From cold to hot irradiated gaseous exoplanets: Fingerprints of chemical disequilibrium in atmospheric spectra

Karan Molaverdikhani; Paul Molli\`ere; Thomas Henning

REVIEW 3 major objections 5 minor 1 cited by

From cold to hot irradiated gaseous exoplanets: Fingerprints of chemical disequilibrium in atmospheric spectra

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A grid of 84,672 chemical kinetic models finds that the Methane Valley, the 800-1500 K band where methane should dominate, survives vertical mixing, so methane detections still encode C/O and cloud information.

desk verdict A solid, honest grid study whose Methane Valley result is real but whose quantitative edges are provisional until the temperature structure is allowed to respond to the chemistry. read the letter →

arxiv 1908.09847 v1 pith:OJ5QKONS submitted 2019-08-26 astro-ph.EP

Karan Molaverdikhani , Thomas Henning , Paul Mollière This is my paper · ORCID

classification astro-ph.EP

keywords exoplanetatmosphereschemicaldisequilibriumverticalmixingmethanevalleyquenchingpressuretransmissionspectroscopyJWSTdetectabilitykineticmodel

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper introduces a chemical kinetic model, ChemKM, and uses it to ask whether vertical mixing erases the spectral fingerprints of chemical disequilibrium in irradiated gas-giant exoplanets. Its central case is that the Methane Valley, the band between roughly 800 and 1500 K where, above a C/O threshold, methane dominates transmission spectra, survives the addition of mixing because the model finds the same valley in diffusion-equilibrium abundances. If that is right, methane detections and non-detections in that temperature band remain readable as diagnostics of C/O and cloud formation rather than being artifacts of transport. The same grid singles out a JWST sweet spot, planets near 1000-1800 K around M dwarfs with low surface gravity, high metallicity, and C/O near unity, where disequilibrium signals should be strongest.

What carries the argument

The engine is ChemKM, a 1D chemical kinetic model that solves the continuity-diffusion equation for more than 100 species and 1000 reactions, including eddy and molecular diffusion, photolysis, condensation, and optional influxes. The argument is carried by combining it with a quantitative quenching metric, the geometric coefficient of variation (gCV) of each species' abundance, with $gCV_i=0.05$ marking the onset of disequilibrium, and with self-consistent temperature-pressure profiles computed under radiative-convective and thermochemical equilibrium. The named object that organizes the results is the Methane Valley, the 800-1500 K band where methane becomes the dominant transmission-spectrum feature above a C/O threshold; the model's key comparison is diffusion-equilibrium spectra versus thermochemical-equilibrium spectra on a grid of more than 84,000 cases.

What would settle it

A self-consistent calculation in which the temperature profile responds to disequilibrium abundances, or an observing campaign that finds no preferential methane detection among 800-1500 K planets with C/O above the threshold, would settle the claim. A practical version: compare JWST spectra of two matched samples inside and outside the valley, controlling for clouds; if methane occurrence does not rise across the valley boundary, the prediction fails.

Watch

Extended reading notes

Core claim

The load-bearing discovery is the survival of the Methane Valley under vertical mixing. Starting from 28,224 self-consistent cloud-free atmospheric models and adding three mixing strengths ($K_{zz}=10^6$, $10^9$, and $10^{12}$ cm$^2$ s$^{-1}$), the authors compute 84,672 chemical kinetic models in diffusion equilibrium. They find that quenching pressure decreases with effective temperature but scatters widely with $[{\rm Fe/H}]$, $\log(g)$, and ${\rm C/O}$, and that the transmission spectra of most models change most at five wavelength windows near 1, 3.3, 4.5, 12, and 15 $\mu$m, with the 3.3 $\mu$m CH$_4$ feature the single most sensitive tracer. Despite these changes, the region between 800 and 1500 K where methane is expected to dominate above a C/O threshold persists, and the first robust CH$_4$ detection on an irradiated planet falls inside it. In the Spitzer IRAC color diagrams the two main populations barely move with mixing, so off-population points are attributed mainly to clouds; only planets cooler than about 900 K with C/O below 0.25 show strong mixing-induced deviations.

Load-bearing premise

The temperature-pressure profile of every modelled atmosphere is fixed at its radiative-convective, thermochemical-equilibrium value, and the chemistry is not allowed to feed back and change the temperature structure; if disequilibrium chemistry alters the temperature structure, the predicted quenching pressures and detectability maps would shift.

