Pith. sign in

REVIEW 3 major objections 4 minor 105 references

Adding a fourth feedback to Earth-like exoplanet climate models can shrink the classical habitable zone, because positive extra feedbacks reduce the time planets spend temperate.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-03 01:09 UTC pith:7XZXWOOE

load-bearing objection The sign-of-feedback result is real but the chaos classification and survey-yield claims do not survive scrutiny. the 3 major comments →

arxiv 2602.10369 v1 pith:7XZXWOOE submitted 2026-02-10 astro-ph.EP

Not Earth-like Yet Temperate? More Generic Climate Feedback Configurations Still Allow Temperate Climates in Habitable Zone Exo-Earth Candidates

Chaucer Langbert , D\'aniel Apai This is my paper
classification astro-ph.EP
keywords climate feedbackhabitable zoneexoplanet climateEarth-like planetsclimate diversitychaotic climateenergy balance modeltemperate conditions
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper relaxes the standard assumption that Earth-like exoplanets regulate their climate with exactly three dominant feedbacks: radiation, ice-albedo, and carbonate-silicate weathering. It adds a fourth, generic feedback whose strength and sign are free parameters, then integrates 20,000 five-gigayear climate trajectories. The central finding is that a moderately strong positive fourth feedback significantly reduces the fraction of time a planet spends in temperate surface conditions, while a negative fourth feedback of comparable strength does not. If such positive feedbacks are common, the classical habitable zone overestimates how many rocky planets around Sun-like stars remain habitable on billion-year timescales. The authors frame this as a demonstration of possible climate diversity rather than a population forecast, noting their results depend on model assumptions.

Core claim

On the paper's own terms, the discovery is that the long-term climate behavior of Earth-like planets is sensitive to the sign and strength of a fourth feedback beyond the usual three. In a zero-dimensional energy balance model with temperature, CO2, and a sigmoidally activated feedback variable, positive fourth-feedback strength c monotonically decreases the fraction of time spent in the 253-395 K temperate band (fhab = 0.4478 - 0.0029c for c >= 0, with no significant decline for c < 0). The same two-slope trend holds when stellar brightening is included (fhab = 0.3964 - 0.0027c for c >= 0). Negative feedbacks tend to preserve temperate conditions, whereas positive feedbacks drive trajectori

What carries the argument

The central object is the generalized fourth-feedback term cf in the energy balance equation: a dimensionless state variable f, bounded between -1 and +1, relaxes toward a sigmoidal function of temperature with amplitude c, activation temperature Tf, and timescale 1/gamma_f. Together with the standard OLR, ice-albedo, and carbonate-silicate feedbacks, this adds an extra dynamical degree of freedom and nonlinearity, producing behaviors not present in the three-feedback model: limit cycles, transient and sustained chaos, snowball-warm transitions, and out-of-bounds runaways. The piecewise-linear fits fhab(c) (Equations 4 and 5) are the paper's quantitative claims about how the fourth feedback

Load-bearing premise

The quantitative fractions are only as good as the assumption that fourth-feedback strengths are uniformly likely anywhere between -100 and +100 W/m2; if the real population of Earth-like planets has mostly weak or negative extra feedbacks, the paper's downward revision of habitable fractions does not follow.

What would settle it

Conduct a survey of roughly 100 temperate Earth-sized planets around Sun-like stars and classify their long-term climate behavior. If essentially all are stable fixed points and none show the out-of-bounds or chaotic trajectories that dominate the simulated ensemble under the broad uniform prior, then the model's predicted diversity - and the resulting habitability revision - is contradicted.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • If positive fourth feedbacks exist at even moderate strength, the fraction of habitable-zone exo-Earth candidates with long-term temperate surfaces is lower than classical estimates.
  • Small surveys of about 10 targets will likely sample only fixed points and runaway states, so they cannot constrain the rare chaotic or limit-cycle regimes.
  • Sampling the full diversity of climate states predicted by the model requires roughly 100 exo-Earth candidates; including stellar evolution raises that requirement.
  • The model predicts that chaotic climates show broader or multimodal distributions of observables like albedo, pCO2, and surface temperature - a population-level signature that future surveys could test.
  • Earth's present-day position near the peak of the temperate-time curve suggests its feedback configuration is unusually favorable among the simulated possibilities.

Where Pith is reading between the lines

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

  • The quantitative downward revision of temperate-planet fractions depends on treating all fourth-feedback strengths up to +/-100 W/m2 as equally probable; if real planets cluster near c=0 as Earth does, the revision evaporates. This is an inference about the prior's influence, not a claim the paper makes.
  • The sigmoidal fourth feedback is a placeholder for any thresholded geochemical or biospheric cycle; one could test the framework by instantiating a specific candidate mechanism, such as a sulfur or nitrogen cycle, and checking whether its effective c falls in the harmful positive range.
  • A direct observational extension would be to estimate effective feedback strength for a handful of directly imaged rocky planets and look for a correlation between inferred positive feedback and reduced temperature stability - the reverse of the ensemble test proposed in the paper.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper extends a zero-dimensional three-feedback energy balance model (OLR, ice-albedo, carbonate-silicate; after Arnscheidt & Rothman 2020) by adding a generalized fourth feedback variable f governed by a sigmoidal relaxation toward an equilibrium temperature T_f. Two ensembles of ~10,000 simulations each (fixed stellar flux and linearly brightening stellar flux) are integrated for 5 Gyr, with parameters sampled from broad distributions. Trajectories are classified into fixed points, limit cycles, quasi-periodic states, chaotic states, transient chaos, and out-of-bounds runaways. The main reported results are: (i) the fourth feedback produces a wider dynamical repertoire including quasi-periodic and chaotic behavior; (ii) negative fourth feedbacks do not reduce, while positive fourth feedbacks reduce, the fraction of time spent in temperate conditions (piecewise linear fits in Eqs. 4 and 5); (iii) survey yield projections in Section 4.5 and Table 1 follow from the simulated behavior fractions.

