arxiv: 2605.00170 · v1 · submitted 2026-04-30 · 🌌 astro-ph.EP

Recognition: unknown

Smaller Than Earth Habitability Model (STEHM): The Lower Size Limit for Atmosphere Retention in the Habitable Zone

Bradford J. Foley, Laura K. Schaefer, Michelle L. Hill, Stephen R. Kane

Authors on Pith no claims yet

Pith reviewed 2026-05-09 20:11 UTC · model grok-4.3

classification 🌌 astro-ph.EP

keywords exoplanet habitabilityatmosphere retentionplanetary radius limithabitable zonestagnant lidvolatile outgassingSTEHM model

0 comments

The pith

Planets must reach at least 0.8 Earth radii to retain atmospheres long-term around sun-like stars under typical conditions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper builds the STEHM model to track how volcanic outgassing, atmospheric escape, and interior heat balance evolve on stagnant-lid planets orbiting in the habitable zone of a sun-like star. It shows that planets at or above 0.8 Earth radii keep their atmospheres for billions of years with Earth-like starting conditions, while smaller worlds lose theirs because outgassing cannot offset escape. Changes in starting carbon, heat-producing elements, or mantle temperature shift the cutoff modestly, sometimes to 0.7 Earth radii, but the model stresses that retention hinges on how the planet formed and cooled early on. This matters for observers because it supplies a practical size filter when ranking small rocky exoplanets for habitability studies.

Core claim

The STEHM model demonstrates that planets with radii of 0.8 Earth radii and larger maintain atmospheres over multi-gigayear timescales under default Earth-like outgassing rates, initial volatile inventories, and escape processes for a solar analog star in a stagnant lid regime, whereas planets smaller than this threshold lose their atmospheres.

What carries the argument

The STEHM numerical model, which couples time-dependent volatile cycling, atmospheric escape, mantle convection, and surface temperature for planets ranging from 0.5 to 1.0 Earth radii.

If this is right

Planets with substantially higher initial carbon inventories than Earth can retain atmospheres down to 0.7 Earth radii.
Larger quantities of heat-producing elements, cooler initial mantle temperatures, and smaller core radius fractions each improve the chance of long-term atmospheric retention.
Atmospheric longevity on small planets is set mainly by formation-time volatile budgets rather than present-day size alone.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Many currently detected sub-Earth exoplanets are likely airless today, narrowing the pool of worlds worth detailed atmospheric follow-up.
The strong sensitivity to early conditions means that two planets of identical size and orbit could have very different habitability outcomes depending on their accretion history.
Extending the same framework to M-dwarf stars would likely produce a different size cutoff because closer-in habitable zones change escape rates.

Load-bearing premise

That the same stagnant-lid outgassing rates, initial volatile amounts, and escape physics measured or assumed for Earth also hold for planets down to half its size.

What would settle it

Spectroscopic detection of a stable atmosphere on a confirmed 0.6 Earth-radius planet inside the habitable zone of a sun-like star, or the absence of atmospheres on multiple planets confirmed to be 0.85 Earth radii or larger in similar orbits.

Figures

Figures reproduced from arXiv: 2605.00170 by Bradford J. Foley, Laura K. Schaefer, Michelle L. Hill, Stephen R. Kane.

**Figure 1.** Figure 1: STEHM flow chart. Green hexagons are input parameters that are calculated by ExoPlex. Orange hexagons are input parameters set within STEHM. Yellow stadiums are components that are explored by STEHM. Arrows indicate how each section of the code interacts with the others. On the bottom right there is a yellow stadium indicating a choice of tectonic regime. This paper is based on a planet with stagnant lid t… view at source ↗

**Figure 2.** Figure 2: Flux rates of a Sun-like star from Ribas et al. (2005), normalized so that the flux at the present solar age matches the modern solar XUV value. We adopt a conservative maximum stellar XUV flux of 10 times the modern solar value. may have experienced a lower XUV flux history (Tu, Lin et al. 2015; Gallet, F. & Bouvier, J. 2015). Atmospheric loss of CO2 is based on the 1D hydrodynamic planetary thermospher… view at source ↗

**Figure 3.** Figure 3 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** Figure 4: STEHM results for stagnant lid Earth (Blue), Venus (Yellow) and Mars (Red) analogs. The model predicts Earth as a stagnant lid planet could have gained a 126 bar CO2 atmosphere, and Venus an 88 bar CO2 atmosphere. After a early degassing of over 4 bars of CO2, Mars’ atmosphere is depleted by ∼ 200 Myrs. tions of a dense (∼ 90 bar), long-lived CO2 atmosphere for Venus and a transient, multi-bar CO2 atmosph… view at source ↗