Editorial extensions

If this is right

Transmission spectra of planets with effective temperature between 800 and 1500 K can be read as tests of C/O and cloud formation even when vertical mixing is strong, because mixing does not erase the Methane Valley.
JWST programs that target 1000-1800 K planets around M dwarfs with low surface gravity, high metallicity, and C/O near unity maximize the chance of seeing disequilibrium fingerprints.
The five spectral windows near 1, 3.3, 4.5, 12, and 15 $\mu$m are the most promising places to look for vertical-mixing signatures in transmission.
Observed outliers in Spitzer IRAC two-color diagrams are more likely to be caused by clouds than by vertical mixing, except for very cold planets with C/O below 0.25, where mixing can matter.
Quenching pressure is not a single number per planet: it decreases with effective temperature but varies widely with metallicity, gravity, and C/O, so retrieval recipes that assume a constant quenched abundance are not generally valid.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the Methane Valley is as robust as claimed, the same grid logic could be turned on emission spectra: planets in the valley should show correlated CH$_4$ emission and absorption behavior that separates cloud effects from transport effects more cleanly than transmission alone.
The gCV metric could be borrowed by retrieval codes as a cheap quench indicator, replacing the constant-quench-abundance assumption; doing so might change inferred $K_{zz}$ values in re-analyses of methane-deficient planets such as GJ 436b.
A coupled calculation letting chemistry alter the temperature profile is the natural next test; if it shifts quench pressures, the valley's edges and the JWST sweet spot could move by more than the current error bars.
The cold, very-low-C/O outliers singled out by the color maps are concrete follow-up targets for high-resolution spectroscopy of CO and CH$_4$ lines, since they are the only class where mixing is predicted to push a planet off the main color populations.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Short version: this paper deserves a serious referee. The genuinely new pieces are the gCV quenching metric and an 84,672-model grid run at three Kzz values; the useful result is that the Methane Valley from Paper I still shows up after vertical mixing. The benchmark against Venot et al. (2012) for HD 189733b is a real external anchor, and the independent CH4 detection on HD 102195b falling inside the valley is the kind of external hit that separates this from a self-referential exercise. The appendix verification is unusually thorough for this literature.

The soft spots are real but not fatal. The biggest one is the one the paper itself flags in A.6: ChemKM keeps the TP profiles fixed at thermochemical equilibrium while the composition evolves. Since CH4 and CO are major opacity sources in exactly the 800-1500 K band, a disequilibrium composition that changes abundances could move the thermal structure, which would shift quench pressures and the transition C/O values in Figure 8. Section 3.4 even concedes that the C/O ~ 0.95 minimum-IR-opacity region could be chemically and radiatively unstable and calls for a self-consistent calculation. So the strongest statement the presented runs justify is that the valley survives under a static equilibrium-TP assumption; the quantitative window and threshold are provisional until the feedback loop is tested. I do not think this sinks the paper: the Venot benchmark, the Appendix B checks, and the persistence of the valley at Kzz=10^12 all point the same way.

Two smaller issues. The gCV = 0.05 threshold is asserted rather than derived; a short sensitivity test around that value would harden every figure that uses it. And the Spitzer color-map discussion leads to a "deviations are likely clouds" conclusion that goes beyond a cloud-free grid; the authors say clouds are the next paper, which is fair, but Section 3.5 reads a bit stronger than the models support. Minor: the grid is promised to be public but the cited link is not a data release, and for a paper this grid-heavy, shipping the grid and spectra matters.

Who is this for? Anyone choosing JWST targets or building retrieval priors for hot and warm Jupiters, and modelers who want a quenching metric that is easy to compute. Yes, send it to peer review. Ask for: (1) a static-vs-self-consistent TP sensitivity test, or at minimum an explicit statement that the valley boundaries are preliminary; (2) gCV threshold sensitivity; (3) the actual grid and spectra release.

Referee Report

3 major / 5 minor

Summary. The paper presents ChemKM, a 1D chemical kinetic model for irradiated exoplanet atmospheres, and applies it to a large grid of 84,672 models built from petitCODE cloud-free, radiative-convective equilibrium temperature-pressure profiles. The model is benchmarked against the Venot et al. (2012) HD 189733b photochemical model, with good agreement except in the microbar regime, where molecular diffusion and photolysis dominate. The authors introduce a geometric coefficient of variation (gCV) and assert that gCV_i = 0.05 marks the onset of disequilibrium for species i. Using this metric, they find that quenching pressures depend on effective temperature, surface gravity, metallicity, and C/O ratio. The central claim is that the 'Methane Valley' (roughly 800-1500 K, above a C/O threshold) still exists when vertical mixing is included, supported by the CH4 detection on HD 102195b. The paper further recommends JWST targets with Teff between 1000 and 1800 K around M dwarfs with low gravity, high metallicity, and C/O near unity, and presents Spitzer color maps suggesting that the two main color populations are largely insensitive to vertical mixing, with deviations attributed to clouds.

