Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Depletion of gaseous CO in protoplanetary disks by surface-energy-regulated ice formation


Empirical constraints of fundamental properties of protoplanetary disks are essential for understanding planet formation and planetary properties1,2. Carbon monoxide (CO) gas is often used to constrain disk properties3. However, estimates show that the CO gas abundance in disks is depleted relative to expected values4,5,6,7, and models of various disk processes impacting the CO abundance could not explain this depletion on observed ~1 Myr timescales8,9,10,11,12,13,14. Here we demonstrate that surface energy effects on particles in disks, such as the Kelvin effect, that arise when ice heterogeneously nucleates onto an existing particle can efficiently trap CO in its ice phase. In previous ice formation models, CO gas was released when small ice-coated particles were lofted to warmed disk layers. Our model can reproduce the observed abundance, distribution and time evolution of gaseous CO in the four most studied protoplanetary disks7. We constrain the solid and gaseous CO inventory at the midplane and disk diffusivities and resolve inconsistencies in estimates of the disk mass—three crucial parameters that control planetary formation.

This is a preview of subscription content, access via your institution

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: The distribution of gaseous CO is regulated by preferential condensation of CO onto large particles.
Fig. 2: The radial evolution of CO in the disk around TW Hya.
Fig. 3: The amount of CO gas depletion depends on the disk diffusion timescale.
Fig. 4: Surface-energy-regulated ice formation can describe CO gas abundances for a variety of observed disks.

Data availability

Observational CO data are published in refs. 6,7,15,71,72,73,74,75,77,78 (see Methods for more detail). Due to the large size of the data files, the full microphysical data generated by the simulations presented in this work are available from the corresponding author upon reasonable request.

Code availability

The numerical models used in this work are not public. However, they are available from the corresponding author upon reasonable request.


  1. Pollack, J. B. et al. Formation of the giant planets by concurrent accretion of solids and gas. Icarus 124, 62–85 (1996).

    Article  ADS  Google Scholar 

  2. Öberg, K. I., Murray-Clay, R. & Bergin, E. A. The effects of snowlines on C/O in planetary atmospheres. Astrophys. J. Lett. 743, L16 (2011).

    Article  ADS  Google Scholar 

  3. Andrews, S. M. Observations of protoplanetary disk structures. Annu. Rev. Astron. Astrophys. 58, 483–528 (2020).

    Article  ADS  Google Scholar 

  4. Ansdell, M. et al. ALMA survey of Lupus protoplanetary disks. I. Dust and gas masses. Astrophys. J. 828, 46 (2016).

    Article  ADS  Google Scholar 

  5. Bergin, E. A. et al. An old disk still capable of forming a planetary system. Nature 493, 644–646 (2013).

    Article  ADS  Google Scholar 

  6. Schwarz, K. R. et al. The radial distribution of H2 and CO in TW Hya as revealed by resolved ALMA observations of CO isotopologues. Astrophys. J. 823, 91 (2016).

    Article  ADS  Google Scholar 

  7. Zhang, K., Bergin, E. A., Schwarz, K., Krijt, S. & Ciesla, F. Systematic variations of CO gas abundance with radius in gas-rich protoplanetary disks. Astrophys. J. 883, 98 (2019).

    Article  ADS  Google Scholar 

  8. Zhang, K., Schwarz, K. R. & Bergin, E. A. Rapid evolution of volatile CO from the protostellar disk stage to the protoplanetary disk stage. Astrophys. J. Lett. 891, L17 (2020).

    Article  ADS  Google Scholar 

  9. Bergner, J. B. et al. An evolutionary study of volatile chemistry in protoplanetary disks. Astrophys. J. 898, 97 (2020).

    Article  ADS  Google Scholar 

  10. Dodson-Robinson, S. E. et al. Ionization-driven depletion and redistribution of CO in protoplanetary disks. Astrophys. J. Lett. 866, 2 (2018).

    Google Scholar 

  11. Schwarz, K. R. et al. Unlocking CO depletion in protoplanetary disks. I. The warm molecular layer. Astrophys. J. 856, 85 (2018).