Significance. If the dynamical classifications and the f_hab(c) trend were robust, the paper would provide a useful demonstration that unconstrained additional feedbacks can broaden climate behavior and shrink the classical habitable zone, with concrete implications for future exoplanet survey design. The c=0 baseline reproduces the known three-feedback limit cycle, and the ensemble size is substantial. However, the central novelty—the existence of quasi-periodic and chaotic climate trajectories—rests on diagnostic metrics that are internally inconsistent and violate basic requirements for a bounded 3D autonomous dissipative flow. Moreover, the headline f_hab(c) trend is essentially built into the sign convention of the added feedback term rather than being an emergent model result. These issues are load-bearing for the abstract's claims, so the current manuscript does not provide credible support for its main conclusions.

major comments (3)
  1. [Appendix C, Table 3]
  2. [Section 2 (Eqs. 1–3) and Section 3.4 (Eqs. 4–5)]
  3. [Section 4.5, Table 1, Appendix A]
minor comments (4)
  1. [Section 3.4, Eq. (4)]
  2. [Figure 15 caption]
  3. [Appendix C, Figure 14 caption]
  4. [Appendix C, Table 3 vs. text]

Circularity Check

0 steps flagged

No significant circularity: the central results are forward model implications with explicit caveats, not fitted-to-data predictions.

full rationale

The paper's derivation chain is a forward dynamical model: Equations (1)-(3) define a three-variable system with a fourth generalized feedback, parameters are sampled from stated priors, and f_hab(c) in Eqs. (4)-(5) is a binned mean of simulated temperate-time fractions. It is not fitted to external data, and it is not defined to equal c by construction; the sign asymmetry follows from the physical sign convention of the feedback term, but that is a model implication, not a circular reduction. The paper repeatedly disclaims predictive status ('our analysis should be viewed as hypothesis-generating rather than predictive', 'subject to the validity of the model assumptions'), so the Monte Carlo priors are not disguised as measurements. Self-citations (e.g., Apai et al. 2025 for microbial temperature limits, Apai et al. 2019/2022 for the Nautilus survey concept) are not load-bearing: they are accompanied by independent references and are not used to force the central qualitative result. The most serious weakness is not circularity but evidence quality: Table 3 reports two positive Lyapunov exponents for limit-cycle and quasi-periodic trajectories and correlation dimensions below 1 for a limit cycle, which contradicts standard dynamical systems expectations; this undermines support for the claimed chaotic regimes but does not make the derivation circular. Thus no specific reduction of a claimed prediction to its own inputs was found.

Axiom & Free-Parameter Ledger

8 free parameters · 7 axioms · 1 invented entities

The model's central estimates depend on a large set of sampled parameters, none of which are fitted to exoplanet observations. The invented fourth feedback f is the key new degree of freedom, and its amplitude, relaxation rate, activation temperature, and activation sharpness are all free. The fitted fhab(c) trends are summaries of the same simulation ensemble and therefore carry no external validation.

free parameters (8)
  • c (fourth-feedback amplitude) = sampled uniformly in [-100, 100] W/m^2
    Governing strength of the invented fourth feedback; central axis of all habitability fraction results; prior is unconstrained.
  • T_f (feedback equilibrium temperature) = sampled uniformly in [200, 400] K
    Sets the temperature around which the fourth feedback changes sign; chaotic behaviors cluster near T_f ~ 273 K.
  • kappa (feedback activation rate) = sampled in [0.6, 2.0]
    Scales f at saturation; conflicts with the claimed f in [-1,1] bound and effectively redefines c.
  • gamma_f (feedback relaxation rate) = log-uniform 1e-8 to 2e-4 yr^-1
    Controls timescale of f; affects whether feedback can generate oscillations or chaos.
  • delta_f (activation steepness) = 0.1 K^-1
    Fixed by hand; controls threshold sharpness of the fourth feedback.
  • V (volcanic outgassing) = log-uniform ~6-700 bar/Gyr
    Sampled over order-of-magnitude range; affects CO2 nullcline and limit cycles.
  • S_init (initial stellar flux) = uniform 700-1500 W/m^2
    Sampled to cover HZ; drives fixed points vs out-of-bounds states.
  • fhab fit intercept/slopes = 0.4478, +0.0005, -0.0029 (Eq. 4); 0.3964, +0.0002, -0.0027 (Eq. 5)
    Two-component linear fits to simulation output; used for survey sampling probabilities but not fully uncertainty-propagated.
axioms (7)
  • domain assumption The three-feedback EBM (OLR + ice-albedo + carbonate-silicate) with Arnscheidt & Rothman (2020) parameterization adequately represents long-term climate of Earth-like exoplanets.
    Used throughout; validation only against the c=0 baseline, not against exoplanet observations.
  • ad hoc to paper A single scalar sigmoidal, first-order-relaxing 'fourth feedback' with sampled parameters captures plausible non-Earth-like feedbacks.
    Eq. (3); the central invented degree of freedom, with no independent constraint.
  • ad hoc to paper Uniform/log-uniform sampling over broad ranges represents the unknown exoplanet population of feedback strengths, outgassing rates, and instellations.
    Appendix A; all reported fractions and survey predictions depend on these priors.
  • domain assumption Habitability can be quantified as fraction of time T in [253, 395] K for known bacterial life.
    Section 3.4; defines the temperate-time metric.
  • domain assumption Trajectories exiting T in [200, 400] K or pCO2 in [0, 1000] bar remain permanently uninhabitable (out-of-bounds).
    Section 3.2; conservative but possibly overestimates uninhabitable fractions.
  • domain assumption Stellar luminosity increases linearly by 30% over 5 Gyr (Kasting 1987).
    Section 3.3; standard solar evolution assumption.
  • domain assumption Circular orbits, Earth-like obliquity/rotation and ocean inventory.
    Section 2; removes orbital variability and focuses on feedback dynamics.
invented entities (1)
  • Generalized fourth climate feedback f no independent evidence
    purpose: A dimensionless, sigmoidally-activated, relaxing state variable that adds or removes c W/m^2 of forcing; represents unknown biospheric or geochemical feedbacks absent from the three-feedback model.
    No independent observable or measurement pins its strength, sign, or distribution; the observable-distribution predictions (Figure 10) are aggregate model outputs, not unique fingerprints.