Significance. If correct, the persistence of the Methane Valley under vertical mixing is an important result: it validates the authors' earlier classification scheme from Paper I, and gives observers an actionable, falsifiable statement that CH4 detections and non-detections in the 800-1500 K range are diagnostic of clouds or other processes rather than diffusive disequilibrium. The paper's strengths are its unusually broad parameter coverage, the explicit external benchmark against Venot et al. (2012), and the verification tests in Appendix B showing that kinetic steady states converge to Gibbs free-energy equilibrium in the appropriate limits. The JWST target-selection recommendations and the Spitzer color-population analysis are directly useful for planning observations. However, the significance is tempered by the static temperature-pressure treatment, which is acknowledged in Appendix A.6, and by the asserted rather than sensitivity-tested gCV threshold. These issues affect the quantitative boundaries of the Methane Valley, the transition C/O values in Figure 8, and the detectability maps in Figures 5-7, even though the qualitative survival of the valley may be robust.

major comments (3)

[Appendix A.6; Sections 3.4 and 3.5] The manuscript's central claim that the Methane Valley survives vertical mixing rests on TP profiles that are computed in radiative-convective/thermochemical equilibrium and held fixed while the composition evolves. Appendix A.6 states this explicitly: 'the current version of ChemKM only considers the TP structure statically.' In the 800-1500 K valley, CH4 and CO are major opacity sources, so a disequilibrium abundance change can alter the thermal structure, which in turn shifts the quenching pressures, the transition C/O lines in Figure 8, and the detectability maps in Figures 5-7. Section 3.4 itself concedes that the feedback 'could make the inversion ... chemically and radiatively unstable' and calls for a self-consistent disequilibrium calculation. I ask the authors to demonstrate, on a representative subset spanning the valley boundaries, that iterating the disequilibrium abundances back into the radiative model leaves the valley's existence and approximate boundaries unchanged, or alternatively to state explicitly how large the uncertainty in the valley boundaries is. Without this, the strongest claim in the abstract and conclusions goes beyond what the presented runs justify.
[Section 3.3, Eq. (4)] The gCV metric is a useful diagnostic, but the threshold gCV_i = 0.05 for the onset of disequilibrium is asserted without sensitivity analysis. The paper's quantitative quenching-pressure results, the parameter dependencies reported in Section 3.3, and the 'constant profiles' caveat indicated by the dotted line in Figure 4 all depend on this calibration. Please show how the quenching-pressure maps change if the threshold is varied over, say, 0.01-0.1, or compare the gCV-based quenching levels with a timescale-based criterion for a representative subset. This test would establish whether the reported dependencies on Teff, log g, [Fe/H], and C/O are robust features of the model or artifacts of the chosen threshold.
[Section 3.5 and Figure 9] The abstract and conclusions state that deviations of observations from the equilibrium Spitzer color maps are 'likely due to the presence of clouds and not disequilibrium processes.' This goes beyond the model, which contains no clouds and samples only three discrete Kzz values. The paper's own text is more cautious, calling clouds 'a strong contender' and deferring cloud modeling to the next paper. The authors should either soften the public-facing conclusion to 'not explained by the diffusive disequilibrium processes considered here' or provide a quantitative argument that cloud opacity in the IRAC bandpasses dominates the expected disequilibrium shifts. As written, the cloud conclusion is an interpretation rather than a result of this paper's calculations.

minor comments (5)