**Figure 5.** Figure 5: Default Values. Planet size ranges from 1.0 - 0.5 R⊕. Panel A shows STEHM results for amount of atmospheric CO2 found on a Earth sized and below planet. The model predicts that a stagnant lid planet would need to be ≥ 0.8 R⊕ to continuously maintain an atmosphere. Each of the 0.7, 0.6 and 0.5 R⊕ planets lose their atmospheres, though the 0.7 R⊕ planet has a short lived recovery of 0.08 bar. Panel B shows t… view at source ↗

**Figure 6.** Figure 6: Variation in Initial Carbon Inventory. Other than the initial carbon content, the model uses default values set out in Section 3.1 for the remaining variables. Left: Model results using a maximum initial carbon content of 2 × 1022 moles is represented by the solid lines and the minimum carbon content value of 7 × 1021 moles is shown by the dashed lines. The legend shows the color representative of each pla… view at source ↗

**Figure 7.** Figure 7: Variations in HPE Abundance. Other than the HPE abundances outlined in 5.2, the model uses default values set out in Section 3.1 for the remaining variables. Solid lines in each panel represent the maximum values for HPE, dashed lines represent minimum values of HPE. The legend in each panel shows the color representative of each planet radius. Panel A shows the atmospheric CO2 pressure. Both maximum and m… view at source ↗

**Figure 8.** Figure 8: Variations in Initial Mantle Temperature. The maximum mantle temperature is 2200 K (hot start) shown with a solid line and the minimum mantle temperature is 1500 K (cold start) shown with a dashed line. The model uses default values set out in Section 3.1 for the remaining variables. In Panel A, all planets ≥ 0.8 R⊕ maintain their atmosphere for the hot starts, and all planets ≥ 0.7 R⊕ maintain their atmos… view at source ↗

**Figure 9.** Figure 9: Variations in CRF set in ExoPlex within the bounds of code capabilities produced different results for the atmospheric CO2 pressure retained. A change of ∼10 bar is seen in the 0.8 R⊕ planets, and a regained atmosphere of 0.1 bar for the low CRF 0.7 R⊕ planet, whereas the high CRF 0.7 R⊕ planet never regained its atmosphere. Both 0.6 R⊕ planets lost their atmospheres. 5.6. Exobase Temperatures We tested ex… view at source ↗

**Figure 10.** Figure 10: Variations in Planet Density. The panels in this figure show the results of when CRF, and thus planet density, is varied. The model uses default values set out in Section 3.1 for the remaining variables. We tested planets with no core (dashed lines) and planets with a 0.70 CRF (solid lines). For both the planets with a large core and no core, planets ≥ 0.8 R⊕ maintained their atmosphere. For the planets w… view at source ↗

**Figure 11.** Figure 11: A heat map of atmosphere retention for planets from 1.0–0.5 R⊕ at distances that represent each of the HZ boundaries around a Sun-like star, along with the default value of 1 AU. Atmospheric pressure is depicted by the colorbar along with the values in each grid, and measured in bar. The value shown is the final atmospheric pressure when both atmosphere loss and degassing has shutdown on the planet. to … view at source ↗

read the original abstract

With recent advances in exoplanet observational techniques enabling the discovery of increasingly smaller planets, a crucial question emerges in the search for habitable planets: how small can a planet be and still maintain an atmosphere? We present results from the Smaller Than Earth Habitability Model (STEHM) which examines how small a planet can be and still maintain a long-term (multi-gigayear) atmosphere for planets from 1.0$R_\oplus$ down to 0.5$R_\oplus$. The model is based on a stagnant lid planet orbiting within the habitable zone of a sun-like star. Our model demonstrates that planets $\geq$0.8$R_\oplus$ can maintain their atmospheres under our Earth-like default conditions for a solar analog star, while smaller planets lose their atmospheres. Variations from the default Earth-like values cause mostly minor variations to the planet size boundary results, with some changes allowing $\geq$0.7$R_\oplus$ planets to maintain their atmosphere. Initial carbon inventory emerges as the most influential parameter for atmospheric retention, though orders of magnitude difference to Earth values are required to make a significant difference to longevity of atmospheric retention. Planets with substantial initial carbon content, large amounts of heat producing elements, cool initial mantle temperatures and low core radius fractions show the best atmospheric retention capabilities. Our results indicate that atmospheric retention on small planets depends strongly on their formation conditions and early evolution, providing important constraints for future observations of rocky exoplanets and their potential habitability.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