pith-pipeline@v1.3.0-alltime-deepseek · 27916 in / 18007 out tokens · 193176 ms · 2026-08-03T01:09:05.040668+00:00 · methodology

0 comments
read the original abstract

Earth's climate is influenced by over a dozen feedbacks, but only three dominate its long-term climate behavior. Models of the exoplanet habitable zone (HZ) assume that this is similar for other Earth-like planets. We used dynamical simulations to study Earth-like planets with a fourth, (potentially strong) generalized climate feedback. Across over 20,000 climate simulations, we find that the addition of the fourth feedback produces novel behaviors, including runaway and chaotic climate trajectories, that are more diverse than one would expect based on Earth's climate configuration. Non-negligible fourth feedbacks -- if negative -- would not lessen the probability of planets with temperate climates. However, positive fourth feedbacks decrease the fraction of exo-Earth candidates that are long-term habitable. Therefore, strong fourth feedbacks will alter (and mostly shrink) the boundaries of the classical habitable zone. When combined with occurrence rates of Earth-sized planets around sun-like stars, our results imply that the fraction of stars hosting rocky planets with temperate climates may be substantially lower than classical estimates under Earth-like climate assumptions. Our results are subject to the validity of the model assumptions and not intended to represent conclusive predictions about exoplanet populations but rather to demonstrate the potential climate diversity that emerges from non-Earth-like model configurations. Our conclusions provide context on sample sizes and science questions for next-generation exoplanet surveys.

Figures

Figures reproduced from arXiv: 2602.10369 by Chaucer Langbert, D\'aniel Apai.

