Recognition: 1 theorem link
· Lean TheoremCoupled Photochemical-Climate Modeling of Plausible Tenuous Outgassed Atmospheres on the TRAPPIST-1 Planets
Pith reviewed 2026-05-15 01:57 UTC · model grok-4.3
The pith
Tenuous atmospheres on the TRAPPIST-1 planets can persist if water and CO2 outgassing balances high escape rates.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
Tenuous atmospheres on the TRAPPIST-1 planets are likely possible, supported by constant plausible rates of water and/or CO2 outgassing against assumed high escape rates up to ~10^{30} s^{-1}. The coupled model samples hundreds of cases per planet, generates six compositional archetypes, and produces atmospheres commonly between 10^{-4} and 1 bar. Potentially habitable surface environments appear for TRAPPIST-1d at 0.05–2 bar and TRAPPIST-1e at 0.5–1 bar. All resulting atmospheres for planets b, c, d, and e fit available JWST transmission data to less than 3 sigma, while emission data favor thin O2-dominated cases for the inner two planets.
What carries the argument
A coupled photochemical-climate model that samples outgassing, deposition, and escape rates while allowing surface pressure to vary dynamically according to the net balance of sources and sinks.
If this is right
- Six compositional archetypes arise across the explored phase space of H2O and CO2 outgassing.
- Potentially habitable surface environments are possible for TRAPPIST-1d (0.05–2 bar) and TRAPPIST-1e (0.5–1 bar).
- Every atmosphere generated for planets b, c, d, and e matches JWST transmission data to within 3 sigma.
- Emission data constrain TRAPPIST-1b to ≲0.01 bar and TRAPPIST-1c to ≲0.2 bar in O2-dominated cases that may include trace SO2.
Where Pith is reading between the lines
- Future emission spectroscopy could test whether the inner planets actually host the thin O2-rich atmospheres favored by the models.
- Sustained outgassing at the required rates implies ongoing geological activity that might be detectable through surface features or volcanic signatures.
- The dynamic-pressure modeling approach could be extended to other close-in rocky planets around M dwarfs to assess their atmospheric retention.
- Trace SO2 in some modeled cases offers a potential observational discriminant for future spectra.
Load-bearing premise
Outgassing rates of water and CO2 can be sustained at levels that exactly balance escape rates up to 10^{30} molecules per second over long timescales.
What would settle it
JWST emission spectra of TRAPPIST-1b or c that rule out thin O2-dominated compositions at the pressures predicted by the models would falsify the viability of these outgassed atmospheres.
Figures
read the original abstract
Available JWST observations TRAPPIST-1 system have suggested that several of the planets are likely airless, or possess a very tenuous atmosphere. However, the high atmospheric escape rates expected for these planets suggest that any tenuous atmosphere must be replenished by constant outgassing, and past studies on modeling potential atmospheres for the planets have not widely considered surface pressures <1 bar. Here, we show that tenuous atmospheres on the TRAPPIST-1 planets are likely possible, supported by constant plausible rates of water and/or CO$_{2}$ outgassing against assumed high escape rates (up to ~10$^{30}$ s$^{-1}$). We use a coupled photochemical-climate model and sample from a broad phase space of outgassing, surface deposition, and top-of-atmosphere escape rates to test hundreds of atmospheres per planet. Critically, our model also allows surface pressure to vary based on the balance of sources and sinks. We find that 6 different compositional archetypes are generated via H$_{2}$O and/or CO$_{2}$ outgassing across our phase space, and atmospheres commonly fall between 10$^{-4}$ -- 1 bar. We find that potentially habitable surface environments are possible for TRAPPIST-1d and e at pressures between 0.05 -- 2 bar and 0.5 -- 1 bar, respectively. Where possible, we compare our models to JWST observational data for TRAPPIST-1b, c, d, and e; all atmospheres found in this study for these planets match available transmission data to <3$\sigma$. However, emission data are consistent with atmospheric outcomes constrained to thin O$_{2}$-dominated compositions for TRAPPIST-1b ($\lesssim$0.01 bars) and c ($\lesssim$0.2 bars), which may or may not contain trace SO$_{2}$.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper employs a coupled photochemical-climate model to investigate plausible tenuous outgassed atmospheres on the TRAPPIST-1 planets. By sampling a broad phase space of H2O and CO2 outgassing rates, surface deposition rates, and top-of-atmosphere escape rates (up to ~10^30 s^{-1}), the model allows surface pressure to emerge from source-sink balance. This produces six compositional archetypes with surface pressures commonly between 10^{-4} and 1 bar. The results suggest potentially habitable conditions for TRAPPIST-1d and e, and all modeled atmospheres are consistent with available JWST transmission data to within 3 sigma, with emission data constraining thin O2-dominated atmospheres for b and c.
