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Formation of secondary atmospheres on terrestrial planets by late disk accretion

A Publisher Correction to this article was published on 18 August 2020

This article has been updated


Recently, gas disks have been discovered around main-sequence stars well beyond the usual protoplanetary disk lifetimes (that is, 10 Myr), when planets have already formed1,2,3,4. These gas disks, mainly composed of CO, carbon and oxygen5,6,7, seem to be ubiquitous3 in systems with planetesimal belts (similar to our Kuiper belt), and can last for hundreds of millions of years8. Planets orbiting in these gas disks will accrete9,10 a large quantity of gas that will transform their primordial atmospheres into new secondary atmospheres with compositions similar to that of the parent gas disk. Here we quantify how large a secondary atmosphere can be created for a variety of observed gas disks and for a wide range of planet types. We find that gas accretion in this late phase is very important and an Earth’s atmospheric mass of gas is readily accreted on terrestrial planets in very tenuous gas disks. In slightly more massive disks, we show that massive CO atmospheres can be accreted, forming planets with up to sub-Neptune-like pressures. Our results demonstrate that new secondary atmospheres with high metallicities and high C/O ratios will be created in these late gas disks, resetting their primordial compositions inherited from the protoplanetary disk phase, and providing a new birth to planets that lost their atmosphere to photoevaporation or giant impacts. We therefore propose a new paradigm for the formation of atmospheres on low-mass planets, which can be tested with future observations (James Webb Space Telescope (JWST), Extremely Large Telescope (ELT), Atmospheric Remote-sensing Infrared Exoplanet Large-survey (ARIEL). We also show that this late accretion would show a very clear signature in sub-Neptunes or cold exo-Jupiters. Finally, we find that accretion creates cavities in late gas disks, which could be used as a new planet detection method, for low-mass planets a few to a few tens of astronomical units from their host stars.

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Fig. 1: Formation of massive secondary atmospheres.
Fig. 2: Pressure and density evolution of an initially desiccated planet embedded in a late gas disk.
Fig. 3: Signature of late gas accretion on giant planets.
Fig. 4: Cavity created by a low-mass planet in a late gas disk.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

Code availability

The particular scripts used for the analysis are made in python and available on reasonable request from the corresponding author.

Change history


  1. 1.

    Dent, W. R. F. et al. Molecular gas clumps from the destruction of icy bodies in the β Pictoris debris disk. Science 343, 1490–1492 (2014).

    ADS  Google Scholar 

  2. 2.

    Lieman-Sifry, J. et al. Debris disks in the scorpius-centaurus OB association resolved by ALMA. Astrophys. J. 828, 25 (2016).

    ADS  Google Scholar 

  3. 3.

    Moór, A. et al. Molecular gas in debris disks around young A-type stars. Astrophys. J. 849, 123 (2017).

    ADS  Google Scholar 

  4. 4.

    Matrà, L., Öberg, K. I., Wilner, D. J., Olofsson, J. & Bayo, A. On the ubiquity and stellar luminosity dependence of exocometary CO gas: detection around M dwarf TWA 7. Astron. J. 157, 117 (2019).

    ADS  Google Scholar 

  5. 5.

    Cataldi, G. et al. Herschel/HIFI observations of ionised carbon in the β Pictoris debris disk. Astron. Astrophys. 563, A66 (2014).

    Google Scholar 

  6. 6.

    Kral, Q., Matrà, L., Wyatt, M. C. & Kennedy, G. M. Predictions for the secondary CO, C and O gas content of debris discs from the destruction of volatile-rich planetesimals. Mon. Not. R. Astron. Soc. 469, 521–550 (2017).

    ADS  Google Scholar 

  7. 7.

    Higuchi, A. E. et al. Detection of submillimeter-wave [C i] emission in gaseous debris disks of 49 Ceti and β Pictoris. Astrophys. J. 839, L14 (2017).

    ADS  Google Scholar 

  8. 8.

    Matrà, L. et al. Detection of exocometary CO within the 440 Myr old Fomalhaut belt: a similar CO+CO2 ice abundance in exocomets and Solar System comets. Astrophys. J. 842, 9 (2017).

    ADS  Google Scholar 

  9. 9.

    Lee, E. J., Chiang, E. & Ormel, C. W. Make super-Earths, not Jupiters: accreting nebular gas onto solid cores at 0.1 au and beyond. Astrophys. J. 797, 95 (2014).

