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arxiv: 2607.06491 · v1 · pith:6UXJHJMA · submitted 2026-07-07 · astro-ph.EP · astro-ph.IM

A parameterised approach to disequilibrium retrievals in the JWST era: Application to NIRCam observations of HD 189733b

Jake Taylor , Shang-Min Tsai , Vivien Parmentier , Chloe Fisher , Michael Line This is my paper

Reviewed by Pith2026-07-08 03:59 UTCglm-5.2pith:6UXJHJMAopen to challenge →

classification astro-ph.EP astro-ph.IM
keywords exoplanet atmospheresatmospheric retrievaldisequilibrium chemistryquench pressurevertical mixingJWSTHD 189733btransmission spectroscopy
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The pith

Two free parameters fix disequilibrium biases in JWST exoplanet retrievals

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

This paper argues that the standard assumption of chemical equilibrium in exoplanet atmospheric retrievals produces systematically wrong estimates of carbon-to-oxygen ratio and metallicity whenever vertical mixing is present, and that the fix is cheap: add two free parameters representing the quench pressures for carbon-bearing and nitrogen-bearing species. At pressures above the quench point, abundances are frozen at their deep-atmosphere equilibrium values rather than following equilibrium throughout. Using synthetic JWST spectra of the hot Jupiter HD 189733b generated with a full kinetic chemistry model, the authors show that equilibrium retrievals drift further from truth as mixing strength increases, while the two-parameter quenching framework recovers the correct bulk composition in most cases. Applied to real JWST/NIRCam transmission data of HD 189733b, the disequilibrium model is favoured over equilibrium with a log Bayes factor of 7.3, with the carbon quench pressure retrieved at roughly 50 bar, implying strong vertical mixing. The paper also introduces a three-parameter parameterisation for the vertical profile of hydrogen sulfide (H2S), consisting of a deep well-mixed abundance, a break pressure, and a power-law decline, which it applies to the same data to tentatively locate the boundary of the photochemically active region at around 0.6 millibar.

Core claim

The central object is the quench pressure parameterisation (Eq. 3): for each chemical family (carbon or nitrogen), a single pressure level is retrieved above which the volume mixing ratio is held constant at its equilibrium value at that pressure. This two-parameter extension to standard equilibrium retrievals is shown to recover unbiased C/O and [M/H] from synthetic spectra where vertical mixing is present, while standard equilibrium retrievals do not. On real JWST/NIRCam data of HD 189733b, the framework yields a log Bayes factor of 7.3 over equilibrium and places the carbon quench pressure at approximately 1.7 bar (or deeper, at roughly 50 bar, in the variant without the H2S parameteriser

What carries the argument

quench_pressure_parameterisation

If this is right

  • Future exoplanet retrieval studies that assume chemical equilibrium should routinely include quench pressure parameters for carbon and nitrogen species, as the paper demonstrates measurable bias when they are omitted.
  • Retrieved quench pressures can serve as proxies for vertical mixing strength, linking transmission spectroscopy to deep atmospheric dynamics that are otherwise unobservable.
  • The H2S vertical profile parameterisation, if validated on planets with both H2S and SO2 spectral features, could map the transition between the quenched region and the photochemically active region in exoplanet atmospheres.
  • The degeneracy between the disequilibrium model and the equilibrium-plus-H2S model on HD 189733b can be broken with NIRISS/SOSS observations, where the two models diverge by over 50 ppm.

Where Pith is reading between the lines

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

  • If quench pressures are reliably retrievable from JWST spectra, a sample of hot Jupiters with measured quench pressures could be used to calibrate eddy diffusion prescriptions in general circulation models, providing an observational anchor for a parameter that is currently set by theory alone.
  • The fact that nitrogen and carbon quench at different pressures, and that both are independently retrieved, suggests that multi-instrument wavelength coverage spanning both CH4 and NH3 spectral features is necessary to break degeneracies between the two quench parameters.
  • The H2S break pressure interpretation as the photochemical boundary could be tested by comparing retrieved break pressures across a temperature gradient of hot Jupiters, since photochemical timescales scale with temperature and the boundary should shift predictably.