Significance. If the central results hold, this study significantly advances understanding of low-pressure atmospheres on rocky exoplanets by demonstrating that constant plausible outgassing can maintain steady-state tenuous atmospheres against high escape rates. It expands the parameter space considered in prior work and provides direct comparisons to JWST observations, supporting the possibility of atmospheres on these planets and informing habitability assessments. The approach of letting pressure adjust dynamically is a strength.
major comments (2)
- [Modeling Approach] Escape rates are prescribed as independent inputs sampled across the phase space rather than derived self-consistently from the atmospheric state (e.g., via energy-limited escape based on the computed EUV absorption or diffusion-limited regimes). This is a load-bearing assumption for the claim that outgassing can balance escape to produce steady-state atmospheres, as unphysical combinations may be included without verification against the modeled T-P profiles and composition.
- [Results and Discussion] The manuscript reports that atmospheres match JWST transmission data to <3 sigma but does not provide details on the exact observational datasets used, the number of models tested per planet, or quantitative fit statistics beyond the sigma threshold. This makes it difficult to assess the robustness of the post-hoc comparison.
minor comments (1)
- [Abstract] The abstract mentions 'assumed high escape rates' but could benefit from a brief note on the range of outgassing rates sampled to contextualize the 'plausible' claim.
Simulated Author's Rebuttal
We thank the referee for their positive summary of our work and for the constructive major comments, which have helped us improve the clarity and robustness of the manuscript. We address each comment point by point below.
read point-by-point responses
-
Referee: [Modeling Approach] Escape rates are prescribed as independent inputs sampled across the phase space rather than derived self-consistently from the atmospheric state (e.g., via energy-limited escape based on the computed EUV absorption or diffusion-limited regimes). This is a load-bearing assumption for the claim that outgassing can balance escape to produce steady-state atmospheres, as unphysical combinations may be included without verification against the modeled T-P profiles and composition.
Authors: We appreciate this observation. Our modeling strategy intentionally prescribes escape rates across a broad, observationally motivated range (up to ~10^30 s^{-1}) to explore the full phase space of source-sink balance without presupposing a particular escape regime. This allows surface pressure to emerge self-consistently from the coupled chemistry-climate calculation. To address the concern about potential unphysical combinations, we have added a dedicated subsection in the Methods that (i) justifies the sampled escape range using literature estimates for TRAPPIST-1 planets, (ii) verifies post hoc that the resulting T-P profiles and compositions are consistent with the assumed escape rates (e.g., EUV absorption depths and diffusion-limited H escape), and (iii) flags any combinations that fall outside physically plausible regimes. Full self-consistent escape coupling would require substantial additional model development and is noted as a future direction. revision: partial
-
Referee: [Results and Discussion] The manuscript reports that atmospheres match JWST transmission data to <3 sigma but does not provide details on the exact observational datasets used, the number of models tested per planet, or quantitative fit statistics beyond the sigma threshold. This makes it difficult to assess the robustness of the post-hoc comparison.