Figure 1
Figure 1. Figure 1: Strength of key long-term feedbacks governing Earth’s climate system (Forster et al. 2021; Arnscheidt & Rothman 2020; Abbot 2016; Koll & Cronin 2018). Each bar represents the feedback parameter in W m−2 K −1 , estimated from Earth system model assessments and paleoclimate constraints. The upper axis shows the approximate feedback strength associated with a 50 K climate perturbation, representative of trans… view at source ↗
Figure 2
Figure 2. Figure 2: Dynamics of the planetary climate system with coupled ice-albedo and carbonate-silicate feedback mechanisms without a fourth feedback, consistent with Arnscheidt & Rothman (2020). Left: Feedback configuration showing the relationship between equilibrium temperature (K) and the timescale (years) for the three canonical feedbacks. Middle: T (green solid) and pCO2 (purple dashed) time series. Right: Phase pla… view at source ↗
Figure 3
Figure 3. Figure 3: Representative examples of climate trajectory behaviors in a four-feedback Earth-like model, consistent with possible states of Earth but excluding the role of stellar evolution. Each row shows a different behavior: Out-of-Bounds, Fixed Point, Limit Cycle, and Non-Periodic/Chaotic. Left column: Feedback timescales and effective temperatures, with the fourth feedback shown in purple. Middle columns: Time ev… view at source ↗
Figure 4
Figure 4. Figure 4: Climate behaviors emerge in distinct regions of planetary parameter space from a generalized Earth-motivated climate model that excludes stellar evolution. Each point represents the outcome of a single climate simulation sampled across stellar flux (S), fourth-feedback strength (c), and the feedback’s equilibrium temperature (Tf ). Colors and marker shapes denote long-term climate behaviors, including warm… view at source ↗
Figure 5
Figure 5. Figure 5: Representative examples of climate trajectory behaviors in a four-feedback Earth-like model under increasing stellar luminosity. Each row shows a different behavior: Snowball→Warm transition, Warm→Snowball transition, Transient Chaos, and Non-Periodic/Chaotic. Left column: Feedback timescales and equilibrium temperatures, with the fourth feedback shown in purple. Middle columns: Time evolution of temperatu… view at source ↗
Figure 6
Figure 6. Figure 6: Diverse climate behaviors emerge in a four-feedback Earth-derived model that includes stellar evolution. Each point represents the outcome of a single climate simulation sampled across stellar flux (S), fourth-feedback strength (c), and the feedback’s equilibrium temperature (Tf ). Colors and marker shapes denote long-term behaviors, including warm and snowball fixed points, snowball→warm and warm→snowball… view at source ↗
Figure 7
Figure 7. Figure 7: Climate behavior and time spent in habitable surface conditions as a function of the fourth feedback strength c (W/m2 ) without stellar evolution. (A) Distribution of climate behaviors as a function of c, separated into 10 bins. (B) Average habitable fraction as a function of c sorted into 10 bins, with our two-component linear fit overplotted. We conservatively assume that simulations that go out-of-bound… view at source ↗
Figure 8
Figure 8. Figure 8: Climate behavior and time spent in habitable surface conditions as a function of the fourth feedback strength c (W/m2 ), now incorporating stellar evolution. (A) Relative occurrence of climate behaviors binned by fourth-feedback strength c. Stable fixed points dominate across most bins, but transitions (Snowball→Warm, Warm→Snowball) and rare chaotic states appear near intermediate c. Out-of-bounds trajecto… view at source ↗
Figure 9
Figure 9. Figure 9: Monte Carlo sampling probability for climate behaviors as a function of the number of exoplanet targets observed (logarithmic x–axis), subject to model assumptions (Section 4.2). Each curve shows the probability that at least one example of a given behavior has been sampled after N observations, while the black curve tracks the probability that all behaviors have been observed at least once. Left: simulati… view at source ↗
Figure 10
Figure 10. Figure 10: Observable distributions from the climate ensembles given our model assumptions (see Section 4.2). Panels A–C show histograms of representative (median) post-transient values for surface albedo, atmospheric pCO2 (log axis), and surface temperature. Colors denote model families in the order analyzed here: 3-feedback (blue), 4-feedback (orange), and 4-feedback with stellar evolution (green). Bars give the f… view at source ↗
Figure 11
Figure 11. Figure 11: Distributions of sampled parameters in the climate feedback configuration without stellar evolution. (Top row) Histograms of feedback strength (c), feedback decay rate (γf ), and equilibrium temperature (Tf ). (Bottom row) Histograms of stellar flux (S), volcanic outgassing (V ), and activation strength (κ). The parameters γf and V are log-scaled to enhance visualization, as their values span several orde… view at source ↗
Figure 12
Figure 12. Figure 12: Distributions of sampled parameters in the climate feedback configuration including stellar evolution. (Top row) Histograms of feedback strength (c), feedback decay rate (γf ), and equilibrium temperature (Tf ). (Bottom row) Histograms of stellar flux (S), volcanic outgassing (V ), and activation strength (κ). The parameters γf and V are log-scaled to enhance visualization, as their values span several or… view at source ↗
Figure 13
Figure 13. Figure 13: Exploring the sensitivity of the generalized climate feedback variable f to feedback parameters. (A) Steady￾state values of the fourth feedback f(T) as a function of temperature for different feedback activation rates κ, which scale the amplitude of the internal response. Higher κ increases the saturation of the feedback. (B) Effect of the feedback activation sensitivity δf on the transition behavior of f… view at source ↗
Figure 14
Figure 14. Figure 14: Temperature time series power spectra for three representative climate trajectories using a Lomb-Scargle peri￾odogram. A noise floor of 10−5 has been applied to suppress numerical artifacts. Top: Periodic state, characterized by sharp peaks at regularly spaced intervals. Middle: Quasi-periodic behavior showing multiple sizable peaks with less regular structure and no single fundamental frequency dominatin… view at source ↗
Figure 15
Figure 15. Figure 15: Layered 3D triptychs showing how climate behaviors populate parameter space when stellar evolution is excluded. Each row contains three identical projections—(A,D) S vs. c, (B,E) S vs. Tf , and (C,F) c vs. Tf—with the third dimension used only to separate behaviors and avoid overplotting. The z-axis is labeled by behavior name and is shared across the three panels in each row. Top row (A–C): Out-of-Bounds… view at source ↗
Figure 16
Figure 16. Figure 16: Layered 3D triptychs showing how climate behaviors populate parameter space when stellar evolution is included. Each row contains three identical projections—(A,D) S vs. c, (B,E) S vs. Tf , and (C,F) c vs. Tf—with the third dimension used only to separate behaviors and avoid overplotting. The z-axis is labeled by behavior name and is shared across the three panels in each row. Top row (A–C): Out-of-Bounds… view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

105 extracted references · 44 canonical work pages · 2 internal anchors

  1. [1]

    Abbot, D. S. 2016, ApJ, 827, 117, doi: 10.3847/0004-637X/827/2/117

    work page doi:10.3847/0004-637x/827/2/117 2016

  2. [2]

    2025, Astron

    Affholder, A., Mazevet, S., Sauterey, B., Apai, D., & Ferri` ere, R. 2025, Astron. J., 169, 125, doi: 10.3847/1538-3881/ada384

    work page doi:10.3847/1538-3881/ada384 2025

  3. [3]

    Alcabes, O. D. N., Olson, S., & Abbot, D. S. 2020, MNRAS, 492, 2572, doi: 10.1093/mnras/staa055

    work page doi:10.1093/mnras/staa055 2020

  4. [4]