    Article  ADS  Google Scholar 

  12. Krijt, S., Schwarz, K. R., Bergin, E. A. & Ciesla, F. J. Transport of CO in protoplanetary disks: consequences of pebble formation, settling, and radial drift. Astrophys. J. 864, 1 (2018).

    Article  Google Scholar 

  13. Krijt, S. et al. CO depletion in protoplanetary disks: a unified picture combining physical sequestration and chemical processing. Astrophys J. 899, 134 (2020).

    Article  ADS  Google Scholar 

  14. Yu, M., Evans, N. J., Dodson-Robinson, S. E., Willacy, K. & Turner, N. J. Disk masses around solar-mass stars are underestimated by CO observations. Astrophys. J. 841, 39 (2017).

    Article  ADS  Google Scholar 

  15. Zhang, K., Bosman, A. D. & Bergin, E. A. Excess C/H in protoplanetary disk gas from icy pebble drift across the CO snowline. Astrophys. J. Lett. 891, L16 (2020).

    Article  ADS  Google Scholar 

  16. Flaherty, K. M. et al. A three-dimensional view of turbulence: constraints on turbulent motions in the HD 163296 protoplanetary disk using DCO+. Astrophys. J. 843, 150 (2017).

  17. Flaherty, K. M. et al. Turbulence in the TW Hya disk. Astrophys. J. 856, 117 (2018).

  18. Flaherty, K. M. et al. Measuring turbulent motion in planet-forming disks with ALMA: a detection around DM Tau and nondetections around MWC 480 and V4046 Sgr. Astrophys. J. 895, 109 (2020).

  19. Powell, D., Murray-Clay, R. & Schlichting, H. E. Using ice and dust lines to constrain the surface densities of protoplanetary disks. Astrophys. J. 840, 93 (2017).

    Article  ADS  Google Scholar 

  20. Powell, D., Murray-Clay, R., Pérez, L. M., Schlichting, H. E. & Rosenthal, M. New constraints from dust lines on the surface densities of protoplanetary disks. Astrophys. J. 878, 116 (2019).

    Article  ADS  Google Scholar 

  21. Franceschi, R. et al. Mass determination of protoplanetary disks from dust evolution. Astron. Astrophys. 657, 74 (2021).

  22. McClure, M. K. et al. Mass measurements in protoplanetary disks from hydrogen deuteride. Astrophys. J. 831, 167 (2016).

    Article  ADS  Google Scholar 

  23. Lacy, J. H., Knacke, R., Geballe, T. R. & Tokunga, A. T. Detection of absorption by H2 in molecular clouds: a direct measurement of the H2:CO ratio. Astrophys. J. Lett. 428, L69-72 (1994).

  24. Ballering, N. P., Cleeves, L. I. & Anderson, D. E. Simulating observations of ices in protoplanetary disks. Astrophys. J. 920, 115 (2021).

  25. Konopacky, Q. M. et al. Detection of carbon monoxide and water absorption lines in an exoplanet atmosphere. Science 339, 1398–1401 (2013).

  26. Barman, T. S. et al. Simultaneous detection of water, methane, and carbon monoxide in the atmosphere of exoplanet HR8799 b. Astrophys. J. 804, 62 (2015).

    Article  ADS  Google Scholar 

  27. Lavie, B. et al. HELIOS-RETRIEVAL: an open-source, nested sampling atmospheric retrieval code; application to the HR 8799 exoplanets and inferred constraints for planet formation. Astron. J. 154, 91 (2017).

    Article  ADS  Google Scholar 

  28. Wang, J. et al. On the chemical abundance of HR 8799 and the planet c. Astrophys. J. 160, 150 (2020).

    Google Scholar 

  29. Powell, D., Zhang, X., Gao, P. & Parmentier, V. Formation of silicate and titanium clouds on hot Jupiters. Astrophys. J. 860, 18 (2018).

    Article  ADS  Google Scholar 

  30. Gao, P., Marley, M. S. & Ackerman, A. S. Sedimentation efficiency of condensation clouds in substellar atmospheres. Astrophys. J. 855, 86 (2018).

    Article  ADS  Google Scholar 

  31. Birnstiel, T., Klahr, H. & Ercolano, B. A simple model for the evolution of the dust population in protoplanetary disks. Astron. Astrophys. 539, A148 (2012).