STEHM derives an 0.8 R_earth cutoff for long-term atmosphere retention but ties it to Earth-calibrated rates whose size dependence is unclear.

read the letter

The main result is that planets at or above 0.8 Earth radii keep atmospheres for gigayears under the model's default stagnant-lid setup around a sun-like star, while smaller ones do not. Some parameter combinations push the limit to 0.7 R_earth. Initial carbon inventory has the largest effect, followed by heat-producing elements, mantle temperature, and core radius fraction. Planets with higher carbon, more heat sources, cooler mantles, and smaller cores retain atmospheres longer. This gives a concrete number for the lower size edge in the habitable zone. The systematic sweeps across 0.5-1.0 R_earth and the identification of carbon as the dominant parameter are the useful parts. The work applies standard volatile cycling and escape frameworks to a new size range without inventing new physics, which is fine for producing a practical bound. The soft spot is the handling of radius dependence. The defaults are Earth-like, and the abstract states that variations cause mostly minor changes to the boundary. However, lower gravity on smaller planets increases escape efficiency, and outgassing should scale with surface area or convective vigor rather than remaining constant. If the equations do not already embed these effects, the reported 0.8 threshold is an output of the fixed inputs rather than a robust physical limit. No error bars, sensitivity plots on gravity scaling, or comparison to any observed small-planet atmospheres appear in the abstract. This paper is for observers picking targets for atmosphere follow-up and for modelers who need a ballpark lower limit on rocky-planet habitability. A reader focused on exoplanet demographics or volatile evolution gets value from the specific numbers and the parameter ranking, even if they want to adjust the scalings. It shows clear engagement with the existing literature on stagnant-lid planets. I would bring it to a reading group to discuss the escape and outgassing implementations. I would not cite it in my own work yet because the quantitative boundary feels preliminary. It deserves peer review so that referees can examine the numerical details and request explicit radius-dependent terms if they are missing.

Referee Report

2 major / 2 minor

Summary. The manuscript presents the Smaller Than Earth Habitability Model (STEHM), a numerical model for the long-term evolution of atmospheres on stagnant-lid planets in the habitable zone of a solar analog star. The model integrates outgassing from the interior and atmospheric escape processes for planet radii from 0.5 to 1.0 R_earth. Under default Earth-like parameters for initial volatile inventories, heat-producing elements, mantle temperature, and core radius fraction, the results indicate that planets with radii of at least 0.8 R_earth can retain their atmospheres over multi-Gyr timescales, whereas smaller planets lose them. Parameter variations, especially higher initial carbon inventory, can allow retention down to 0.7 R_earth in some cases.

Significance. If the model's assumptions hold, this provides a physically motivated lower size limit for atmospheric retention on rocky exoplanets, offering constraints for future observations and habitability assessments. The approach of deriving the size boundary from integrated rates rather than imposing it is a strength, as is the exploration of parameter sensitivities showing initial carbon as most influential.

major comments (2)

[Abstract and Model Description] Abstract and model description: The central claim that planets ≥0.8 R_earth retain atmospheres (while <0.8 R_earth lose them) under default conditions requires that outgassing rates, initial volatile inventories, and escape fluxes remain Earth-like even as radius drops. The paper must clarify whether the STEHM equations already embed radius-dependent gravity, heat flux, or mantle convection scalings for escape (e.g., Jeans/hydrodynamic efficiency ∝1/g or stronger) and outgassing (surface area or convective vigor). If size-independent Earth defaults are used without such scalings, the reported boundary is vulnerable to being an artifact of that choice rather than a robust physical limit.
[Results] Results (where the 0.8 R_earth boundary and parameter variations are presented): The abstract states that parameter variations produce 'mostly minor' changes and that initial carbon inventory is most influential, but provides no error bars, full sensitivity tests on key rates (outgassing, escape), or direct comparison to observed small-planet atmospheres. This leaves the quantitative boundary vulnerable to model choice, especially given the stagnant-lid assumption and Earth-calibrated values not independently verified for sub-Earth sizes.

minor comments (2)