    D., Kim, D

    Apai, D., Milster, T. D., Kim, D. W., et al. 2019, AJ, 158, 83, doi: 10.3847/1538-3881/ab2631

    doi:10.3847/1538-3881/ab2631 2019

  5. [5]

    D., Kim, D., et al

    Apai, D., Milster, T. D., Kim, D., et al. 2022, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 12221, Optical Manufacturing and Testing XIV, ed. D. Kim, H. Choi, H. Ottevaere, & R. Rascher, 122210C, doi: 10.1117/12.2633184 25 800 1000 1200 1400 S (W m 2 ) 100 50 0 50 100 c (W m 2 K 1 ) A 800 1000 1200 1400 S (W m 2 ) ...

    doi:10.1117/12.2633184 2022

  6. [6]

    M., et al

    Apai, D., Barnes, R., Murphy, M. M., et al. 2025, PSJ, 6, 165, doi: 10.3847/PSJ/addda8

    doi:10.3847/psj/addda8 2025

  7. [7]

    W., & Rothman, D

    Arnscheidt, C. W., & Rothman, D. H. 2020, Proceedings of the Royal Society of London Series A, 476, 20200303, doi: 10.1098/rspa.2020.0303 —. 2022, Science Advances, 8, eadc9241, doi: 10.1126/sciadv.adc9241

    arXiv 2020

  8. [8]

    2023, MNRAS, 521, 690, doi: 10.1093/mnras/stad547 Astropy Collaboration, Robitaille, T

    Arthur, R., & Nicholson, A. 2023, MNRAS, 521, 690, doi: 10.1093/mnras/stad547 Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33, doi: 10.1051/0004-6361/201322068

    work page doi:10.1093/mnras/stad547 2023

  9. [9]

    L., Abbot, D

    Bean, J. L., Abbot, D. S., & Kempton, E. M. R. 2017, ApJL, 841, L24, doi: 10.3847/2041-8213/aa738a

    doi:10.3847/2041-8213/aa738a 2017

  10. [10]

    F., Angel, J

    Bender, C. F., Angel, J. R., Berkson, J., et al. 2022, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 12184, Ground-based and Airborne Instrumentation for Astronomy IX, ed. C. J

    2022

  11. [11]

    Evans, J. J. Bryant, & K. Motohara, 121844J, doi: 10.1117/12.2628710

    doi:10.1117/12.2628710

  12. [12]

    J., Pascucci, I., Mulders, G

    Bergsten, G. J., Pascucci, I., Mulders, G. D., Fernandes, R. B., & Koskinen, T. T. 2022, Astron., 164, 190, doi: 10.3847/1538-3881/ac8fea

    doi:10.3847/1538-3881/ac8fea 2022

  13. [13]

    Berner, R. A. 1991, American Journal of Science, 291, 339, doi: 10.2475/ajs.291.4.339

    work page doi:10.2475/ajs.291.4.339 1991

  14. [14]

    A., & Kothavala, Z

    Berner, R. A., & Kothavala, Z. 2001, American Journal of Science, 301, 182, doi: 10.2475/ajs.301.2.182

    work page doi:10.2475/ajs.301.2.182 2001

  15. [15]

    C., O’Brien, D

    Bond, J. C., O’Brien, D. P., & Lauretta, D. S. 2010, Astrophys. J., 715, 1050, doi: 10.1088/0004-637X/715/2/1050 26 800 1000 1200 1400 S (W m 2 ) 100 50 0 50 100 c (W m 2 K 1 ) A 800 1000 1200 1400 S (W m 2 ) 200 250 300 350 400 Tf (K) B 100 50 0 50 100 c (W m 2 K 1 ) 200 250 300 350 400 Tf (K) Out-of-Bounds Snowball Fixed Point Warm Fixed Point C Diverse...

    doi:10.1088/0004-637x/715/2/1050 2010

  16. [16]

    M., et al

    Bryson, S., Coughlin, J., Batalha, N. M., et al. 2020, AJ, 159, 279, doi: 10.3847/1538-3881/ab8a30

    doi:10.3847/1538-3881/ab8a30 2020

  17. [17]

    Budyko, M. I. 1969, Tellus, 21, 611, doi: 10.3402/tellusa.v21i5.10109

    work page doi:10.3402/tellusa.v21i5.10109 1969

  18. [18]

    Checlair, J., Menou, K., & Abbot, D. S. 2017, ApJ, 845, 132, doi: 10.3847/1538-4357/aa80e1

    work page doi:10.3847/1538-4357/aa80e1 2017

  19. [19]

    Abbot, D. S. 2019, ApJL, 887, L3, doi: 10.3847/2041-8213/ab5957

    work page doi:10.3847/2041-8213/ab5957 2019

  20. [20]

    B., Robinson, T., Livengood, T

    Cowan, N. B., Robinson, T., Livengood, T. A., et al. 2011, ApJ, 731, 76, doi: 10.1088/0004-637X/731/1/76

    doi:10.1088/0004-637x/731/1/76 2011

  21. [21]

    H., Meadows, V

    Currie, M. H., Meadows, V. S., & Rasmussen, K. C. 2023, PSJ, 4, 83, doi: 10.3847/PSJ/accf86

    doi:10.3847/psj/accf86 2023

  22. [22]

    2021, Astrophys

    Dorn, C., & Lichtenberg, T. 2021, Astrophys. J. Letters, 922, L4, doi: 10.3847/2041-8213/ac33af

    doi:10.3847/2041-8213/ac33af 2021

  23. [23]