[Section 3.3, Eq. (4)] The notation in Eq. (4), where s_ln is defined as the sample standard deviation of log-transformed abundances and then written as s_ln = s ln(10), is confusing because s is already a standard deviation. Please define a single symbol and state clearly whether the base-10 or natural logarithm is used throughout.
[Section 3.4, paragraph 6] There is a typo in the phrase 'a further self-consistent disequilibirum chemistry calculation must be performed'; 'disequilibirum' should be 'disequilibrium'.
[Figure 5 caption] The caption uses fragments 'T op)' and 'Bottom)' rather than complete statements; also 'T op' should be 'Top'.
[Figure 7] The color maps are individually scaled, so the 20, 50, and 100 ppm contours are not directly comparable across panels. A common color scale or a statement that each panel is individually normalized would improve readability.
[Section 3.1 and Table 1] The HD 189733b benchmark comparison would benefit from a quantitative statement of the agreement level, not only the statement that abundances are 'almost identical' except in the microbar regime. A table or figure listing maximum differences in the overlapping pressure range would make the benchmark more reproducible.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the Methane Valley result is re-derived with a new kinetic model and benchmarked against external work; the static-TP limitation is a modeling caveat, not a circular step.

full rationale

The central claim, that the Methane Valley (800–1500 K with a C/O threshold) survives vertical mixing, is not definitionally circular. In Paper I the valley was defined under thermochemical-equilibrium, cloud-free conditions; this paper recomputes transition C/O ratios with the new ChemKM kinetic model at Kzz values of 10^6, 10^9, and 10^12 cm2/s, so the survival claim is a new model output rather than a restatement of the input grid. The paper itself states: "Regardless of the naming of these classes, there exists a ‘Methane Valley’ in both thermochemical equilibrium and vertical mixing cases," which is presented as a result of the kinetic calculations shown in Figure 8, not as an assumed premise. No fitted parameter is renamed as a prediction: the grid scan is exploratory, no parameter is fit to the HD 102195b detection, and that detection is used only as external supporting evidence. The self-citations to Molaverdikhani et al. (2019) and petitCODE provide the baseline grid and classification, but the new contribution is the addition of vertical mixing and a full kinetic network; the conclusion is therefore not forced by those citations. The benchmark against Venot et al. (2012) uses the same chemical network, but this is standard code verification and the paper's substantive claims do not rest on that agreement. The limitation explicitly stated in Appendix A.6, "the current version of ChemKM only considers the TP structure statically," is a genuine modeling caveat: if disequilibrium chemistry changes the temperature-pressure structure, the valley boundaries and transition C/O values could shift. Section 3.4 similarly notes that a "self-consistent disequilibirum chemistry calculation must be performed" to assess the feedback on minimum-IR-opacity inversions. These are correctness and robustness concerns, not circularity: the derivation chain does not reduce to its own inputs, and the paper identifies the missing self-consistency rather than hiding it. Overall, the derivation is self-contained as a model study, with external benchmarks and an external detection providing independent checks.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central claims rely on a static temperature structure, a constant and coarsely sampled eddy diffusion coefficient, the choice of the Venot et al. (2012) network, the cloud-free 1D approximation, and the hand-set gCV threshold. None of these is independently derived in this paper, and the gCV threshold in particular is an ad hoc criterion for defining quenching.

free parameters (3)

gCV quenching threshold = 0.05
Chosen to mark the onset of disequilibrium in Section 3.3; no independent derivation or sensitivity analysis is provided.
Eddy diffusion coefficient Kzz = 10^6, 10^9, 10^12 cm^2/s
Three discrete constant-with-altitude values used across the grid; not fitted, but the choice of values and constancy is an assumption.
Internal temperature T_int = 200 K
Set for all models to avoid interior contribution in Section 2.2; varying it would change cold planet results.

assumptions (5)

domain assumption Temperature-pressure profiles are computed under radiative-convective and thermochemical equilibrium and held fixed while chemistry evolves.
Section A.6 states ChemKM 'only considers the TP structure statically'; spectral predictions in Sections 3.4-3.5 inherit this one-way coupling.
domain assumption Eddy diffusion is parameterized as a single constant Kzz independent of altitude and species.
Section 2.1 parameterizes mixing by a constant Kzz; real 3D atmospheres have altitude-dependent mixing, and the three values may not bracket reality.
domain assumption The Venot et al. (2012) chemical network with updated photolysis cross-sections is accurate for these planets.
Section 2.1 and Appendix A.2 adopt this network; the benchmark agreement with Venot et al. (2012) is for one planet, HD 189733b.
domain assumption The atmospheres are cloud-free and 1D.
Section 2.2 describes the cloud-free grid; clouds are deferred to a future paper, yet the Spitzer color interpretation in Section 3.5 attributes outliers to clouds.
ad hoc to paper gCV_i >= 0.05 marks the onset of disequilibrium.
Section 3.3 asserts the threshold without deriving it from a physical timescale comparison or error analysis.