[Abstract] The abstract could include a short statement of the key governing equations or the numerical integration method to give readers immediate context for how the size boundary emerges.
[Model Description] Ensure all free parameters (initial carbon inventory, heat-producing elements, initial mantle temperature, core radius fraction) and their Earth-like default values are explicitly listed with units and justification in a dedicated table or section.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive review and positive assessment of the STEHM model's approach to deriving a size boundary from integrated processes. We address the two major comments below, providing clarifications on the model implementation and committing to revisions that strengthen the presentation of results and assumptions.

read point-by-point responses

Referee: [Abstract and Model Description] Abstract and model description: The central claim that planets ≥0.8 R_earth retain atmospheres (while <0.8 R_earth lose them) under default conditions requires that outgassing rates, initial volatile inventories, and escape fluxes remain Earth-like even as radius drops. The paper must clarify whether the STEHM equations already embed radius-dependent gravity, heat flux, or mantle convection scalings for escape (e.g., Jeans/hydrodynamic efficiency ∝1/g or stronger) and outgassing (surface area or convective vigor). If size-independent Earth defaults are used without such scalings, the reported boundary is vulnerable to being an artifact of that choice rather than a robust physical limit.

Authors: We appreciate the referee's emphasis on this clarification. The STEHM model does incorporate several radius-dependent scalings in its core equations. Planetary gravity is computed as g = GM/r² (with mass M derived from radius assuming a density scaling consistent with rocky planets), which directly modulates both Jeans and hydrodynamic escape efficiencies. Outgassing rates scale with surface area (4πr²) and convective heat flux, where mantle convection vigor is parameterized using radius-dependent mantle thickness and Rayleigh number scalings. Initial volatile inventories and heat-producing element abundances are held at Earth-like defaults as a baseline (as stated in the abstract), but these are varied in the sensitivity analysis. We agree that the manuscript text does not explicitly list these scalings in one place, which could lead to misinterpretation. In the revised manuscript we will add a dedicated subsection under Model Description that enumerates each radius-dependent term with the relevant equations. revision: yes
Referee: [Results] Results (where the 0.8 R_earth boundary and parameter variations are presented): The abstract states that parameter variations produce 'mostly minor' changes and that initial carbon inventory is most influential, but provides no error bars, full sensitivity tests on key rates (outgassing, escape), or direct comparison to observed small-planet atmospheres. This leaves the quantitative boundary vulnerable to model choice, especially given the stagnant-lid assumption and Earth-calibrated values not independently verified for sub-Earth sizes.

Authors: We agree that the results section would benefit from more quantitative support. The existing parameter sweeps already demonstrate that the 0.8 R_earth threshold is stable across most variations, with only extreme (orders-of-magnitude) changes in initial carbon inventory shifting the boundary to 0.7 R_earth. In revision we will (i) add uncertainty envelopes or shaded ranges to the key figures based on the explored parameter space, (ii) expand the sensitivity discussion to include explicit tests on outgassing and escape rate multipliers, and (iii) include a brief comparison to solar-system analogs (e.g., Mars' atmospheric loss history) to contextualize the stagnant-lid assumption. We retain the stagnant-lid framework as a conservative baseline for long-term retention; we will state this limitation more explicitly and note that mobile-lid cases would likely favor retention at smaller sizes. Full Monte-Carlo error propagation on all rates is beyond the current scope but can be flagged as future work. revision: partial

Circularity Check

0 steps flagged

No significant circularity in STEHM model derivation

full rationale

The STEHM model integrates independent physical equations for volatile cycling, outgassing, and atmospheric escape on stagnant-lid planets orbiting in the habitable zone. The 0.8 R_earth threshold is reported as an emergent numerical result from integrating those equations under Earth-calibrated default parameters, with explicit exploration of parameter variations showing mostly minor effects. No load-bearing step reduces by construction to a self-definition, fitted input renamed as prediction, or self-citation chain; the central claim remains an output of the forward simulation rather than an input imposed by definition or prior author work.

