The atmospheric vertical structure of Uranus and Neptune from thermochemical models: the impact of model assumptions

Abstract: The composition and temperature-pressure profile of the atmospheres of Uranus and Neptune are not well-determined. As observational data are limited, we often rely on chemical equilibrium computations to infer atmospheric abundances and cloud formation. The inferred atmospheric structures, however, strongly depend on several fundamental assumptions such as the elemental abundances and ratios, the condensation properties of the assumed species, or a reference temperature for the adiabatic structure. In this study we investigate the effects of different metallicities (1 to 80 solar), element ratios (C/O and S/N, from 0.1 to 2 and 0.19 to 1.6) and 1 bar temperatures (66 to 86 K) on the vertical structure of ice giant atmospheres. In particular, we use the chemical equilibrium code \texttt{FastChem} to derive mixing ratios and cloud structures for CH$_4$, NH$_3$, H$_2$S, H$_2$O and NH$_4$SH. We find that the models are very sensitive to the assumed parameters, yielding drastically different possible atmospheric structures. For the cases considered here, we find that mixing ratios and cloud deck altitudes can vary by more than an order of magnitude. Additionally, thermal profiles can differ by several tens of kelvins due to composition and 1-bar temperature. We advise that future ground-based observations and a dedicated mission to Uranus and/or Neptune are required to better characterize the atmospheric structure and composition of ice giants.

• The paper demonstrates that thermochemical equilibrium models produce highly non-unique atmospheric structures, with plausible assumptions changing deep mixing ratios by factors of up to 50 and temperatures by tens of kelvins.
• Metallicity controls the overall condensate inventory, while C/O affects methane clouds and S/N determines whether NH₃ or H₂S forms the main observable cloud deck, with S/N near unity marking the transition.
• A 5 K change in the 1-bar temperature can produce roughly 25 K differences at 100 bar and strongly alter cloud locations, showing why observations across multiple wavelengths and future orbiter–probe missions are needed.

Motivation and scope

Uranus and Neptune have each been visited only once, by Voyager 2, and the composition and temperature–pressure ($T$–$P$) structure of their atmospheres remain poorly constrained. Because remote observations are limited to regions above the uppermost cloud deck (a few bars at most), the vertical composition and cloud structure below must be inferred from chemical equilibrium calculations. Such inferences depend on several fundamental but uncertain assumptions: the atmospheric metallicity $Z$, the elemental abundance ratios C/O and S/N, and the reference temperature at 1 bar that anchors the adiabatic thermal profile. This paper by Douçot et al. (2608.13157) quantifies how sensitive the predicted vertical structures of ice giant atmospheres are to these assumptions.

The work is motivated both by Solar System science — the NASA Decadal Survey identified a Uranus Orbiter and Probe as its highest priority for 2023–2032 [NAP26522] — and by exoplanetology, since intermediate-mass planets resembling Uranus and Neptune are among the most common planetary types known. Atmospheric characterization is the essential link between observable properties and deeper interior processes, so establishing which atmospheric structures are compatible with current constraints is a prerequisite for interpreting future data.

Method: FastChem with rainout condensation

The authors use the open-source chemical equilibrium code FastChem [2018MNRAS.479..865S, 2024MNRAS.527.7263K], which solves the law of mass action together with element conservation for roughly 500 gas-phase and condensate species. Condensation is treated iteratively: at each $(P,T)$ point the code selects the stable set of condensates satisfying Gibbs' phase rule, and applies a rainout approximation whereby condensed material is removed from the overlying atmosphere and no longer participates in chemistry. The authors emphasize that this "rainout condensation chemistry" neglects precipitation settling fluxes and differs from standard equilibrium schemes in which condensates remain in exchange with the gas.

The thermal profiles follow the moist-adiabat formalism of Leconte et al. [2017A&A...598A..98L], with H$_2$O adopted as the single reference vapor controlling the lapse rate. Three regimes are considered: an upper saturated moist-convective region, a deep dry layer once the vapor reaches a prescribed deep mixing ratio $q_{int} = 0.25$, and — when the vapor abundance exceeds a critical value — a convectively inhibited radiative layer following the radiative gradient $\nabla_r$. Reference profiles use 1-bar temperatures of 76 K (Uranus) and 72 K (Neptune) from Voyager 2 radio occultations [1987JGR....9214987L, 1990GeoRL..17.1733L].