    ADS  Google Scholar 

  10. 10.

    Lee, E. J. & Chiang, E. To cool is to accrete: analytic scalings for nebular accretion of planetary atmospheres. Astrophys. J. 811, 41 (2015).

    ADS  Google Scholar 

  11. 11.

    Kóspál, Á. et al. ALMA observations of the molecular gas in the debris disk of the 30 Myr old star HD 21997. Astrophys. J. 776, 77 (2013).

    ADS  Google Scholar 

  12. 12.

    Zuckerman, B. & Song, I. A 40 Myr old gaseous circumstellar disk at 49 Ceti: massive CO-rich comet clouds at young A-type stars. Astrophys. J. 758, 77 (2012).

    ADS  Google Scholar 

  13. 13.

    Kral, Q. & Latter, H. The magnetorotational instability in debris-disc gas. Mon. Not. R. Astron. Soc. 461, 1614–1620 (2016).

    ADS  Google Scholar 

  14. 14.

    Kral, Q. et al. A self-consistent model for the evolution of the gas produced in the debris disc of β Pictoris. Mon. Not. R. Astron. Soc. 461, 845–858 (2016).

    ADS  Google Scholar 

  15. 15.

    Kral, Q. et al. Around HD 131835: reinterpreting young debris discs with protoplanetary disc levels of CO gas as shielded secondary discs. Mon. Not. R. Astron. Soc. 489, 3670–3691 (2019).

    ADS  Google Scholar 

  16. 16.

    Testi, L. et al. Hunting for planets in the HL tau disk. Astrophys. J. 812, L38 (2015).

    ADS  Google Scholar 

  17. 17.

    Thureau, N. D. et al. An unbiased study of debris discs around A-type stars with Herschel. Mon. Not. R. Astron. Soc. 445, 2558–2573 (2014).

    ADS  Google Scholar 

  18. 18.

    Keppler, M. et al. Discovery of a planetary-mass companion within the gap of the transition disk around PDS 70. Astron. Astrophys. 617, A44 (2018).

    Google Scholar 

  19. 19.

    Müller, A. et al. Orbital and atmospheric characterization of the planet within the gap of the PDS 70 transition disk. Astron. Astrophys. 617, L2 (2018).

    ADS  Google Scholar 

  20. 20.

    Haffert, S. Y. et al. Two accreting protoplanets around the young star PDS 70. Nat. Astron. 3, 749–754 (2019).

    ADS  Google Scholar 

  21. 21.

    Nimmo, F. & Kleine, T. How rapidly did mars accrete? Uncertainties in the Hf–W timing of core formation. Icarus 191, 497–504 (2007).

    ADS  Google Scholar 

  22. 22.

    Jacobsen, S. B. The Hf–W isotopic system and the origin of the Earth and Moon. Annu. Rev. Earth Planet. Sci. 33, 531–570 (2005).

    ADS  Google Scholar 

  23. 23.

    Owen, J. E. Atmospheric escape and the evolution of close-in exoplanets. Annu. Rev. Earth Planet. Sci. 47, 67–90 (2019).

    ADS  Google Scholar 

  24. 24.

    Yalinewich, A. & Schlichting, H. Atmospheric mass-loss from high-velocity giant impacts. Mon. Not. R. Astron. Soc. 486, 2780–2789 (2019).

    ADS  Google Scholar 

  25. 25.

    Quintana, E. V., Barclay, T., Borucki, W. J., Rowe, J. F. & Chambers, J. E. The frequency of giant impacts on Earth-like worlds. Astrophys. J. 821, 126 (2016).

    ADS  Google Scholar 

  26. 26.

    Lopez, E. D. & Fortney, J. J. Understanding the mass–radius relation for sub-Neptunes: radius as a proxy for composition. Astrophys. J. 792, 1 (2014).

    ADS  Google Scholar 

  27. 27.

    Lee, E. J. & Chiang, E. Breeding super-Earths and birthing super-puffs in transitional disks. Astrophys. J. 817, 90 (2016).

    ADS  Google Scholar 

  28. 28.

    Grimm, S. L. et al. The nature of the TRAPPIST-1 exoplanets. Astron. Astrophys. 613, A68 (2018).

    Google Scholar 

  29. 29.

    Kreidberg, L. et al. Clouds in the atmosphere of the super-Earth exoplanet GJ1214b. Nature 505, 69–72 (2014).