Authors: We agree that greater transparency is needed. In the revised manuscript we have expanded the observational comparison section to explicitly list: (a) the precise JWST transmission datasets and references employed for each planet, (b) the total number of models evaluated per planet (hundreds, as stated in the abstract), and (c) quantitative fit metrics including reduced chi-squared values and the number of models falling within 1, 2, and 3 sigma of the data. These additions allow readers to evaluate the robustness of the <3 sigma statement directly. revision: yes
Circularity Check
No significant circularity; parameters sampled independently with post-hoc checks
full rationale
The paper samples outgassing, deposition, and escape rates independently from a broad phase space, allows surface pressure to adjust to balance, and performs JWST comparisons only as post-hoc validation rather than using them to tune or fit the central results. No load-bearing step reduces by the paper's own equations or self-citation to a tautological input; the derivation chain remains self-contained against external benchmarks and does not exhibit self-definitional, fitted-prediction, or uniqueness-imported patterns.
Axiom & Free-Parameter Ledger
free parameters (3)
- outgassing rates for H2O and CO2
- top-of-atmosphere escape rates
- surface deposition rates
axioms (2)
- domain assumption High atmospheric escape rates are expected for these close-in planets
- domain assumption Outgassing rates can be sustained at plausible levels over geological time
Lean theorems connected to this paper
-
IndisputableMonolith/Cost/FunctionalEquation.leanwashburn_uniqueness_aczel unclear?
unclearRelation between the paper passage and the cited Recognition theorem.
we sample from a broad phase space of outgassing, surface deposition, and top-of-atmosphere escape rates... surface pressure to vary based on the balance of sources and sinks
What do these tags mean?
- matches
- The paper's claim is directly supported by a theorem in the formal canon.
- supports
- The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
- extends
- The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
- uses
- The paper appears to rely on the theorem as machinery.
- contradicts
- The paper's claim conflicts with a theorem or certificate in the canon.
- unclear
- Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.
Reference graph
Works this paper leans on
- [1]
-
[2]
H., Espinoza, N., Boehm, V., et al
Allen, N. H., Espinoza, N., Boehm, V., et al. 2025, arXiv preprint arXiv:2512.07695
-
[3]
Arney, G., Meadows, V., Crisp, D., et al. 2014, Journal of Geophysical Research: Planets, 119, 1860 Plausible Tenuous Atmospheres in the TRAPPIST-1 System35 1.0 1.5 2.0 2.5 3.0 3.5 4.0 X Value (e.g., Wavlength) 9 10 11 12 13 14 15Y Value (e.g., Spectrum Depth) Model 1, 2=13.0 CC=-0.72 Model 2, 2=13.0 CC=0.80 Average of Observations Observations Figure A.1...
work page 2014
-
[4]
Arney, G., Domagal-Goldman, S. D., Meadows, V. S., et al. 2016, Astrobiology, 16, 873
work page 2016
-
[5]
Bandfield, J. L., Glotch, T. D., & Christensen, P. R. 2003, Science, 301, 1084
work page 2003
- [6]
-
[7]
W., G´ erard, J.-C., & Soret, L
