S, 2017.1.01167.S, 2017.1.01460.S, 2018.1.00028.S, 2018.A.00030.S, 2018.1.00689.S, 2018.1.00958.S, 2018.1.01255.S, 2018.1.01230.S, 2018.1.01755.S, 2019.1.01051.S. ALMA is a partnership of ESO (representing its member states), NSF (USA), and NINS (Japan), together with NRC (Canada), MOST and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO, and NAOJ.

Software References

This paper used the following softwares CASA (CASA Team 2022), mcfost (Pinte et al. 2006, 2009), Matplotlib (Hunter 2007), Numpy (Harris et al. 2020), scipy (Virtanen et al. 2020), CARTA (10.5281/zenodo.3377984).

Data Availability

The data can be found on zenodo (zenodo.14054952). The models are also available (zenodo.14056832).

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Additional details

Related works

Is new version of
Discussion Paper: arXiv:2503.05872 (arXiv)
Is supplemented by
Dataset: 10.5281/zenodo.14054952 (DOI)
Dataset: 10.5281/zenodo.14056832 (DOI)

Funding

European Union
101039651
Fondazione Cariplo
2022-1217
European Union
101053020
Science and Technology Facilities Council
ST/P000592/1
European Union
101124282
European Union
101041466

Dates

Accepted
2025-02-22
Available
2025-05-12
Published online

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Caltech groups
Division of Physics, Mathematics and Astronomy (PMA)
Publication Status
Published