Load-bearing premise

The H2S parameterisation is an ad hoc functional form with three free parameters and no derivation from photochemical kinetics, applied to real data where only a single spectral feature constrains H2S. The paper itself notes that the disequilibrium model and the equilibrium-plus-H2S model are statistically indistinguishable given current observations, so the physical interpretation of the break pressure as the photochemical boundary rests on a model preference that is not yet

What would settle it

If a retrieval assuming chemical equilibrium on a planet with known strong vertical mixing recovers the correct C/O and [M/H] without quench parameters, or if the quench pressure framework fails to recover known input values on synthetic spectra with mixing strengths between the four tested Kzz values, the parameterisation's utility would be undermined.

Figures

Figures reproduced from arXiv: 2607.06491 by Chloe Fisher, Jake Taylor, Michael Line, Shang-Min Tsai, Vivien Parmentier.

Figure 1
Figure 1. Figure 1: Left: Model transmission spectra of a hot Jupiter with system parameters corresponding to HD 189733b. The spectra were generated by post-processing chemical abundance profiles from VULCAN using NemesisPy. Five atmospheric models are shown: one assuming chemical equilibrium, and four incorporating varying strengths of vertical mixing, parameterised by different eddy diffusion coefficients (Kzz). The lower p… view at source ↗
Figure 2
Figure 2. Figure 2: The volume mixing ratios of the key species investigated in this study. Each panel shows the volume mixing ratio for a given molecule and multiple Kzz values. We plot the input TP profile with a dashed purple line. The metallicity and C/O ratios assumed in these models are solar. MNRAS 000, 1–13 (2025) [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Heatmap of the reduced χ 2 values for all of the simulations described in Section 2.1. We label each panel with the value of the reduced χ 2 and colour-code with the corresponding colour-bar for easier visual inspection. We have split into two heatmaps, one for each TP parameterisation assumed. MNRAS 000, 1–13 (2025) [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Violin plots of the retrieved C/O values for the different instrument modes. The top panel shows the retrieved C/O values when assuming a Madhusudhan & Seager (2009) TP profile, the bottom panel shows the retrieved C/O values when assuming a Parmentier & Guillot (2014) TP profile. The horizontal dashed lines represent the true value of C/O. The error bars represent the 1-σ uncertainties. The colours repres… view at source ↗
Figure 5
Figure 5. Figure 5: Violin plots of the retrieved [M/H] values for the different instrument modes. The top panel shows the retrieved [M/H] values when assuming a Madhusudhan & Seager (2009) TP profile, the bottom panel shows the retrieved C/O values when assuming a Parmentier & Guillot (2014) TP profile. The horizontal dashed lines represent the true value of C/O. The error bars represent the 1-σ uncertainties. The colours re… view at source ↗
Figure 6
Figure 6. Figure 6: The retrieved quenching pressures from the elemental and molecular quenching simulations. The colour of the violin plots corresponds to the quench parameter being retrieved, with purple, blue, red, and yellow being the elemental carbon, elemental nitrogen, CH4, and NH3, respectively. The horizontal dashed lines represent the true values of the quenching pressures, with the triangle for the approximate carb… view at source ↗
Figure 7
Figure 7. Figure 7: Comparison of the two models that best describe the observations. In red, we present the model where we have used our disequilibrium parameterisation described in Section 2.2, and in purple, we show the model where we have assumed chemical equilibrium and used the H2S parameterisation as described in Section 4.1. The bottom panel shows the difference between the models. Parameter DisEq (with H2S) DisEq Che… view at source ↗
Figure 8
Figure 8. Figure 8: Panels showing the TP profiles and volume mixing ratios of the molecules modelled in the disequilibrium (blue), chemical equilibrium with H2S parameterisation, and free chemistry (red) analyses. Each profile has a 1-σ envelope. [*]) at the University of Leicester, managed by the University of Le￾icester Research Computing Service on behalf of the STFC DiRAC HPC Facility (www.dirac.ac.uk). The DiRAC service… view at source ↗
read the original abstract