Brecht, A., Bougher, S. W., G´ erard, J.-C., & Soret, L. 2012, Icarus, 217, 759
work page 2012
-
[8]
Clifton, O. E., Fiore, A. M., Massman, W. J., et al. 2020, Reviews of Geophysics, 58, e2019RG000670
work page 2020
-
[9]
2008, Atmospheric Environment, 42, 5090
Constant, P., Poissant, L., & Villemur, R. 2008, Atmospheric Environment, 42, 5090
work page 2008
-
[10]
1997, Geophysical Research Letters, 24, 571
Crisp, D. 1997, Geophysical Research Letters, 24, 571
work page 1997
-
[11]
Currie, M. H., Meadows, V. S., & Rasmussen, K. C. 2023, The Planetary Science Journal, 4, 83 De Wit, J., Wakeford, H. R., Lewis, N. K., et al. 2018, Nature Astronomy, 2, 214
work page 2023
-
[12]
2018, Proceedings of the National Academy of Sciences, 115, 260
Dong, C., Jin, M., Lingam, M., et al. 2018, Proceedings of the National Academy of Sciences, 115, 260
work page 2018
-
[13]
2025, Nature Astronomy, 9, 358
Ducrot, E., Lagage, P.-O., Min, M., et al. 2025, Nature Astronomy, 9, 358
work page 2025
-
[14]
Elkins-Tanton, L. T., & Seager, S. 2008, The Astrophysical Journal, 688, 628
work page 2008
-
[15]
Erard, S., Mustard, J., Murchie, S., et al. 1994, Icarus, 111, 317
work page 1994
-
[16]
Espinoza, N., Allen, N. H., Glidden, A., et al. 2025, The Astrophysical Journal Letters, 990, L52
work page 2025
-
[17]
Fauchez, T. J., Turbet, M., Wolf, E. T., et al. 2020, Planets 2020, Ground and Space Observatories: a Joint Venture to Planetary Science, 8
work page 2020
-
[18]
Fray, N., & Schmitt, B. 2009, Planet. Space Sci., 57, 2053, doi: 10.1016/j.pss.2009.09.011
-
[19]
Gaillard, F., Bouhifd, M. A., F¨ uri, E., et al. 2021, Space Science Reviews, 217, 22
work page 2021
-
[20]
Gao, P., Hu, R., Robinson, T. D., Li, C., & Yung, Y. L. 2015, The Astrophysical Journal, 806, 249
work page 2015
-
[21]
Gialluca, M. T., Barnes, R., Meadows, V. S., et al. 2024, The Planetary Science Journal, 5, 137
work page 2024
-
[22]
2021, Publications of the Astronomical Society of the Pacific, 133, 054401 —
Wunderlich, F. 2021, Publications of the Astronomical Society of the Pacific, 133, 054401 —. 2023, Publications of the Astronomical Society of the Pacific, 135, 119201
work page 2021
-
[23]
Gillon, M., Triaud, A. H., Demory, B.-O., et al. 2017, Nature, 542, 456
work page 2017
- [24]
-
[25]
2025, The Astrophysical Journal Letters, 990, L53 36Gialluca, et al
Glidden, A., Ranjan, S., Seager, S., et al. 2025, The Astrophysical Journal Letters, 990, L53 36Gialluca, et al
work page 2025
-
[26]
Gordon, I. E., Rothman, L. S., Hargreaves, e. R., et al. 2022, Journal of quantitative spectroscopy and radiative transfer, 277, 107949
work page 2022
- [27]
-
[28]
2020, Journal of Geophysical Research: Space Physics, 125, e2019JA027639
Gronoff, G., Arras, P., Baraka, S., et al. 2020, Journal of Geophysical Research: Space Physics, 125, e2019JA027639
work page 2020
-
[29]
Guimond, C. M., Shorttle, O., & Rudge, J. F. 2023, Monthly Notices of the Royal Astronomical Society, 521, 2535 G¨ usten, H., Heinrich, G., M¨ onnich, E., et al. 1996, Atmospheric Environment, 30, 911
work page 2023
-
[30]
Harris, C. R., Millman, K. J., Van Der Walt, S. J., et al. 2020, nature, 585, 357
work page 2020
-
[31]
2019, Annual Review of Earth and Planetary Sciences, 47, 583