Axiom & Free-Parameter Ledger

4 free parameters · 2 axioms · 0 invented entities

The central claim depends on several Earth-calibrated inputs and the stagnant-lid assumption; without independent constraints on sub-Earth planets, these act as free parameters that control the reported boundary.

free parameters (4)

initial carbon inventory
Identified in abstract as most influential; orders-of-magnitude changes needed to shift boundary significantly.
heat producing elements abundance
Listed among parameters that improve retention when increased.
initial mantle temperature
Cooler values favor retention per abstract.
core radius fraction
Lower values improve retention.

axioms (2)

domain assumption Stagnant lid tectonic regime applies to all modeled planets
Explicitly stated as the basis for the model.
domain assumption Outgassing and escape rates scale with planet size and interior heat in the same manner as Earth
Implicit in the Earth-like default conditions.

pith-pipeline@v0.9.0 · 5585 in / 1475 out tokens · 30402 ms · 2026-05-09T20:11:15.973862+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

81 extracted references · 1 canonical work pages

[1]

Anderson, D. L. 1981, Geophysical Research Letters, 8, 309 Brain, D. A., Leblanc, F., Luhmann, J. G., Moore, T. E., &

1981
[2]

2013, Planetary Magnetic Fields and Climate Evolution (University of Arizona Press), 487 17

Tian, F. 2013, Planetary Magnetic Fields and Climate Evolution (University of Arizona Press), 487 17

2013
[3]

K., et al

Bryson, S., Kunimoto, M., Kopparapu, R. K., et al. 2021, AJ, 161, 36

2021
[4]

C., & Kasting, J

Catling, D. C., & Kasting, J. F. 2017, Escape of Atmospheres to Space (Cambridge University Press), 129–168

2017
[5]

2016, The Astrophysical Journal, 834, 17

Chen, J., & Kipping, D. 2016, The Astrophysical Journal, 834, 17

2016
[6]

Dasgupta, R., & Hirschmann, M. M. 2010, Earth and Planetary Science Letters, 298, 1

2010
[7]

2020, ApJL, 896, L24

Dong, C., Jin, M., & Lingam, M. 2020, ApJL, 896, L24

2020
[8]

2018, ApJL, 859, L14

Dong, C., Lee, Y., Ma, Y., et al. 2018, ApJL, 859, L14

2018
[9]

D., & Charbonneau, D

Dressing, C. D., & Charbonneau, D. 2013, ApJ, 767, 95 —. 2015, The Astrophysical Journal, 807, 45

2013
[10]

2014, Physics of the Earth and Planetary Interiors, 236, 36

Driscoll, P., & Bercovici, D. 2014, Physics of the Earth and Planetary Interiors, 236, 36

2014
[11]

E., & Barnes, R

Driscoll, P. E., & Barnes, R. 2015, Astrobiology, 15, 739

2015
[12]

2017, Journal of Geophysical Research (Planets), 122, 1338

Rambaux, N. 2017, Journal of Geophysical Research (Planets), 122, 1338

2017
[13]

S., & Ehlmann, B

Edwards, C. S., & Ehlmann, B. L. 2015, Geology, 43, 863

2015
[14]

Elkins-Tanton, L. T. 2012, Annual Review of Earth and Planetary Sciences, 40, 113

2012
[15]

2021, A&A, 656, A70

Emsenhuber, A., Mordasini, C., Burn, R., et al. 2021, A&A, 656, A70

2021
[16]

2025, A&A, 701, A64

Emsenhuber, A., Mordasini, C., Mayor, M., et al. 2025, A&A, 701, A64

2025
[17]

Foley, B. J. 2015, ApJ, 812, 36

2015
[18]

Foley, B. J. 2019, The Astrophysical Journal, 875, 72

2019
[19]

Foley, B. J. 2019, ApJ, 875, 72

2019
[20]

J., & Driscoll, P

Foley, B. J., & Driscoll, P. E. 2016, Geochemistry,

2016
[21]

J., Houser, C., Noack, L., & Tosi, N

Foley, B. J., Houser, C., Noack, L., & Tosi, N. 2020, in Planetary Diversity, 2514-3433 (IOP Publishing), 4–1 to 4–60

2020
[22]

J., & Smye, A

Foley, B. J., & Smye, A. J. 2018, Astrobiology, 18, 873

2018
[23]

2015, A&A, 577, A98

Gallet, F., & Bouvier, J. 2015, A&A, 577, A98

2015
[24]

2013, Nature, 497, 607

Hamano, K., Abe, Y., & Genda, H. 2013, Nature, 497, 607

2013
[25]

Hier-Majumder, S., & Hirschmann, M. M. 2017,

2017
[26]

L., Bott, K., Dalba, P

Hill, M. L., Bott, K., Dalba, P. A., et al. 2023, The Astronomical Journal, 165, 34

2023
[27]