Atmospheric retrievals are a widely used technique for inferring the physical and chemical properties of exoplanetary atmospheres from observed spectra. A common simplifying assumption in such analyses is that the atmosphere is in thermochemical equilibrium, which allows the use of precomputed chemical abundance grids as a function of pressure, temperature, metallicity ([M/H]), and carbon-to-oxygen ratio (C/O). However, exoplanet atmospheres often deviate from equilibrium, particularly at lower temperatures or in the presence of strong vertical mixing. In this work, we investigate the impact of disequilibrium chemistry on retrieval outcomes by generating synthetic James Webb Space Telescope (JWST) observations of HD\,189733\,b with varying strengths of vertical mixing. We demonstrate that assuming thermochemical equilibrium can lead to significant biases in the retrieved atmospheric parameters, including incorrect estimates of C/O and [M/H]. To address this, we incorporate transport-induced quenching of carbon and nitrogen-bearing species into the retrieval framework by allowing the quench pressures to be free parameters. We show that this approach recovers the correct bulk atmospheric properties in most cases. Finally, we apply our disequilibrium retrieval model to published JWST/NIRCam transmission observations of HD\,189733\,b and find tentative evidence for quenching. We also find tentative evidence for the photochemically active region of the atmosphere via a newly developed H$_2$S parameterisation, this is the first time this has been constrained in a hot Jupiter atmosphere.

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.

Referee Report

4 major / 8 minor

Summary. This paper presents a parameterised disequilibrium retrieval framework in which the quench pressures of carbon- and nitrogen-bearing species are treated as free parameters, with abundances truncated at the quench pressure following Eq. (3). The method is validated on synthetic JWST observations generated with VULCAN (forward model) and retrieved with NemesisPy/FastChem (retrieval model), testing multiple instrument configurations, mixing strengths, and TP profile parameterisations. The framework is then applied to published JWST/NIRCam transmission observations of HD 189733b, where the authors also introduce an ad hoc H2S vertical profile parameterisation to account for photochemical depletion. The synthetic tests demonstrate that the disequilibrium framework recovers bulk C/O and [M/H] more accurately than chemical equilibrium when vertical mixing is present, and the real-data application yields a carbon quench pressure of log P_q,C ~ 1.7 bar.

Significance. The quench-pressure parameterisation is a sensible and computationally efficient middle ground between free-chemistry and full kinetic-grid retrievals, and the synthetic retrieval tests are well designed: the forward (VULCAN) and retrieval (NemesisPy/FastChem) models are genuinely independent, priors are stated, and multiple instrument configurations and TP profiles are tested. The application to real JWST/NIRCam data and the introduction of an H2S vertical-gradient parameterisation are timely. However, the central real-data claim of 'tentative evidence for quenching' rests on a model comparison that is more nuanced than presented, as detailed below.

