Formation of secondary atmospheres on terrestrial planets by late disk accretion


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.The exoplanet atmospheres we study may not be primary atmospheres. Models show that the accretion of gas late in a planetary system’s formation may completely replace the primary atmospheres of terrestrial planets. These secondary atmospheres are likely to have high metallicities and high C/O ratios.

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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.


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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.

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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 (2020).

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