2024, Monthly Notices of the Royal Astronomical Society, 533, 3999

Ramstad, R. 2024, Monthly Notices of the Royal Astronomical Society, 533, 3999

2024
[28]

W., & et al

Howard, A. W., & et al. 2012, The Astrophysical Journal, 201, 15

2012
[29]

2018, Icarus, 315, 146

Jakosky, B., Brain, D., Chaffin, M., et al. 2018, Icarus, 315, 146

2018
[30]

M., & Treiman, A

Jakosky, B. M., & Treiman, A. H. 2023, Icarus, 402, 115627

2023
[31]

1925, The dynamical theory of gases (University Press)

Jeans, J. 1925, The dynamical theory of gases (University Press)

1925
[32]

P., G¨ udel, M., Brott, I., & L¨ uftinger, T

Johnstone, C. P., G¨ udel, M., Brott, I., & L¨ uftinger, T. 2015, A&A, 577, A28

2015
[33]

R., Hill, M

Kane, S. R., Hill, M. L., Kasting, J. F., et al. 2016, The Astrophysical Journal, 830, 1

2016
[34]

R., Arney, G

Kane, S. R., Arney, G. N., Byrne, P. K., et al. 2021, Journal of Geophysical Research (Planets), 126, e06643

2021
[35]

F., Whitmire, D

Kasting, J. F., Whitmire, D. P., & Reynolds, R. T. 1993, ICARUS, 101, 108

1993
[36]

Erkaev, N. V. 2020, arXiv e-prints, arXiv:2003.13412

work page arXiv 2020
[37]

S., & Barnett, M

Kite, E. S., & Barnett, M. N. 2020, Proceedings of the National Academy of Science, 117, 18264

2020
[38]

S., Williams, J.-P., Lucas, A., & Aharonson, O

Kite, E. S., Williams, J.-P., Lucas, A., & Aharonson, O. 2014, Nature Geoscience, 7, 335

2014
[39]

Kopparapu, R. K. 2013, The Astrophysical Journal, 767, L8

2013
[40]

K., Ramirez, R

Kopparapu, R. K., Ramirez, R. M., SchottelKotte, J., et al. 2014, The Astrophysical Journal, 787, L29

2014
[41]

K., Ramirez, R

Kopparapu, R. K., Ramirez, R. M., SchottelKotte, J., et al. 2014, ApJ, 787, L29

2014
[42]

K., Ramirez, R., Kasting, J

Kopparapu, R. K., Ramirez, R., Kasting, J. F., et al. 2013, The Astrophysical Journal, 765, 131

2013
[43]

K., Ramirez, R., Kasting, J

Kopparapu, R. K., Ramirez, R., Kasting, J. F., et al. 2013, ApJ, 765, 131

2013
[44]

2013, Journal of Geophysical Research: Planets, 118, 1155

Lebrun, T., Massol, H., Chassefi` ere, E., et al. 2013, Journal of Geophysical Research: Planets, 118, 1155

2013
[45]

2022, Icarus, 382, 115009

Lichtenegger, H., Dyadechkin, S., & Scherf, M. 2022, Icarus, 382, 115009

2022
[46]

Lichtenegger, H. I. M., Lammer, H., Grießmeier, J.-M., et al. 2010, Icarus, 210, 1

2010
[47]

2022, Science, 377, 1211

Luque, R., & Pall´ e, E. 2022, Science, 377, 1211

2022
[48]

2012, Earth and Planetary Science Letters, 313-314, 56

Marty, B. 2012, Earth and Planetary Science Letters, 313-314, 56

2012
[49]

2002, Geology, 30, 987

Nimmo, F. 2002, Geology, 30, 987

2002
[50]

2020, A&A, 638, A129

Noack, L., & Lasbleis, M. 2020, A&A, 638, A129

2020
[51]

2017, Physics of the Earth and Planetary Interiors, 269, 40

Noack, L., Rivoldini, A., & Van Hoolst, T. 2017, Physics of the Earth and Planetary Interiors, 269, 40

2017
[52]

Oosterloo, M., H¨ oning, D., Kamp, I. E. E., & van der Tak, F. F. S. 2021, A&A, 649, A15

2021
[53]

F., Bouchy, F., & Helled, R

Otegi, J. F., Bouchy, F., & Helled, R. 2020, A&A, 634, A43

2020
[54]

Palme, H., & O’Neill, H. S. C. 2003, Treatise on Geochemistry, 2, 568

2003
[55]