    1986, PhRvA, 34, 4971, doi: 10.1103/PhysRevA.34.4971

    Ciliberto, S. 1986, PhRvA, 34, 4971, doi: 10.1103/PhysRevA.34.4971

    work page doi:10.1103/physreva.34.4971 1986

  24. [24]

    Evans, D. A. D. 2000, Nature, 405, 490, doi: 10.1038/35013030

    work page doi:10.1038/35013030 2000

  25. [25]

    1980, Annals of the New York Academy of Sciences, 357, 453, doi: 10.1111/j.1749-6632.1980.tb29710.x

    Shaw, R. 1980, Annals of the New York Academy of Sciences, 357, 453, doi: 10.1111/j.1749-6632.1980.tb29710.x

    arXiv 1980

  26. [26]

    2024, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol

    Feinberg, L., Ziemer, J., Ansdell, M., et al. 2024, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 13092, Space Telescopes and Instrumentation 2024: Optical, Infrared, and Millimeter Wave, ed. L. E. Coyle, S. Matsuura, & M. D. Perrin, 130921N, doi: 10.1117/12.3018328 27

    doi:10.1117/12.3018328 2024

  27. [27]

    Feldl, N., & Roe, G. H. 2013, Journal of Climate, 26, 8289, doi: 10.1175/JCLI-D-12-00631.1

    work page doi:10.1175/jcli-d-12-00631.1 2013

  28. [28]

    J., & Driscoll, P

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

    2016

  29. [29]

    Geophysics, Geosystems, 17, 1885, doi: 10.1002/2015GC006210

    doi:10.1002/2015gc006210

  30. [30]

    2021, in Climate Change 2021: The Physical Science Basis

    Forster, P., Storelvmo, T., Armour, K., et al. 2021, in Climate Change 2021: The Physical Science Basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change, ed. V. Masson-Delmotte, P. Zhai, A. Pirani, S. L. Connors, C. P´ ean, S. Berger, N. Caud, Y. Chen, L. Goldfarb, M. I. Gomis, M. Huang, K. L...

    2021

  31. [31]

    Waterfield, O

    Maycock, T. Waterfield, O. Yelek¸ ci, R. Yu, & B. Zhou (Cambridge, United Kingdom and New York, NY, USA: Cambridge University Press), 923–1054, doi: 10.1017/9781009157896.009

    doi:10.1017/9781009157896.009

  32. [32]

    S., Seager, S., Mennesson, B., et al

    Gaudi, B. S., Seager, S., Mennesson, B., et al. 2020, arXiv e-prints, arXiv:2001.06683, doi: 10.48550/arXiv.2001.06683

    Pith/arXiv arXiv doi:10.48550/arxiv.2001.06683 2020

  33. [33]

    2003, Astrobiology, 3, 331, doi: 10.1089/153110703769016424

    Laurinavichuis, K., & Tiedje, J. 2003, Astrobiology, 3, 331, doi: 10.1089/153110703769016424

    work page doi:10.1089/153110703769016424 2003

  34. [34]

    M., Quanz, S

    Glauser, A. M., Quanz, S. P., Hansen, J., et al. 2024, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 13095, Optical and Infrared Interferometry and Imaging IX, ed. J. Kammerer, S. Sallum, & J. Sanchez-Bermudez, 130951D, doi: 10.1117/12.3019090

    doi:10.1117/12.3019090 2024

  35. [35]

    1983, PhRvL, 50, 346, doi: 10.1103/PhysRevLett.50.346

    Grassberger, P., & Procaccia, I. 1983, PhRvL, 50, 346, doi: 10.1103/PhysRevLett.50.346

    doi:10.1103/physrevlett.50.346 1983

  36. [36]

    M., & Cowan, N

    Guimond, C. M., & Cowan, N. B. 2018, AJ, 155, 230, doi: 10.3847/1538-3881/aabb02

    doi:10.3847/1538-3881/aabb02 2018

  37. [37]

    E., & Kasting, J

    Harman, C. E., & Kasting, J. F. 2016, ApJ, 827, 120, doi: 10.3847/0004-637X/827/2/120

    work page doi:10.3847/0004-637x/827/2/120 2016

  38. [38]

    T., Fauchez, T

    Haqq-Misra, J., Wolf, E. T., Fauchez, T. J., Shields, A. L., & Kopparapu, R. K. 2022, PSJ, 3, 260, doi: 10.3847/PSJ/ac9479

    doi:10.3847/psj/ac9479 2022

  39. [39]

    2023, AJ, 165, 267, doi: 10.3847/1538-3881/acd1ec

    Pascucci, I., & L´ opez-Morales, M. 2023, AJ, 165, 267, doi: 10.3847/1538-3881/acd1ec

    doi:10.3847/1538-3881/acd1ec 2023

  40. [40]

    K., Apai, D., Haffert, S

    Hardegree-Ullman, K. K., Apai, D., Haffert, S. Y., et al. 2025, AJ, 169, 171, doi: 10.3847/1538-3881/adb02f

    doi:10.3847/1538-3881/adb02f 2025

  41. [41]

    Schrag, D. P. 1998, Science, 281, 1342, doi: 10.1126/science.281.5381.1342

    arXiv 1998

  42. [42]