    Article  ADS  MATH  Google Scholar 

  32. Lambrechts, M. & Johansen, A. Forming the cores of giant planets from the radial pebble flux in protoplanetary discs. Astron. Astrophys. 572, A107 (2014).

    Article  ADS  Google Scholar 

  33. Chen, J.-P., Hazra, A. & Levin, Z. Parameterizing ice nucleation rates using contact angle and activation energy derived from laboratory data. Atmos. Chem. Phys. 8, 7431–7449 (2008).

    Article  ADS  Google Scholar 

  34. Campbell, J. M., Meldrum, F. C. & Christenson, H. K. Observing the formation of ice and organic crystals in active sites. Proc. Natl Acad. Sci. USA 114, 810–815 (2017).

  35. Nachbar, M. et al. Laboratory measurements of heterogeneous CO2 ice nucleation on nanoparticles under conditions relevant to the Martian mesosphere. J. Geophys. Res. Planets 121, 753–769 (2016).

  36. Pruppacher, H. R. and Klett, J. D. Microphysics of Clouds and Precipitation (Kluwer, 1997).

  37. Määttänen, A., Vehkamäki, H., Lauri, A., Napari, I. & Kulmala, M. Two-component heterogeneous nucleation kinetics and an application to Mars. J. Chem. Phys. 127, 134710 (2007).

    Article  ADS  Google Scholar 

  38. Wood, S. E. Nucleation and Growth of Carbon Dioxide Ice Crystals in the Martian Atmosphere. Ph.D. thesis, Univ. of California, Los Angeles (1999).

  39. Fletcher, N. H. Size effect in heterogeneous nucleation. J. Chem. Phys. 29, 572–576 (1958).

    Article  ADS  Google Scholar 

  40. Fletcher, N. H. The Physics of Rainclouds (Cambridge Univ. Press, 1962).

  41. Hobbs, P. V. Ice Physics (Oxford, Clarendon, 1974).

  42. Campbell, J. M. & Christenson, H. K. Nucleation- and emergence-limited growth of ice from pores. Phys. Rev. Lett. 120, 165701 (2018).

  43. Holden, M. A., Campbell, J. M., Meldrum, F. C., Murray, B. J. & Christenson, H. K. Active sites for ice nucleation differ depending on nucleation mode. Proc. Natl Acad. Sci. USA 118, e2022859118 (2021).

  44. Hakimian, A. et al. Freezing of few nanometers water droplets. Nat. Commun. 12, 6973 (2021).

    Article  ADS  Google Scholar 

  45. Laffon, C. et al. Laboratory-based sticking coefficients for ices on a variety of small-grain analogues. Nat. Astron 5, 445–450 (2021).

    Article  ADS  Google Scholar 

  46. Cleeves, L. I. et al. The ancient heritage of water ice in the solar system. Science 345, 1590–1593 (2014).

  47. Cooke, I. R. et al. CO diffusion and desorption kinetics in CO2 ices. Astrophys. J. 852, 75 (2018).

  48. Wylie, L. The Vapor Pressure of Solid Argon, Carbon Monoxide, Methane, Nitrogen, and Oxygen from Their Triple Points to the Boiling Point of Hydrogen. Thesis, Georgia Institute of Technology (1958).

  49. Hill, R. Nucleation of thin films. Nature 210, 512–513 (1966).

    Article  ADS  Google Scholar 

  50. Pathak, H., Mullick, K., Tanimura, S. & Wyslouzil, B. E. Nonisothermal droplet growth in the free molecular regime. Aerosol Sci. Technol. 47, 1310–1324 (2013).

    Article  ADS  Google Scholar 

  51. Zhang, X., Pandis, S. N. & Seinfeld, J. H. Diffusion-limited versus quasi-equilibrium aerosol growth. Aerosol Sci. Technol. 46, 874–885 (2012).

    Article  ADS  Google Scholar 

  52. Bogdan, A. Ice clouds: atmospheric ice nucleation concept versus the physical chemistry of freezing atmospheric drops. J. Phys. Chem. A 122, 7777–7781 (2018).