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Cite this review

Pith. "Pith review of From cold to hot irradiated gaseous exoplanets: Fingerprints of chemical disequilibrium in atmospheric spectra." pith.science (2026). https://pith.science/paper/OJ5QKONS

@misc{pith2026190809847,
  author       = {Pith},
  title        = {Pith review of: From cold to hot irradiated gaseous exoplanets: Fingerprints of chemical disequilibrium in atmospheric spectra},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OJ5QKONS}},
  note         = {Machine review of arXiv:1908.09847}
}

abstract

Almost all planetary atmospheres are affected by disequilibrium chemical processes. In this paper we introduce our recently developed Chemical Kinetic Model (\texttt{ChemKM}). We show that the results of our HD189733b model are in good agreement with previously published results, except at $\mu$bar regime, where molecular diffusion and photochemistry are the dominant processes. We thus recommend careful consideration of these processes when abundances at the top of the atmosphere are desired. We also propose a new metric for a quantitative measure of quenching levels. By applying this metric, we find that quenching pressure decreases with the effective temperature of planets, but it also varies significantly with other atmospheric parameters such as [Fe/H], log(g), and C/O. In addition, we find that the "Methane Valley", a region between 800 and 1500K where above a certain C/O threshold value a greater chance of CH$_4$ detection is expected, still exists after including the vertical mixing. The first robust CH$_4$ detection on an irradiated planet (HD102195b) places this object within this region; supporting our prediction. We also investigate the detectability of disequilibrium spectral fingerprints by JWST, and suggest focusing on the targets with T$_{eff}$ between 1000 and 1800K, orbiting around M-dwarfs, having low surface gravity but high metallicity and a C/O ratio value around unity. Finally, constructing Spitzer color-maps suggests that the main two color-populations are largely insensitive to the vertical mixing. Therefore any deviation of observational points from these populations are likely due to the presence of clouds and not disequilibrium processes. However, some cold planets (T$_{eff}<$900K) with very low C/O ratios ($<$0.25) show significant deviations; making these planets interesting cases for further investigation.

Figures

Figures reproduced from arXiv: 1908.09847 by the authors.

**Figure 1.** HD 189733b photochemical model comparison. Left) The temperature structure. Rest of panels) ChemKM’s calculated abundances of CH4, CO2, NH3, HCN, and H at thermochemical equilibrium (solid blue lines) and photo-diffusion equilibrium (solid red lines), compared with the results of Venot et al. (2012) (black lines). The results are in good agreement except at and above the µbar regime, where photolysis reactions and m… view at source ↗

**Figure 2.** Effect of vertical mixing on CH4 abundances at the top of the atmosphere. (a) A simple parametric GJ 436b−like TP structure, adapted from Madhusudhan & Seager (2011). (b) CH4 abundance profiles caused by different Kzz values. Stronger mixing causes a deeper quenching level, but does not guarantee a monotonic abundance variation. (c) CH4 abundance at TOA as a function of Kzz in this particular case. (d) Variation of … view at source ↗

**Figure 3.** A quantitative definition of disequilibrium. We use the results of our diffusion verification model (presented in [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Figures from the paper (19 more)

**Figure 4.** Figure 4: A quantitative determination of quenching levels in our grid of chemical kinetic models for Kzz=1012 cm2 s −1 cases. (a) Density plot of quenching levels of all species. In general, Pquench decreases to lower pressures as temperature increases, but its variation at any…

**Figure 5.** Figure 5: Variation of transmission spectrum due to disequilibrium chemistry for a Jupiter-sized planet orbiting a G5-type star with solar metallicity, C/O∼0.5, and surface gravity of 3.5. Top) Methane abundance decreases as a result of added vertical mixing with Kzz=1012 cm2 s …

**Figure 6.** Figure 6: Occurrence rate of maximum variation in the transmission spectra, max(∆TD), within JWST’s wavelength range. Five wavelength regions show the highest occurrences, namely ∼1 µm (CH4, H2O, or CO), ∼3.3 µm (mostly CH4), ∼4.5 µm (CO2 or CO), ∼12 µm (CH4), and ∼15 µm (CH4).…

**Figure 7.** Figure 7: The average maximum variation in the transmission spectra, max(∆TD), due to the disequilibrium for a Jupiter-size planet. Dark-blue represents the parameter-space with the highest max(∆TD). Colormaps are scaled for each panel to show the patterns in more detail. Region…