    ADS  Google Scholar 

  30. 30.

    Charnay, B., Meadows, V., Misra, A., Leconte, J. & Arney, G. 3D modeling of GJ1214b’s atmosphere: formation of inhomogeneous high clouds and observational implications. Astrophys. J. 813, L1 (2015).

    ADS  Google Scholar 

  31. 31.

    Morley, C. V. et al. Thermal emission and reflected light spectra of super Earths with flat transmission spectra. Astrophys. J. 815, 110 (2015).

    ADS  Google Scholar 

  32. 32.

    Morley, C. V., Kreidberg, L., Rustamkulov, Z., Robinson, T. & Fortney, J. J. Observing the atmospheres of known temperate Earth-sized planets with JWST. Astrophys. J. 850, 121 (2017).

    ADS  Google Scholar 

  33. 33.

    Benneke, B. et al. A sub-Neptune exoplanet with a low-metallicity methane-depleted atmosphere and Mie-scattering clouds. Nat. Astron. 3, 813–821 (2019).

    ADS  Google Scholar 

  34. 34.

    Fraine, J. et al. Water vapour absorption in the clear atmosphere of a neptune-sized exoplanet. Nature 513, 526–529 (2014).

    ADS  Google Scholar 

  35. 35.

    Wakeford, H. R. et al. HAT-P-26b: a neptune-mass exoplanet with a well-constrained heavy element abundance. Science 356, 628–631 (2017).

    ADS  Google Scholar 

  36. 36.

    Benneke, B. et al. Water vapor and clouds on the habitable-zone sub-Neptune exoplanet K2-18b. Astrophys. J. 887, L14 (2019).

    ADS  Google Scholar 

  37. 37.

    Tsiaras, A., Waldmann, I. P., Tinetti, G., Tennyson, J. & Yurchenko, S. N. Water vapour in the atmosphere of the habitable-zone eight-Earth-mass planet K2-18 b. Nat. Astron. 3, 1086–1091 (2019).

    ADS  Google Scholar 

  38. 38.

    Konopacky, Q. M., Barman, T. S., Macintosh, B. A. & Marois, C. Detection of carbon monoxide and water absorption lines in an exoplanet atmosphere. Science 339, 1398–1401 (2013).

    ADS  Google Scholar 

  39. 39.

    GRAVITY Collaboration et al. Peering into the formation history of β Pictoris b with VLTI/GRAVITY long baseline interferometry. Astron. Astrophys. 633, A110 (2020).

    Google Scholar 

  40. 40.

    Charnay, B. et al. A self-consistent cloud model for brown dwarfs and young giant exoplanets: comparison with photometric and spectroscopic observations. Astrophys. J. 854, 172 (2018).

    ADS  Google Scholar 

  41. 41.

    Janson, M. et al. Direct imaging detection of methane in the atmosphere of GJ 504 b. Astrophys. J. 778, L4 (2013).

    ADS  Google Scholar 

  42. 42.

    Macintosh, B. et al. Discovery and spectroscopy of the young jovian planet 51 Eri b with the gEmini Planet Imager. Science 350, 64–67 (2015).

    ADS  Google Scholar 

  43. 43.

    Skemer, A. J. et al. The LEECH exoplanet imaging survey: characterization of the coldest directly imaged exoplanet, GJ 504 b, and evidence for superstellar metallicity. Astrophys. J. 817, 166 (2016).

    ADS  Google Scholar 

  44. 44.

    Cataldi, G. et al. ALMA resolves C i emission from the β Pictoris debris disk. Astrophys. J. 861, 72 (2018).

    ADS  Google Scholar 

  45. 45.

    Xie, J.-W., Brandeker, A. & Wu, Y. On the unusual gas composition in the β Pictoris debris disk. Astrophys. J. 762, 114 (2013).

    ADS  Google Scholar 

  46. 46.

    Lynden-Bell, D. & Pringle, J. E. The evolution of viscous discs and the origin of the nebular variables. Mon. Not. R. Astron. Soc. 168, 603–637 (1974).

    ADS  Google Scholar 

  47. 47.

    Shakura, N. I. & Sunyaev, R. A. Reprint of 1973A&A….24. 337S. Black holes in binary systems. Observational appearance. Astron. Astrophys. 500, 33 (1973).

    ADS  Google Scholar 

  48. 48.