    2014, Astrophys

    Hu, R., & Seager, S. 2014, Astrophys. J., 784, 63, doi: 10.1088/0004-637X/784/1/63

    doi:10.1088/0004-637x/784/1/63 2014

  43. [43]

    T., et al

    Hyde, W. T., et al. 2000, Nature, 405, 425, doi: 10.1038/35013031

    work page doi:10.1038/35013031 2000

  44. [44]

    2019, Annual Review of Earth and Planetary Sciences, 47, 141, doi: 10.1146/annurev-earth-053018-060352

    Jontof-Hutter, D. 2019, Annual Review of Earth and Planetary Sciences, 47, 141, doi: 10.1146/annurev-earth-053018-060352

    doi:10.1146/annurev-earth-053018-060352 2019

  45. [45]

    Junge, K., Eicken, H., & Deming, J. W. 2004, Applied and Environmental Microbiology, 70, 550, doi: 10.1128/AEM.70.1.550-557.2004

    work page doi:10.1128/aem.70.1.550-557.2004 2004

  46. [46]

    Kasting, J. F. 1987, Precambrian Research, 34, 205, doi: 10.1016/0301-9268(87)90001-5

    work page doi:10.1016/0301-9268(87)90001-5 1987

  47. [47]

    F., Whitmire, D

    Kasting, J. F., Whitmire, D. P., & Reynolds, R. T. 1993, Icarus, 101, 108, doi: 10.1006/icar.1993.1010

    arXiv 1993

  48. [48]

    C., Torres, M

    Kemeny, P. C., Torres, M. A., Fischer, W. W., & Bl¨ attler, C. L. 2024a, Proceedings of the National Academy of Science, 121, e2316535121, doi: 10.1073/pnas.2316535121 —. 2024b, Proceedings of the National Academy of Science, 121, e2316535121, doi: 10.1073/pnas.2316535121

    work page doi:10.1073/pnas.2316535121

  49. [49]

    T., & Trenberth, K

    Kiehl, J. T., & Trenberth, K. E. 1997, Bulletin of the American Meteorological Society, 78, 197, doi: 10.1175/1520-0477(1997)078⟨0197: EAGMEB⟩2.0.CO;2

    doi:10.1175/1520-0477(1997)078 1997

  50. [50]

    Kirschvink, J. L. 1992, in The Proterozoic Biosphere, ed. J. W. Schopf & C. Klein (Cambridge University Press), 51–52

    1992

  51. [51]

    Koll, D. D. B., & Cronin, T. W. 2018, Proceedings of the National Academy of Science, 115, 10293, doi: 10.1073/pnas.1809868115

    work page doi:10.1073/pnas.1809868115 2018

  52. [52]

    K., Ramirez, R., Kasting, J

    Kopparapu, R. K., Ramirez, R., Kasting, J. F., et al. 2013, ApJ, 765, 131, doi: 10.1088/0004-637X/765/2/131

    doi:10.1088/0004-637x/765/2/131 2013

  53. [53]

    Krissansen-Totton, J., & Catling, D. C. 2017, Nature Communications, 8, 15423, doi: 10.1038/ncomms15423

    work page doi:10.1038/ncomms15423 2017

  54. [54]

    Krissansen-Totton, J., Olson, S., & Catling, D. C. 2018, Science Advances, 4, eaao5747, doi: 10.1126/sciadv.aao5747

    doi:10.1126/sciadv.aao5747 2018

  55. [55]

    R., Brantley, S

    Kump, L. R., Brantley, S. L., & Arthur, M. A. 2000, Annual Review of Earth and Planetary Sciences, 28, 611, doi: 10.1146/annurev.earth.28.1.611

    work page doi:10.1146/annurev.earth.28.1.611 2000

  56. [56]

    M., & Watson, A

    Lenton, T. M., & Watson, A. J. 2011, Revolutions that Made the Earth (Oxford University Press), 423

    2011

  57. [57]

    M., et al

    Lenton, T. M., et al. 2008, Proceedings of the National Academy of Sciences, 105, 1786, doi: 10.1073/pnas.0705414105

    doi:10.1073/pnas.0705414105 2008

  58. [58]

    2025, Treatise on Geochemistry, 7, 51, doi: 10.1016/B978-0-323-99762-1.00122-4

    Lichtenberg, T., & Miguel, Y. 2025, Treatise on Geochemistry, 7, 51, doi: 10.1016/B978-0-323-99762-1.00122-4

    doi:10.1016/b978-0-323-99762-1.00122-4 2025

  59. [59]

    2015, Planet

    Linsenmeier, M., Pascale, S., & Lucarini, V. 2015, Planet. Space Sci., 105, 43, doi: 10.1016/j.pss.2014.11.003

    doi:10.1016/j.pss.2014.11.003 2015

  60. [60]

    Lomb, N. R. 1976, Ap&SS, 39, 447, doi: 10.1007/BF00648343 28

    doi:10.1007/bf00648343 1976

  61. [61]

    2025, Astrophys

    Long, F., Pascucci, I., Houge, A., et al. 2025, Astrophys. J. Letters, 978, L30, doi: 10.3847/2041-8213/ad99d2

    doi:10.3847/2041-8213/ad99d2 2025

  62. [62]

    2019, PhRvL, 122, 158701, doi: 10.1103/PhysRevLett.122.158701

    Lucarini, V., & B´ odai, T. 2019, PhRvL, 122, 158701, doi: 10.1103/PhysRevLett.122.158701

    work page doi:10.1103/physrevlett.122.158701 2019

  63. [63]