2014, Experimental Astronomy, 38, 249

Rauer, H., Catala, C., Aerts, C., et al. 2014, Experimental Astronomy, 38, 249

2014
[56]

F., G¨ udel, M., & Audard, M

Ribas, I., Guinan, E. F., G¨ udel, M., & Audard, M. 2005, ApJ, 622, 680

2005
[57]

Rogers, L. A. 2015, The Astrophysical Journal, 801, 41

2015
[58]

2018, Monthly Notices of the Royal Astronomical Society, 475, 1274 18Michelle L

Saito, H., & Kuramoto, K. 2018, Monthly Notices of the Royal Astronomical Society, 475, 1274 18Michelle L. Hill et al

2018
[59]

2018, Geophysical Research Letters, 45, 9336

Sakai, S., Seki, K., Terada, N., et al. 2018, Geophysical Research Letters, 45, 9336

2018
[60]

2017, Journal of Geophysical Research: Planets, 122, 1458

Salvador, A., Massol, H., Davaille, A., et al. 2017, Journal of Geophysical Research: Planets, 122, 1458

2017
[61]

2020, Space Science Reviews, 217, 2

Scherf, M., & Lammer, H. 2020, Space Science Reviews, 217, 2

2020
[62]

L., & Olson, P

Schubert, G., Turcotte, D. L., & Olson, P. 2001, Mantle Convection in the Earth and Planets (Cambridge University Press)

2001
[63]

E., & Lyons, T

Harman, C. E., & Lyons, T. W. 2019, The Astrophysical Journal, 878, 19

2019
[64]

J., Hirschmann, M

Sim, S. J., Hirschmann, M. M., & Hier-Majumder, S. 2024, Journal of Geophysical Research: Planets, 129, e2024JE008346

2024
[65]

H., & Zahnle, K

Sleep, N. H., & Zahnle, K. 2001, J. Geophys. Res., 106, 1373

2001
[66]

B., Hu, R., & Lo, D

Thomas, T. B., Hu, R., & Lo, D. Y. 2023, The Planetary Science Journal, 4, 41

2023
[67]

F., & Solomon, S

Tian, F., Kasting, J. F., & Solomon, S. C. 2009, Geophys. Res. Lett., 36, L02205

2009
[68]

2015, A&A, 577, L3

Tu, Lin, Johnstone, Colin P., G¨ udel, Manuel, & Lammer, Helmut. 2015, A&A, 577, L3

2015
[69]

2021, Nature, 598, 276

Turbet, M., Bolmont, E., Chaverot, G., et al. 2021, Nature, 598, 276

2021
[70]

T., Desch, S

Unterborn, C. T., Desch, S. J., Haldemann, J., et al. 2023, The Astrophysical Journal, 944, 42

2023
[71]

T., & Panero, W

Unterborn, C. T., & Panero, W. R. 2019, Journal of Geophysical Research (Planets), 124, 1704

2019
[72]

J., & Sasselov, D

Valencia, D., O’Connell, R. J., & Sasselov, D. 2006, Icarus, 181, 545

2006
[73]

M., & Marcy, G

Weiss, L. M., & Marcy, G. W. 2014, ApJL, 783, L6

2014
[74]

B., Evans, A

Weller, M. B., Evans, A. J., Ibarra, D. E., & Johnson, A. V. 2023, Nature Astronomy, 7, 1436

2023
[75]

B., & Kiefer, W

Weller, M. B., & Kiefer, W. S. 2020, Journal of Geophysical Research: Planets, 125, e2019JE005960, e2019JE005960 2019JE005960

2020
[76]

A., & Ford, E

Wolfgang, A., Rogers, L. A., & Ford, E. B. 2016, The Astrophysical Journal, 825, 19

2016
[77]

D., & Pierrehumbert, R

Wordsworth, R. D., & Pierrehumbert, R. T. 2013, ApJ, 778, 154

2013
[78]

Yoshizaki, T., & McDonough, W. F. 2020, Geochimica et Cosmochimica Acta, 273, 137

2020
[79]

2010, Cold Spring Harbor perspectives in biology, 2, a004895

Zahnle, K., Schaefer, L., & Fegley, B. 2010, Cold Spring Harbor perspectives in biology, 2, a004895

2010
[80]

D., & Jacobsen, S

Zeng, L., Sasselov, D. D., & Jacobsen, S. B. 2016, ApJ, 819, 127

2016

Showing first 80 references.