Three parameter sets were explored:

Parameter	Range	Reference value
Metallicity $Z$	1–80 $Z_\odot$	1 $Z_\odot$
C/O	0.1–2.0	0.55
S/N	0.19–1.6	0.19
$P$0	66–86 K	76 K (U), 72 K (N)

Two modeling choices deserve note. First, nitrogen is depleted by a factor of ten relative to other heavy elements at all metallicities, reflecting microwave evidence of NH$P$1 depletion and H$P$2S detection consistent with S/N $P$3 [2018NatAs...2..420I]. Second, the S/N-ratio models deliberately omit this depletion, since applying it would shift the probed ratios to 1.9–16 and miss the critical S/N $P$4 regime governing H$P$5S–NH$P$6 chemistry. The temperature range of $P$710 K intentionally exceeds the formal Voyager 2 uncertainties ($P$82 K), because retrieval-based errors typically understate true uncertainty from atmospheric assumptions [2022PSJ.....3..159G]. The same composition grid is applied to both planets; they differ only through their thermal profiles.

Sensitivity to metallicity

Across 1–80 $P$9, deep mixing ratios of H$Z$0O, CH$Z$1, and H$Z$2S increase by a factor of about 50, while NH$Z$3 increases only by a factor of five due to the imposed nitrogen depletion. Cloud decks respond strongly: the H$Z$4O cloud pressure range expands from 30–80 bar at solar metallicity to 15–650 bar at 80 $Z$5, and CH$Z$6 clouds appear only above 40 $Z$7, spanning 0.2–0.6 bar at 80 $Z$8. The H$Z$9S cloud is the least metallicity-sensitive, remaining near 2–5 bar. NH$(P,T)$0SH always forms near the top of the water cloud (~40 bar), desiccating whichever of H$(P,T)$1S or NH$(P,T)$2 is less abundant; at solar S/N = 0.19, H$(P,T)$3S is the limiting reagent, explaining the absence of an H$(P,T)$4S cloud at 1 $(P,T)$5, whereas at high $(P,T)$6 nitrogen depletion makes H$(P,T)$7S dominant and an H$(P,T)$8S cloud replaces the NH$(P,T)$9 cloud.

A notable discrepancy emerges here: methane condensation is predicted at higher altitudes (0.1–1 bar) than in previous models such as Hueso et al. [2020RSPTA.37890476H], which place the CH$_2$0 cloud base at ~1 bar. In the direct comparison at 20 $_2$1, the present models predict no significant CH$_2$2 cloud at all, thinner H$_2$3O and NH$_2$4SH decks, and systematically lower gas-phase deep mixing ratios. The authors attribute part of this to FastChem's larger species network (~500 species diluting individual MMRs computed against the whole parcel), though they concede this argument alone is insufficient, and partly to the use of present-day rather than protosolar abundances. The implication is that cloud-base pressures inferred from equilibrium models carry a model-dependence comparable to the compositional uncertainty being explored.

Sensitivity to elemental ratios

Varying C/O from 0.1 to 2.0 (via carbon abundance, at fixed $_2$5) increases the CH$_2$6 deep mixing ratio by a factor of 3.5 and thickens the methane cloud by a factor of 1.65; the cloud becomes significant only for C/O $_2$7, reaching 0.22–0.60 bar. Varying S/N from 0.19 to 1.6 (via sulphur abundance) increases the H$_2$8S deep mixing ratio by a factor of ~8 and controls which species condenses: for S/N below ~1, the deep NH$_2$9SH cloud completely desiccates H$q_{int} = 0.25$0S and only NH$q_{int} = 0.25$1 condenses (3.6–8 bar); for S/N above unity, H$q_{int} = 0.25$2S alone condenses at 1.6–4 bar, consistent with the observed H$q_{int} = 0.25$3S detections on both planets [2018NatAs...2..420I, 2019Icar..321..550I]. The NH$q_{int} = 0.25$4SH deck itself remains nearly fixed at 17–42 bar regardless of S/N, since its existence depends only on the co-presence of both gases. These results imply that the identity of the main observable cloud deck is a direct diagnostic of the poorly known bulk S/N ratio.