    Article  Google Scholar 

  53. Leger, A., Gauthier, S., Defourneau, D. & Rouan, D. Properties of amorphous H2O ice and origin of the 3.1-micron absorption. Astron. Astrophys. 117, 164–169 (1983).

    ADS  Google Scholar 

  54. Leger, A., Jura, M. & Omont, A. Desorption from interstellar grains. Astron. Astrophys. 144, 147–160 (1985).

    ADS  Google Scholar 

  55. Ros, K. et al. Effect of nucleation on icy pebble growth in protoplanetary discs. Astron. Astrophys. 629, 65 (2019).

  56. Shakura, N. I. & Sunyaev, R. A. Black holes in binary systems. Observational appearance. Astron. Astrophys. 24, 337 (1973).

    ADS  Google Scholar 

  57. Hartmann, L., Calvet, N., Gullbring, E. & D’Alessio, P. Accretion and the evolution of T Tauri disks. Astrophys. J. 495, 385–400 (1998).

    Article  ADS  Google Scholar 

  58. Stevenson, D. J. & Lunine, J. I. Rapid formation of Jupiter by diffusive redistribution of water vapor in the solar nebula. Icarus 75, 146–155 (1988).

    Article  ADS  Google Scholar 

  59. Cuzzi, J. N. & Zahnle, K. J. Material enhancement in protoplanetary nebulae by particle drift through evaporation fronts. Astrophys. J. 614, 490–496 (2004).

    Article  ADS  Google Scholar 

  60. Ciesla, F. J. & Cuzzi, J. N. The evolution of the water distribution in a viscous protoplanetary disk. Icarus 181, 178–204 (2006).

    Article  ADS  Google Scholar 

  61. Schoonenberg, D. & Ormel, C. W. Planetesimal formation near the snowline: in or out? Astron. Astrophys. 602, A21 (2017).

    Article  ADS  Google Scholar 

  62. Booth, R. A., Clarke, C. J., Madhusudhan, N. & Ilee, J. D. Chemical enrichment of giant planets and discs due to pebble drift. Mon. Not. R. Astron. Soc. 469, 3994–4011 (2017).

    Article  ADS  Google Scholar 

  63. Birnstiel, T., Andrews, S. M., Pinilla, P. & Kama, M. Dust evolution can produce scattered light gaps in protoplanetary disks. Astrophys. J. Lett. 813, L14 (2015).

    Article  ADS  Google Scholar 

  64. Calahan, J. K. et al. The TW Hya Rosetta Stone Project. III. Resolving the gaseous thermal profile of the disk. Astrophys. J. 908, 8 (2021).

  65. Chiang, E. I. & Goldreich, P. Spectral energy distributions of T Tauri stars with passive circumstellar disks. Astrophys. J. 490, 368–376 (1997).

    Article  ADS  Google Scholar 

  66. Xu, R., Bai, X.-N. & Öberg, K. Turbulent-diffusion mediated CO depletion in weakly turbulent protoplanetary disks. Astrophys. J. 835, 162 (2017).

    Article  ADS  Google Scholar 

  67. Mawet, D. et al. Direct imaging of extra-solar planets in star forming regions. Astron. Astrophys. 544, A131 (2012).

    Article  Google Scholar 

  68. Pegues, J. et al. An ALMA survey of H2CO in protoplanetary disks. Astrophys. J. 890, 142 (2020).

    Article  ADS  Google Scholar 

  69. Simon, M., Dutrey, A. & Guilloteau, S. Dynamical masses of T Tauri stars and calibration of pre-main-sequence evolution. Astrophys. J. 545, 1034 (2000).

    Article  ADS  Google Scholar 

  70. Ribas, Á., Hervé, B. & Bruno, M. Protoplanetary disk lifetimes vs. stellar mass and possible implications for giant planet populations. Astron. Astrophys. 576, 52 (2015).

  71. Law, C. J. et al. Molecules with ALMA at Planet-forming Scales (MAPS). III. Characteristics of radial chemical substructures. Astrophys. J. Suppl. Ser. 257, 3 (2021).