major comments (4)
  1. Section 4.1, Table 2: The headline log Bayes factor of 7.3 favouring disequilibrium (DisEq lnZ=571.8 vs ChemEq lnZ=564.5) is computed between models that both omit the H2S parameterisation. The paper itself argues that the H2S parameterisation is necessary because the DisEq framework 'does not take into account sulfur chemistry' and Fu et al. (2024) detect H2S at 4.5 sigma. When H2S is included in both models, the evidence becomes DisEq+H2S (lnZ=569.4) vs ChemEq+H2S (lnZ=569.5), yielding Delta lnZ ~ -0.1 — i.e., no preference for disequilibrium. The paper acknowledges the two models are 'indistinguishable within the error of the observations' but still leads with the 7.3 Bayes factor from the incomplete comparison in the abstract, Section 4.1, and conclusions. The fair comparison (both models including H2S) should be the primary basis for the real-data claim, and the abstract and结论should
  2. Section 4.1, Table 2 and Figure 8: The DisEq (no H2S) model achieves higher evidence (lnZ=571.8) than DisEq+H2S (lnZ=569.4), which is counterintuitive — adding a physically motivated component that matches a 4.5-sigma detection should not decrease evidence. The text (Section 4.1, final paragraph) explains that the DisEq model without H2S elevates CO, CO2, and H2O VMRs via deep quenching, with CO being 'incompatible with the free retrieval.' This suggests the no-H2S model is absorbing the H2S spectral feature into other free parameters, producing a spuriously good fit by misattributing a detected molecule's feature. The paper should explicitly discuss this as a risk of the quenching framework — that deep quenching can inflate CO/CO2/H2O abundances to compensate for missing opacity sources — and clarify why the DisEq+H2S model, which includes the correct absorber, is the more physically可靠
  3. Section 3.3, Eq. (4): The 'true' quench pressures used for validation are derived from the VULCAN models using an ad hoc threshold (a=0.25 for carbon, a=0.1 for nitrogen) applied to adjacent-layer VMR differences. The paper notes that 'the carbon quenching pressure is recovered at higher pressures in the atmosphere compared to the true values.' This systematic offset may be a direct consequence of the threshold definition rather than a retrieval failure: Eq. (4) identifies quenching when the relative VMR difference between adjacent layers falls below 'a', but this is not the same as the chemical-timescale vs mixing-timescale criterion that defines quenching in the kinetic model. The sensitivity of the 'true' quench pressure to the choice of 'a' should be quantified (e.g., by varying a by a factor of 2) to determine whether the systematic offset is a validation failure or an artifact of
  4. Section 4.1, H2S parameterisation: The functional form — a deep well-mixed abundance plus a break pressure and power-law decline — is ad hoc, with no derivation from photochemical kinetics. It is applied to real data where only a single spectral feature constrains H2S (as shown in Figure 1, right panel), and the break pressure is then interpreted as the boundary of the photochemically active region. The paper itself notes the disequilibrium+H2S and equilibrium+H2S models are 'indistinguishable within the error of the observations.' The physical interpretation of P_break as the photochemical boundary should therefore be stated as conditional on the assumed functional form, and the claim of 'first tentative evidence of the constraint on the photochemically active region' should be moderated accordingly.
minor comments (8)
  1. Abstract: 'this is the first time this has been constrained in a hot Jupiter atmosphere' — the H2S constraint is tentative and model-dependent; consider softening.
  2. Section 2.1: The footnote 'For the quenching retrievals, no sulfur chemistry is used' is important context that should be stated more prominently, as it affects the real-data application.
  3. Table 2: The ordering of columns (DisEq+H2S, DisEq, ChemEq+H2S, ChemEq) makes cross-comparison awkward; consider reordering to group with/without H2S.
  4. Figure 7: The bottom panel shows the difference between DisEq and ChemEq+H2S models, but the y-axis range and label are unclear; a clearer annotation of the 50 ppm deviation region would help.
  5. Section 4.1: The statement 'we can begin to constrain the photochemically active regions of exoplanet atmospheres with JWST' is strong given the model degeneracy; should be framed as such.
  6. Table 1 (free chemistry): This table is labelled Table 1 but conflicts with the prior table also labelled Table 1; should be renumbered.
  7. Section 3.3: The statement that nitrogen quenches at deeper levels than carbon is consistent with theory, but the fact that nitrogen quenching hits the 100 bar boundary for high Kzz should be noted as a limitation.
  8. Figure 8: The y-axis labels for VMR panels show inconsistent formatting (e.g., '10 5' vs '10^{-5}'); ensure consistent formatting.

Simulated Author's Rebuttal

4 responses · 0 unresolved

We thank the referee for a thorough and constructive report. The referee correctly identifies that the fair model comparison for the HD 189733b data (both models including H2S) yields no preference for disequilibrium, and we will revise the abstract, Section 4.1, and conclusions to lead with this comparison rather than the incomplete comparison. We also agree that the counterintuitive evidence behaviour of the no-H2S DisEq model should be explicitly discussed as a risk of the quenching framework, that the sensitivity of the 'true' quench pressure to the threshold parameter 'a' should be quantified, and that the H2S parameterisation claims should be moderated. All four major comments will be addressed in revision.

read point-by-point responses

  1. Referee: Section 4.1, Table 2: The headline log Bayes factor of 7.3 favouring disequilibrium is computed between models that both omit the H2S parameterisation. When H2S is included in both models, the evidence becomes DisEq+H2S (lnZ=569.4) vs ChemEq+H2S (lnZ=569.5), yielding Delta lnZ ~ -0.1 — i.e., no preference for disequilibrium. The fair comparison should be the primary basis for the real-data claim, and the abstract and conclusions should be revised accordingly.