**Figure 8.** Figure 8: The effect of vertical mixing on the transition C/O ratios. Upper left) Transition C/O ratios of thermochemically equilibrium models presented in Molaverdikhani et al. (2019). The transmission spectra above the transition lines are expected to be CH4-dominated and belo…

**Figure 9.** Figure 9: Synthetic Spitzer IRAC color–temperature diagrams for cloud-free atmospheres under thermochemical equilibrium (left panels) and diffusion equilibrium (right panels) conditions. Top panels Color diagram based on emission spectroscopy, i.e., IRAC data describes the secon…

**Figure 10.** Figure 10: Numerical instability due to the choice of relative tolerance, rtol, in the numerical solver. Poor numerical convergence occurs at high temperature-pressure regions of the atmosphere, unless a proper rtol value is chosen. Left) Temperature profile of a typical Hot Jup…

**Figure 11.** Figure 11: DVODPK’s running time for a suite of 0D simulations over a broad range of densities and temperatures. The solution of the system of ODEs by DVODPK appears to be less efficient at higher density and temperature conditions. Chemical Network Elements Species Reactions Re…

**Figure 12.** Figure 12: Numerical integrator’s performance for a simple case. The results are compared with the analytical solution of the system. They agree within the numerical errors. been addressed by previous studies as well (e.g. Moses et al. (2011); Venot et al. (2012); Drummond et al…

**Figure 13.** Figure 13: Consistency of the thermodynamic equilibrium composition (dotted straight lines) and ChemKM’s kinetic steady state solutions in a reversible system of reactants in a 0D model setup with T=1560 K and P=10 bar. The result of the thermochemically reversed model is shown …

**Figure 14.** Figure 14: Similar to [PITH_FULL_IMAGE:figures/full_fig_p022_14.png]

**Figure 15.** Figure 15: Time evolution of our 1D model presented in [PITH_FULL_IMAGE:figures/full_fig_p023_15.png]

**Figure 16.** Figure 16: A cross-section of [PITH_FULL_IMAGE:figures/full_fig_p024_16.png]

**Figure 17.** Figure 17: Temporal evolution of the 1D model presented in [PITH_FULL_IMAGE:figures/full_fig_p025_17.png]

**Figure 18.** Figure 18: Top) Local stellar intensity (actinic flux) in logarithmic scale. Lower pressures are color-coded by cooler colors. Bottom) UV absorption cross-section of species in ChemKM (gray). Some of the species with usually major opacity contributions are shown in color. fixed,…

**Figure 19.** Figure 19: Water condensation in a nearly water-saturated Neptune-like planet, i.e. the temperature profile is similar to that of Neptune, but the initial composition is set to 80.8% H2O, 19% He, and the rest is CH4 and CO with molar fraction of 1.2 × 10−3 and 8 × 10−8 respectiv…

**Figure 20.** Figure 20: Condensation and cold-trap on Neptune. Left) Neptune’s temperature structure (red line) and condensation curves of H2O (blue line) and C2H2 (orange line). Rest of panels) Temporal evolution of condensate production, and formation of a cold-trap roughly between 1 and 0…

**Figure 21.** Figure 21: Abundance variations due to 2 × 105 molecules cm−2 s −1 water influx at TOA. The model has a temperature structure similar to the Neptune model presented in [PITH_FULL_IMAGE:figures/full_fig_p028_21.png]

**Figure 22.** Figure 22: Similar to [PITH_FULL_IMAGE:figures/full_fig_p029_22.png]

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

, " * write output.state after.block = add.period write newline

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[2] [2]

write newline

" write newline "" before.all 'output.state := FUNCTION format.doi doi empty "" "doi:" doi * if FUNCTION format.url url empty "" new.block "" url * "" * if FUNCTION format.eprint eprint empty "" archivePrefix empty "" archivePrefix ":" * if eprint field.or.null * if FUNCTION format.pid eprint empty format.doi format.eprint if FUNCTION n.dashify 't := "" t...

[3] [3]

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thebibliography [1] 20pt to REFERENCES 6pt =0pt 10pt plus 3pt =0pt =0pt =1pt plus 1pt =0pt =0pt -12pt =13pt plus 1pt =20pt =13pt plus 1pt \@M =10000 =-1.0em =0pt =0pt 0pt =0pt =1.0em @enumiv\@empty 10000 10000 `\.\@m \@noitemerr \@latex@warning Empty `thebibliography' environment \@ifnextchar \@reference \@latexerr Missing key on reference command Each re...

arXiv 2017

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