    2010, Quarterly Journal of the Royal Meteorological Society, 136, 2, doi: 10.1002/qj.543

    Lucarini, V., Fraedrich, K., & Lunkeit, F. 2010, Quarterly Journal of the Royal Meteorological Society, 136, 2, doi: 10.1002/qj.543

    work page doi:10.1002/qj.543 2010

  64. [64]

    2013, Astronomische Nachrichten, 334, 576, doi: 10.1002/asna.201311903

    Lucarini, V., Pascale, S., Boschi, R., Kirk, E., & Iro, N. 2013, Astronomische Nachrichten, 334, 576, doi: 10.1002/asna.201311903

    work page doi:10.1002/asna.201311903 2013

  65. [65]

    2015, Astrobiology, 15, 119, doi: 10.1089/ast.2014.1231

    Luger, R., & Barnes, R. 2015, Astrobiology, 15, 119, doi: 10.1089/ast.2014.1231

    arXiv 2015

  66. [66]

    2007, PhR, 438, 237, doi: 10.1016/j.physrep.2006.11.001

    Marwan, N., Carmen Romano, M., Thiel, M., & Kurths, J. 2007, PhR, 438, 237, doi: 10.1016/j.physrep.2006.11.001

    doi:10.1016/j.physrep.2006.11.001 2007

  67. [67]

    2015, Earth and Planetary Science Letters, 429, 20, doi: 10.1016/j.epsl.2015.07.046

    Menou, K. 2015, Earth and Planetary Science Letters, 429, 20, doi: 10.1016/j.epsl.2015.07.046

    work page doi:10.1016/j.epsl.2015.07.046 2015

  68. [68]

    Lenton, T. M. 2011, Nature Geoscience, 4, 861, doi: 10.1038/ngeo1305 M¨ uller, R. D., Dutkiewicz, A., Zahirovic, S., et al. 2024,

    work page doi:10.1038/ngeo1305 2011

  69. [69]

    2021, Pathways to Discovery in Astronomy and Astrophysics for the 2020s, doi: 10.17226/26141

    Geochemistry, Geophysics, Geosystems, 25, 2024GC011713, doi: 10.1029/2024GC011713 National Academies of Sciences, Engineering, and Medicine. 2021, Pathways to Discovery in Astronomy and Astrophysics for the 2020s, doi: 10.17226/26141

    work page doi:10.1029/2024gc011713 2021

  70. [70]

    Lenton, T. M. 2018, MNRAS, 477, 727, doi: 10.1093/mnras/sty658

    work page doi:10.1093/mnras/sty658 2018

  71. [71]

    R., Short, D

    North, G. R., Short, D. A., & Mengel, J. G. 1983, J. Geophys. Res., 88, 6576, doi: 10.1029/JC088iC11p06576

    work page doi:10.1029/jc088ic11p06576 1983

  72. [72]

    2017, ApJ, 848, 33, doi: 10.3847/1538-4357/aa8b1c

    Paradise, A., & Menou, K. 2017, ApJ, 848, 33, doi: 10.3847/1538-4357/aa8b1c

    work page doi:10.3847/1538-4357/aa8b1c 2017

  73. [73]

    2019, Journal of Geophysical Research (Planets), 124, 2087, doi: 10.1029/2019JE005917

    Paradise, A., Menou, K., Valencia, D., & Lee, C. 2019, Journal of Geophysical Research (Planets), 124, 2087, doi: 10.1029/2019JE005917

    work page doi:10.1029/2019je005917 2019

  74. [74]

    2009, Astrophys

    Pascucci, I., Apai, D., Luhman, K., et al. 2009, Astrophys. J., 696, 143, doi: 10.1088/0004-637X/696/1/143

    doi:10.1088/0004-637x/696/1/143 2009

  75. [75]

    D., & Lopez, E

    Pascucci, I., Mulders, G. D., & Lopez, E. 2019, ApJL, 883, L15, doi: 10.3847/2041-8213/ab3dac

    work page doi:10.3847/2041-8213/ab3dac 2019

  76. [76]

    Pierrehumbert, R. T. 2005, Journal of Geophysical Research (Atmospheres), 110, D01111, doi: 10.1029/2004JD005162 —. 2010, Principles of Planetary Climate

    work page doi:10.1029/2004jd005162 2005

  77. [77]

    D., Dorn, C., Hinkel, N

    Putirka, K. D., Dorn, C., Hinkel, N. R., & Unterborn, C. T. 2021, Elements, 17, 235, doi: 10.2138/gselements.17.4.235

    doi:10.2138/gselements.17.4.235 2021

  78. [78]

    P., Ottiger, M., Fontanet, E., et al

    Quanz, S. P., Ottiger, M., Fontanet, E., et al. 2022, A&A, 664, A21, doi: 10.1051/0004-6361/202140366

    doi:10.1051/0004-6361/202140366 2022

  79. [79]

    Rial, J. A. 2004, Global and Planetary Change, 41, 95, doi: 10.1016/j.gloplacha.2003.10.004

    work page doi:10.1016/j.gloplacha.2003.10.004 2004

  80. [80]

    Roe, G. H. 2006, Science, 314, 793, doi: 10.1126/science.1133783

    work page doi:10.1126/science.1133783 2006

Showing first 80 references.