    Authors: The referee is correct. The fair comparison is the one in which both models include the H2S parameterisation, and this yields Delta lnZ ~ -0.1, i.e., no statistical preference for disequilibrium over equilibrium. We will revise the abstract, Section 4.1, and the conclusions to lead with this fair comparison. The lnZ=7.3 Bayes factor from the incomplete comparison (both models omitting H2S) will be retained in the text for completeness but explicitly flagged as an incomplete comparison that should not be used as the basis for the quenching claim. The abstract will be revised to state that the disequilibrium and equilibrium models (both including H2S) are statistically indistinguishable for the NIRCam data, and that the tentative evidence for quenching is therefore conditional and would require additional data (e.g., NIRISS/SOSS) to break the degeneracy. revision: yes

  2. Referee: Section 4.1, Table 2 and Figure 8: The DisEq (no H2S) model achieves higher evidence than DisEq+H2S, which is counterintuitive. The no-H2S model may be absorbing the H2S spectral feature into other free parameters (CO, CO2, H2O) via deep quenching, producing a spuriously good fit. The paper should explicitly discuss this as a risk of the quenching framework and clarify why DisEq+H2S is the more physically reliable model.

    Authors: We agree with the referee's interpretation. The evidence pattern is consistent with the no-H2S DisEq model compensating for the missing H2S opacity by elevating CO, CO2, and H2O VMRs through deep quenching, as we note in the final paragraph of Section 4.1. We will add an explicit discussion of this as a known risk of the quenching framework: when an opacity source is missing, deep quenching can inflate the abundances of other species to compensate, producing a spuriously high evidence. This reinforces why the DisEq+H2S model, which includes the correct absorber, is the more physically reliable model and should be the basis for comparison. We will state this clearly in the revised text. revision: yes

  3. Referee: Section 3.3, Eq. (4): The 'true' quench pressures used for validation are derived using an ad hoc threshold (a=0.25 for carbon, a=0.1 for nitrogen) applied to adjacent-layer VMR differences. The systematic offset between retrieved and 'true' quench pressures may be an artifact of the threshold definition rather than a retrieval failure. The sensitivity of the 'true' quench pressure to the choice of 'a' should be quantified (e.g., by varying a by a factor of 2).

    Authors: This is a valid concern. The threshold-based definition of the 'true' quench pressure in Eq. (4) is not equivalent to the chemical-timescale vs mixing-timescale criterion used in the kinetic model, and the systematic offset we report could partly reflect this mismatch. We will quantify the sensitivity of the 'true' quench pressures to the choice of 'a' by varying a by a factor of 2 in each direction (a=0.125 and 0.5 for carbon; a=0.05 and 0.2 for nitrogen) and will add a figure or table showing how the 'true' quench pressures shift. This will allow the reader to assess whether the retrieved offset is comparable to the uncertainty introduced by the threshold definition. We will also add a discussion noting that the threshold-based definition is an approximation and that a timescale-based comparison would be a useful future refinement. revision: yes

  4. Referee: Section 4.1, H2S parameterisation: The functional form is ad hoc, with no derivation from photochemical kinetics. The physical interpretation of P_break as the photochemical boundary should be stated as conditional on the assumed functional form, and the claim of 'first tentative evidence of the constraint on the photochemically active region' should be moderated accordingly.