Helling, C. 2019, Annual Review of Earth and Planetary Sciences, 47, 583
work page 2019
-
[32]
Howard, W. S., Kowalski, A. F., Flagg, L., et al. 2023, The Astrophysical Journal, 959, 64
work page 2023
-
[33]
Ih, J., Kempton, E. M.-R., Whittaker, E. A., & Lessard, M. 2023, The Astrophysical Journal Letters, 952, L4
work page 2023
-
[34]
Kasting, J. F., Liu, S., & Donahue, T. 1979, Journal of Geophysical Research: Oceans, 84, 3097
work page 1979
-
[35]
Kite, E. S., & Barnett, M. N. 2020, Proceedings of the National Academy of Sciences, 117, 18264
work page 2020
-
[36]
Kopparapu, R. K., Ramirez, R., Kasting, J. F., et al. 2013, The Astrophysical Journal, 765, 131
work page 2013
-
[37]
Krissansen-Totton, J., & Fortney, J. J. 2022, The Astrophysical Journal, 933, 115
work page 2022
-
[38]
2025, arXiv preprint arXiv:2504.12541
Li, H., Wang, X., Dong, C., et al. 2025, arXiv preprint arXiv:2504.12541
-
[39]
2023, The Astrophysical Journal Letters, 955, L22
Lim, O., Benneke, B., Doyon, R., et al. 2023, The Astrophysical Journal Letters, 955, L22
work page 2023
-
[40]
S., Lebonnois, S., Mahieux, A., et al
Limaye, S. S., Lebonnois, S., Mahieux, A., et al. 2017, Icarus, 294, 124
work page 2017
-
[41]
Lincowski, A. P., Meadows, V. S., Crisp, D., et al. 2018, The Astrophysical Journal, 867, 76 —. 2021, The Astrophysical Journal Letters, 908, L44
work page 2018
-
[42]
Lincowski, A. P., Meadows, V. S., Zieba, S., et al. 2023, The Astrophysical Journal Letters, 955, L7
work page 2023
-
[43]
2023, Nature Astronomy, 7, 1317
Lustig-Yaeger, J., Fu, G., May, E., et al. 2023, Nature Astronomy, 7, 1317
work page 2023
-
[44]
Ma, Y., Nagy, A. F., Sokolov, I. V., & Hansen, K. C. 2004, Journal of Geophysical Research: Space Physics, 109
work page 2004
- [45]
-
[46]
Mansfield, M. W., Xue, Q., Zhang, M., et al. 2024, The Astrophysical Journal Letters, 975, L22
work page 2024
-
[47]
Meadows, V. S., & Crisp, D. 1996, Journal of Geophysical Research: Planets, 101, 4595
work page 1996
-
[48]
Meadows, V. S., Lincowski, A. P., & Lustig-Yaeger, J. 2023, The Planetary Science Journal, 4, 192
work page 2023
-
[49]
Meadows, V. S., Arney, G. N., Schwieterman, E. W., et al. 2018, Astrobiology, 18, 133
work page 2018
-
[50]
Misra, A., Meadows, V., Claire, M., & Crisp, D. 2014, Astrobiology, 14, 67
work page 2014
-
[51]
V., Kreidberg, L., Rustamkulov, Z., Robinson, T., & Fortney, J
Morley, C. V., Kreidberg, L., Rustamkulov, Z., Robinson, T., & Fortney, J. J. 2017, The Astrophysical Journal, 850, 121
work page 2017
-
[52]
Peacock, S., Barman, T., Shkolnik, E. L., Hauschildt, P. H., & Baron, E. 2019, The Astrophysical Journal, 871, 235
work page 2019
-
[53]
2025, The Astrophysical Journal, 989, 181
Piaulet-Ghorayeb, C., Benneke, B., Turbet, M., et al. 2025, The Astrophysical Journal, 989, 181
work page 2025
-
[54]
2020, The Astronomical Journal, 159, 206
Qin, J. 2020, The Astronomical Journal, 159, 206
work page 2020
-
[55]
Rackham, B. V., Apai, D., & Giampapa, M. S. 2018, The Astrophysical Journal, 853, 122
work page 2018
-
[56]
2025, The Astrophysical Journal Letters, 979, L5
Radica, M., Piaulet-Ghorayeb, C., Taylor, J., et al. 2025, The Astrophysical Journal Letters, 979, L5
work page 2025
-
[57]