    Moór, A. et al. New millimeter CO observations of the gas-rich debris disks 49 Cet and HD 32297. Astrophys. J. 884, 108 (2019).

    ADS  Google Scholar 

  49. 49.

    Marino, S. et al. Population synthesis of exocometary gas around A stars. Mon. Not. R. Astron. Soc. (in the press).

  50. 50.

    Thébault, P. & Augereau, J.-C. Collisional processes and size distribution in spatially extended debris discs. Astron. Astrophys. 472, 169 (2007).

    ADS  Google Scholar 

  51. 51.

    Kral, Q., Thébault, P. & Charnoz, S. LIDT-DD: a new self-consistent debris disc model that includes radiation pressure and couples dynamical and collisional evolution. Astron. Astrophys. 558, A121 (2013).

    ADS  Google Scholar 

  52. 52.

    Wyatt, M. C. Evolution of debris disks. Annu. Rev. Astron. Astrophys. 46, 339–383 (2008).

    ADS  Google Scholar 

  53. 53.

    Dominik, C. & Decin, G. Age dependence of the Vega phenomenon: theory. Astrophys. J. 598, 626 (2003).

    ADS  Google Scholar 

  54. 54.

    Wyatt, M. C. et al. Steady state evolution of debris disks around a stars. Astrophys. J. 663, 365 (2007).

    ADS  Google Scholar 

  55. 55.

    Matrà, L. et al. An empirical planetesimal belt radius–stellar luminosity relation. Astrophys. J. 859, 72 (2018).

    ADS  Google Scholar 

  56. 56.

    Williams, J. P. & Cieza, L. A. Protoplanetary disks and their evolution. Annu. Rev. Astron. Astrophys. 49, 67–117 (2011).

    ADS  Google Scholar 

  57. 57.

    Lee, E. J., Chiang, E. & Ferguson, J. W. Optically thin core accretion: how planets get their gas in nearly gas-free discs. Mon. Not. R. Astron. Soc. 476, 2199 (2018).

    ADS  Google Scholar 

  58. 58.

    Freedman, R. S. et al. Gaseous mean opacities for giant planet and ultracool dwarf atmospheres over a range of metallicities and temperatures. Astrophys. J. Suppl. Ser. 214, 25 (2014).

    ADS  Google Scholar 

  59. 59.

    Tanigawa, T., Ohtsuki, K. & Machida, M. N. Distribution of accreting gas and angular momentum onto circumplanetary disks. Astrophys. J. 747, 47 (2012).

    ADS  Google Scholar 

  60. 60.

    Dorn, C., Mosegaard, K., Grimm, S. L. & Alibert, Y. Interior characterization in multiplanetary systems: TRAPPIST-1. Astrophys. J. 865, 20 (2018).

    ADS  Google Scholar 

  61. 61.

    Robinson, T. D. & Catling, D. C. Common 0.1 bar tropopause in thick atmospheres set by pressure-dependent infrared transparency. Nat. Geosci. 7, 12–15 (2014).

    ADS  Google Scholar 

  62. 62.

    Ormel, C. W., Shi, J.-M. & Kuiper, R. Hydrodynamics of embedded planets’ first atmospheres—II. A rapid recycling of atmospheric gas. Mon. Not. R. Astron. Soc. 447, 3512–3525 (2015).

    ADS  Google Scholar 

  63. 63.

    Béthune, W. & Rafikov, R. R. Envelopes of embedded super-Earths—II. Three-dimensional isothermal simulations. Mon. Not. R. Astron. Soc. 488, 2365–2379 (2019).

    ADS  Google Scholar 

  64. 64.

    Fung, J., Artymowicz, P. & Wu, Y. The 3D flow field around an embedded planet. Astrophys. J. 811, 101 (2015).

    ADS  Google Scholar 

  65. 65.

    D’Angelo, G. & Bodenheimer, P. Three-dimensional radiation-hydrodynamics calculations of the envelopes of young planets embedded in protoplanetary disks. Astrophys. J. 778, 77 (2013).

    ADS  Google Scholar 

  66. 66.

    Dullemond, C. P. et al. RADMC-3D: a multi-purpose radiative transfer tool. Astrophysics Source Code Library ascl:1202.015 (2012).

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We thank G. Rosotti, P. Thebault and A. Shannon for discussions. Q.K. deidcates this paper to Michaël.