    Authors: We agree that the H2S parameterisation is ad hoc and that the interpretation of P_break as the photochemical boundary is conditional on the assumed functional form. We will revise the text to state this conditionality explicitly. The claim of 'first tentative evidence of the constraint on the photochemically active region' will be moderated to reflect that this constraint is conditional on the parameterisation and that, given the statistical indistinguishability of the DisEq+H2S and ChemEq+H2S models, it should be regarded as a tentative demonstration of the approach rather than a definitive measurement. The abstract will be revised accordingly. revision: yes

Circularity Check

1 steps flagged

Largely self-contained; minor partial circularity in quench-pressure validation where VULCAN defines both synthetic data and 'true' quench pressures, but retrieval is spectrally independent.

specific steps
  1. fitted input called prediction [Section 3.3, Eq. 4 and Fig. 6]
    "To determine the quench pressure, we compute the variation of the volume mixing ratio between two layers, and if the difference is sufficiently small, we conclude that it is quenched. We determine this value with the following equation: a > (X_{z+1} - X_z) / X_z (4) where X_z is the volume mixing ratio in layer z, and a is the value we consider the layer difference to be quenched. For carbon species, we assume a = 0.25, and for nitrogen species, we use a = 0.1."

    The synthetic spectra are generated with VULCAN, and the 'true' quench pressures used as validation targets in Fig. 6 are also extracted from the same VULCAN profiles using the ad hoc threshold of Eq. 4. This creates partial circularity: the data source and the truth benchmark are the same model. However, the retrieval itself (FastChem equilibrium + Eq. 3 step function) is spectrally driven and does not access VULCAN's abundance profiles directly, so the quench-pressure recovery is not forced by construction. The circularity is limited to the choice of validation metric, not the retrieval mechanism.

full rationale

The paper's central derivation is largely self-contained. The synthetic-observation validation uses VULCAN to generate spectra and an independent code stack (NemesisPy/FastChem with Eq. 3) to retrieve atmospheric parameters; the C/O and [M/H] recovery tests are genuinely independent of the forward model. The quench-pressure comparison (Section 3.3) has a mild circularity because VULCAN defines both the synthetic data and the 'true' quench pressures via the ad hoc Eq. 4 threshold, but the retrieval infers quench pressures from spectral features alone, so the recovery is not forced by construction. The H2S break-pressure consistency check cites Tsai et al. (2021) (co-author Tsai), but this is a post-hoc validation, not a load-bearing derivation step. The real-data Bayes factor framing (leading with ΔlnZ=7.3 from models that omit H2S, while the fair comparison with H2S yields ΔlnZ≈−0.1) is a presentation/cherry-picking concern, not a circularity in the derivation chain. No step reduces to its inputs by definition or by self-citation.

Axiom & Free-Parameter Ledger

7 free parameters · 4 axioms · 0 invented entities

No new physical entities are postulated.

free parameters (7)
  • log P_q,C = 1.711 bar (real data)
    Carbon quench pressure, free parameter in retrieval
  • log P_q,N = unconstrained (real data)
    Nitrogen quench pressure, free parameter in retrieval
  • log X_H2S,deep = -3.21 (real data)
    Deep H2S abundance, free parameter in H2S parameterisation
  • P_break,H2S = -3.25 bar (real data)
    Break pressure for H2S photochemical decline
  • alpha_H2S
    Power-law slope for H2S decline above break pressure
  • a (carbon quench threshold) = 0.25
    Hand-set threshold for defining quench pressure from VULCAN profiles (Eq. 4)
  • a (nitrogen quench threshold) = 0.1
    Hand-set threshold for defining quench pressure from VULCAN profiles (Eq. 4)
axioms (4)
  • domain assumption Transport-induced quenching can be approximated as a sharp step function in VMR at a single pressure level (Eq. 3)
    Section 2.2, Eq. 3. Real quenching is gradual; the step-function approximation is standard but untested against the full range of kinetic behaviours.
  • domain assumption Carbon and nitrogen species quench independently at different pressure levels
    Section 2.2. Supported by Moses et al. 2011 and Tsai et al. 2018, but the separation assumes no cross-species coupling affects quenching.
  • ad hoc to paper H2S photochemical depletion follows a monotonic power-law decline above a break pressure
    Section 4.1. No derivation from photochemical kinetics; the functional form is chosen for convenience.
  • domain assumption FastChem 3.0 equilibrium abundances are accurate for the relevant P-T regime of HD 189733b
    Section 2.1. Standard assumption but unverified for the specific conditions of this planet.

pith-pipeline@v1.1.0-glm · 19975 in / 4035 out tokens · 282509 ms · 2026-07-08T03:59:46.883989+00:00 · methodology

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