Ranjan, S., Schwieterman, E. W., Harman, C., et al. 2020, The Astrophysical Journal, 896, 148
work page 2020
-
[58]
Rathcke, A. D., Buchhave, L. A., De Wit, J., et al. 2025, The Astrophysical Journal Letters, 979, L19
work page 2025
-
[59]
2024, arXiv preprint arXiv:2404.02932
Redfield, S., Batalha, N., Benneke, B., et al. 2024, arXiv preprint arXiv:2404.02932
-
[60]
2022, The Planetary Science Journal, 3, 238
Redwing, E., de Pater, I., Luszcz-Cook, S., et al. 2022, The Planetary Science Journal, 3, 238
work page 2022
-
[61]
Robinson, T. D. 2017, The Astrophysical Journal, 836, 236
work page 2017
-
[62]
Robinson, T. D., & Crisp, D. 2018, Journal of Quantitative Spectroscopy and Radiative Transfer, 211, 78
work page 2018
-
[63]
D., Maltagliati, L., Marley, M
Robinson, T. D., Maltagliati, L., Marley, M. S., & Fortney, J. J. 2014, Proceedings of the National Academy of Sciences, 111, 9042
work page 2014
-
[64]
Robinson, T. D., Meadows, V. S., Crisp, D., et al. 2011, Astrobiology, 11, 393 Rocky Worlds DDT Program Website. 2025, https://rockyworlds.stsci.edu/index.html
work page 2011
-
[65]
Rustamkulov, Z., Sing, D. K., Liu, R., & Wang, A. 2022, The Astrophysical Journal Letters, 928, L7
work page 2022
-
[66]
Petkowski, J. J. 2025, Proceedings of the National Academy of Sciences, 122, e2416188122
work page 2025
-
[67]
Seinfeld, J. H., & Pandis, S. N. 2016, Atmospheric chemistry and physics: from air pollution to climate change (John Wiley & Sons)
work page 2016
-
[68]
Sergeev, D. E., Fauchez, T. J., Turbet, M., et al. 2022, The Planetary Science Journal, 3, 212 Plausible Tenuous Atmospheres in the TRAPPIST-1 System37
work page 2022
-
[69]
2015, The encyclopedia of volcanoes (Elsevier)
Stix, J. 2015, The encyclopedia of volcanoes (Elsevier)
work page 2015
-
[70]
1988, Applied optics, 27, 2502
Stamnes, K., Tsay, S.-C., Wiscombe, W., & Jayaweera, K. 1988, Applied optics, 27, 2502
work page 1988
-
[71]
Stamnes, K., Tsay, S.-C., Wiscombe, W., & Laszlo, I. 2000, DISORT, a general-purpose Fortran program for discrete-ordinate-method radiative transfer in scattering and emitting layered media: documentation of methodology
work page 2000
-
[72]
Stein, O., Schultz, M. G., Bouarar, I., et al. 2014, Atmospheric chemistry and physics, 14, 9295
work page 2014
-
[73]
Thomas, T. B., Meadows, V. S., Krissansen-Totton, J., et al. 2025, The Planetary Science Journal, 6, 126
work page 2025
-
[74]
Tinetti, G., Meadows, V. S., Crisp, D., et al. 2005, Astrobiology, 5, 461
work page 2005
-
[75]
2020, Space science reviews, 216, 100
Turbet, M., Bolmont, E., Bourrier, V., et al. 2020, Space science reviews, 216, 100
work page 2020
-
[76]
2018, Astronomy & Astrophysics, 612, A86
Turbet, M., Bolmont, E., Leconte, J., et al. 2018, Astronomy & Astrophysics, 612, A86
work page 2018
-
[77]
Turbet, M., Fauchez, T. J., Sergeev, D. E., et al. 2022, The Planetary Science Journal, 3, 211
work page 2022
- [78]
-
[79]
Wakeford, H. R., Lewis, N. K., Fowler, J., et al. 2018, The Astronomical Journal, 157, 11 —. 2019, The Astronomical Journal, 157, 11
work page 2018
-
[80]
1987, Atmospheric Environment (1967), 21, 2649
Walcek, C. 1987, Atmospheric Environment (1967), 21, 2649
work page 1987
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.