Author information




Q.K. led the work, proposed the original idea, wrote the manuscript and produced Figs. 3 and 4. J.D. coded the model and produced Figs. 1 and 2. B.C. provided atmospheric parameters to input into the model, expertise in atmosphere observations and produced the synthetic spectra shown in the paper. All authors contributed to the interpretation of the results and commented on the paper.

Corresponding author

Correspondence to Quentin Kral.

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Extended data

Extended Data Fig. 1 Typical viscous evolution timescales.

We plot the viscous timescale tν as a function of the viscous parameter α for different belt locations (50, 100 and 150 au) and different gas temperatures (10, 30 and 100 K).

Extended Data Fig. 2 Evolution of \(\dot{M}\) with time.

We plot the temporal evolution of \(\dot{M}\) for different belt locations (50 and 100 au) and different initial belt masses (0.1, 1, 10, and 100 M).

Extended Data Fig. 3 GCR for different values of mean molecular weight μ.

Temporal evolution of the gas-to-core ratio (GCR) with varying μ. We note that the GCR grows more slowly than expected for the cases μ = 7 and 14 when \(\dot{M}=1{0}^{-2}\) M/Myr, which is because the theoretical cooling accretion rate becomes smaller than 10−2 M/Myr for lower values of μ (see Extended Data Fig. 4). We also see that for lower values of μ, the accretion is less efficient from the start because the gas disk scaleheight is higher and less gas is accreted (see Extended Data Fig. 5).

Extended Data Fig. 4 Potential accretion rate on a planet Vs. available accretion rates.

We plot the temporal evolution of the potential theoretical accretion rate on a planet \({\dot{M}}_{{\rm{gas}}}\) (numerical derivative with κ varying with time) for different values of planet semi-major axes apl, atmospheric mean molecular weight μ and core mass \({M}_{{\rm{core}}}\). The fiducial model is apl = 1 au, μ = 14, and \({M}_{{\rm{core}}}=1\) M. We overplot horizontal lines with different input rate values of our parameter \(\dot{M}\), including the case of 10−2 M/Myr over 100 Myr to verify whether in the cases studied in this paper the theoretical accretion rate is higher than our \(\dot{M}\) parameter (which is always the case for μ = 28, large \({M}_{{\rm{core}}}\) or distant planets). We note that for the μ = 28 case, the green lines become less steep at large t. This is because as t increases, one reaches the second regime for which − a∕(bt) 1, where \({\dot{M}}_{{\rm{gas}}}\) scales as t−0.4 instead of t−0.7 in the other regime (see Eqs 9 and 10). We also note that for the case at 0.1 au (for which T = 1000 K), the opacity varies more slowly with T for high enough densities and β becomes smaller10, hence leading to a higher \({\dot{M}}_{{\rm{gas}}}\).

Extended Data Fig. 5 Is a planet accreting all gas flowing through the disk?

We plot the Hill sphere radius-to-scaleheight ratio Vs. the distance to host star. For the lowest-mass planets, the Hill sphere radius can be smaller than the disk scaleheight and gas can flow inwards rather than being accreted.

Extended Data Fig. 6 GCR and pressures for a Mars-mass and a distant planet.

Temporal evolution of the gas-to-core ratio (left) and pressure (right) for a Mars-mass (0.1 M at 1.5 au) planet and a distant planet (10 au) with a core mass of 0.5 M up to a GCR of 0.5. In the pressure plot (right), the thick solid line is for the Mars-like planet case and the thinner line is for the core of mass 0.5 M at 10 au. We note that for the Mars-mass case, GCR grows more slowly than expected when \(\dot{M}=1{0}^{-2}\) M/Myr, which is because the theoretical cooling accretion rate becomes smaller than 10−2 M/Myr in this case (see Extended Data Fig. 4).

Extended Data Fig. 7 Hill Vs. Bondi radii.

Hill and Bondi radii Vs. planet mass for different planet semi-major axes.

Extended Data Fig. 8 GCR and pressures for a planet starting with an Earth atmospheric mass.

Temporal evolution of the gas-to-core ratio (left) and pressure (right) starting from a pre-existing atmosphere with an Earth atmospheric mass.

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Supplementary Figs. 1–4 and discussion.

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Kral, Q., Davoult, J. & Charnay, B. Formation of secondary atmospheres on terrestrial planets by late disk accretion. Nat Astron 4, 769–775 (2020).

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