Sensitivity to the 1-bar temperature

Because the profile follows a (moist) adiabat anchored at 1 bar, small changes in $q_{int} = 0.25$5 propagate deeply: a ~5 K difference at 1 bar produces ~25 K differences at 100 bar and ≥40 K below 1000 bar at fixed metallicity. Consequences for condensation are substantial. Cooling from 86 K to 66 K lifts the H$q_{int} = 0.25$6O cloud base from 180 to 510 bar and thins the deck by a factor of 3; the H$q_{int} = 0.25$7S cloud shifts from 1–2 bar to 2.5–8 bar and thins by a factor of 6. Methane is the most temperature-sensitive species: no significant CH$q_{int} = 0.25$8 cloud forms for $q_{int} = 0.25$9 K at 30 $\nabla_r$0, with clouds appearing only at 66 K (0.3–0.8 bar) and 70 K (0.25–0.6 bar). The authors note that more enriched atmospheres could still produce methane clouds at warmer temperatures, so temperature and metallicity effects are not separable.

Combining these sensitivities, the paper identifies four limiting scenarios — cold/poor, warm/poor, cold/rich, and warm/rich atmospheres — ranging from nearly cloud-free to heavily clouded structures, illustrating the non-uniqueness of any single inferred atmospheric model.

Comparison with observations

The models reproduce several observational benchmarks. Predicted H$\nabla_r$1S volume mixing ratios below the cloud base span $\nabla_r$2 (1 $\nabla_r$3) to $\nabla_r$4 (80 $\nabla_r$5), bracketing the observed 0.4–0.8 ppm above the deck and 1–2$\nabla_r$6 below it [2018NatAs...2..420I]. Methane VMRs of 2–3.7$\nabla_r$7 at 40–80 $\nabla_r$8 match the deep values of 2.7–3.5$\nabla_r$9 reported by Sromovsky et al. [2019Icar..317..266S]. The predicted H$Z$0S cloud location (1.6–4 bar) is broadly consistent with the aerosol retrievals of Irwin et al. [2022JGRE..12707189I], who find a CH$Z$1 cloud at 1–2 bar and an H$Z$2S cloud at 5–7 bar, although the models again place methane condensation higher than retrieved. Radio and centimeter observations probing tens of bars suffer from opacity degeneracies among species and reveal deep latitudinal heterogeneity, underscoring that a single 1D model cannot characterize an entire planetary atmosphere.

Limitations and open questions

The authors are explicit that the results rest on thermochemical equilibrium, whereas vertical mixing, photochemistry, cloud microphysics, supersaturation, and atmospheric dynamics can all drive real atmospheres away from this state [2020RSPTA.37890477M, 2024PSJ.....5..101G]. The rainout scheme excludes precipitation settling fluxes; cloud densities should be read as the equilibrium condensate reservoir rather than observable cloud opacity, since nucleation, particle growth, sedimentation, and condensation nuclei availability are not modeled. The moist-adiabat treatment uses a single vapor (H$Z$3O); multi-vapor cross terms, demonstrated for the H$Z$4O–NH$Z$5 system by Li et al. [2018JAtS...75.1063L], are neglected, though NH$Z$6 condensation remains observationally unconfirmed. No meridional or vertical wind shear is included, and the models are 1D and horizontally averaged despite known spatial variability. Only in the convection-inhibition scenario is the internal heat flux considered; otherwise the atmospheric models are formally disconnected from the interior. An additional result shows that when convection is inhibited at the water cloud base ($Z$7), a radiative layer forms with a temperature jump, and the water cloud extent shrinks relative to standard adiabatic cases — a scenario whose realism depends on the assumed deep water abundance. Whether disequilibrium processes, multidimensional dynamics, or microphysics would narrow or widen the parameter space of viable atmospheric structures is left open, as is the question of which of the four limiting scenarios actually applies to either planet.

Conclusion

This study demonstrates that equilibrium models of Uranus and Neptune atmospheres are highly sensitive to their input assumptions: mixing ratios and cloud-deck altitudes vary by more than an order of magnitude across plausible metallicities, elemental ratios, and 1-bar temperatures, and thermal profiles diverge by tens of kelvins at depth. The S/N ratio controls whether H$Z$8S or NH$Z$9 constitutes the observable cloud deck; the 1-bar temperature determines whether methane condenses at all; and metallicity scales the entire condensate inventory. The resulting degeneracy means current data cannot uniquely determine the atmospheric structure of either ice giant. The authors argue that breaking these degeneracies requires new observations across wavelengths — including high-resolution spectroscopy and JWST — and ultimately dedicated orbiter-and-probe missions combining remote sensing with in situ measurements, for which these equilibrium models provide the baseline against which more complex dynamical and disequilibrium frameworks can be developed.