  72. Huang, J. et al. CO and dust properties in the TW Hya disk from high-resolution ALMA observations. Astrophys. J. 852, 122 (2018).

    Article  ADS  Google Scholar 

  73. Nomura, H. et al. ALMA observations of a gap and a ring in the protoplanetary disk around TW Hya. Astrophys. J. Lett. 819, L7 (2016).

    Article  ADS  Google Scholar 

  74. Williams, J. P. & McPartland, C. Measuring protoplanetary disk gas surface density profiles with ALMA. Astrophys. J. 830, 32 (2016).

    Article  ADS  Google Scholar 

  75. Booth, A. S. et al. The first detection of 13C17O in a protoplanetary disk: a robust tracer of disk gas mass. Astrophys. J. Lett. 882, L31 (2019).

    Article  ADS  Google Scholar 

  76. Bosman, Arthur D. et al. Molecules with ALMA at planet-forming scales (MAPS). XV. Tracing protoplanetary disk structure within 20 au. Astrophys. J. Supplementary Series 257, 15 (2021).

  77. Zhang, K. et al. Mass inventory of the giant-planet formation zone in a solar nebula analogue. Nat. Astron 1, 0130 (2017).

    Article  ADS  Google Scholar 

  78. Law, C. J. et al. Molecules with ALMA at Planet-forming Scales (MAPS). IV. Emission surfaces and vertical distribution of molecules. Astrophys. J. Suppl. Ser. 257, 4 (2021).

  79. Kataoka, A. et al. Opacity of fluffy dust aggregates. Astron. Astrophys. 568, A42 (2014).

    Article  Google Scholar 

  80. Ardila, D. R. et al. Hot gas lines in T Tauri stars. Astrophys. J. Suppl. Ser. 207, 1 (2013).

    Article  ADS  Google Scholar 

  81. Kama, M. et al. Volatile-carbon locking and release in protoplanetary disks—a study of TW Hya and HD 100546. Astron. Astrophys. 592, A83 (2016).

    Article  Google Scholar 

Download references


We acknowledge K. Öberg for her feedback on the surface binding properties of CO ice, S. Andrews for his insightful discussion of the outer radii of disks as measured from CO emission and J. Szulagyi for insightful discussions about the temperature structures in protoplanetary disks. This work benefited from the Exoplanet Summer Program in the Other Worlds Laboratory at the University of California, Santa Cruz, a program funded by the Heising–Simons Foundation. D.P. acknowledges support from the Ford Foundation Dissertation Year Fellowship Program and support from NASA (the National Aeronautics and Space Administration) through the NASA Hubble Fellowship grant HST-HF2-51490.001-A awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS5-26555. D.P. and R.M.C. acknowledge support from NSF CAREER grant number AST-1555385. R.M.C and X.Z. acknowledge support from NASA Interdisciplinary Consortia for Astrobiology Research (ICAR) grant 80NSSC21K0597. P.G. acknowledges support from the 51 Pegasi b Fellowship sponsored by the Heising–Simons Foundation and support from NASA through the NASA Hubble Fellowship grant HST-HF2-51456.001-A awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS5-26555. X.Z. acknowledges support from the NASA Solar System Workings Grant 80NSSC19K0791 and the NASA Exoplanet Research Grant 80NSSC22K0236. D.P. is an NHFP Sagan Fellow.

Author information

Authors and Affiliations



D.P., P.G. and R.M.C. conceived of the project. D.P. and P.G. adapted the microphysical model of CO ice formation. D.P. coupled the radial model to the microphysical ice modelling and wrote the manuscript. D.P. and R.M.C. conceived of the concepts used in the model coupling. D.P., X.Z. and R.M.C. conceived several useful tests of the finished model. All authors provided comments used in editing the manuscript.

Corresponding author

Correspondence to Diana Powell.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Astronomy thanks Edwin Bergin, Colette Salyk and the other, anonymous, reviewer(s) for their contribution to the peer review of this work

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Figs. 1–4 and Tables 1–2.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Powell, D., Gao, P., Murray-Clay, R. et al. Depletion of gaseous CO in protoplanetary disks by surface-energy-regulated ice formation. Nat Astron 6, 1147–1155 (2022).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing