Atmospheric diversity of sub-Neptunes from formation with rock, water, and soot

Source: arXiv:2606.20464 · Published 2026-06-18 · By Caroline Dorn, Aaron Werlen, Sean Jordan

TL;DR

This paper addresses the origins of atmospheric diversity in sub-Neptune exoplanets by linking observable atmospheric compositions to the nature of their planetary building blocks—rock, water, and refractory carbonaceous material termed "soot". Leveraging global chemical equilibrium models coupled with atmospheric structure and photochemistry simulations, the authors systematically explore four end-member compositional scenarios representing formation inside the water ice line (rock-only and soot-rock mix) versus beyond it (water-rock and soot-water-rock mixes). Key findings reveal that water-poor planets have atmospheres strongly depleted in carbon-bearing species (CH4 and CO2 < 10^-4 molar fraction), while water-rich formation naturally enhances methane and carbon dioxide abundances, with soot further boosting methane to produce methane-dominated atmospheres. These compositional signatures shape atmospheric C/O ratios, mean molecular weights (MMW), and metal mass fractions, which in turn provide diagnostics of the primordial building blocks and formation environments.

Key findings

• Planets formed from water-poor material (cases 1 and 2) exhibit atmospheric CH4 and CO2 molar fractions below 10^-4.
• Water-rich planets (cases 3 and 4) show increases in atmospheric CH4 by at least four orders of magnitude compared to water-poor cases, driving elevated C/O ratios and metal mass fractions (Z > 0.7 in soot-water-rock case 3).
• The soot-water-rock planet (case 3) develops a methane-dominated atmosphere with mean molecular weight exceeding 17 g/mol, significantly higher than water-rock (case 4) with MMW below 7.5.
• Atmospheric mass fractions vary by about an order of magnitude between volatile-rich (case 3 ~10%) and volatile-poor planets (cases 1, 2, and 4 <1%), with these contrasts lessened at lower magma ocean interface temperatures (2000 K vs 3000 K).
• Gas compositions depend only weakly on the fraction of accreted primordial hydrogen-rich gas over 1–9% planetary mass, indicating bulk planetary composition dominates atmospheric chemistry.
• Vertical profiles show that under strong mixing (high Kzz), molecular abundances are constant with altitude, whereas weak mixing enables photochemical dissociation in upper atmospheres primarily for soot-water-rock (case 3).
• Comparison to JWST observations of sub-Neptunes (K2-18 b, TOI-270 d, TOI-421 b, GJ3470 b, GJ9827 d) broadly supports the model classification: water-rich formation explains methane- and water-rich sources, while water-poor formation explains methane-depleted, water-dominated atmospheres.
• The ratio of H2O/CH4 combined with mean molecular weight provides a powerful two-dimensional diagnostic of formation environment and distinguishes formation inside versus beyond the water ice line.

Methodology — deep read

1. Threat Model & Assumptions: The study models sub-Neptune planets assumed to have formed from varying proportions of three main building blocks—rock, water ice, and soot—representing formation inside and beyond key disk lines (soot line, water ice line). The model assumes global chemical equilibrium between the deep interior (magma ocean and core) and the overlying atmosphere, representing an end-member scenario of full interior–atmosphere chemical coupling. This departs from prior models that assume atmospheres decoupled chemically from interiors. The primordial hydrogen-rich gas accretion is treated parametrically from 1-9% in planetary mass, to capture variation in envelope mass.

2. Data and Compositions: Four compositional end-member planetary cores are considered:

• Case 1: Rock only (100% chondritic rocky material)
• Case 2: Soot-rock (24% soot, 76% rock)
• Case 3: Soot-water-rock (20% soot, 25% water, 55% rock)
• Case 4: Water-rock (40% water, 60% rock, no soot) The soot composition is fixed as C100H77O14 to represent refractory carbonaceous organic matter. Rock compositions follow chondritic abundances of elements; water is taken as ice content.

3. Architecture / Algorithm: The core method uses the global chemical equilibrium (GCE) model (Grimm et al. 2026) with 19 reaction equations and 26 phase components spanning metal, silicate, and gas phases. This thermochemical network accounts for equilibrium abundances of gas species including CH4, CO, CO2, H2O, H2, and refractory species, and also includes carbon partitioning into metal phases from recent advances (Werlen et al. 2025b). Chemical equilibrium calculations determine species mole fractions and atmospheric bulk properties (C/O ratios, metal mass fractions Z, and mean molecular weight MMW) at the atmosphere–magma ocean interface (AMOI).

4. The atmospheric structure above AMOI is modeled using coupled open-source tools:

• FastChem computes thermochemical gas equilibrium at local conditions.
• HELIOS and HELIOS-K generate pressure–temperature (P-T) profiles and wavelength-dependent opacities.
• VULCAN solves chemical kinetics including photochemistry, vertical transport (parameterized by eddy diffusivity Kzz). Iterations between these modules achieve steady-state atmospheric vertical profiles from ~103 bar to 10^-5 bar relevant for observables.

5. Training Regime / Parameters: While no machine learning is applied, models simulate planets of masses 6 and 10 Earth masses, with TAMOI fixed at 3000 K as the fiducial magma ocean temperature, and also tested at 2000 K for sensitivity. The accreted hydrogen gas fraction is varied from 1-9%. Vertical mixing is tested at Kzz = 10^4 and 10^7 cm^2/s.

6. Evaluation Protocol: The predicted atmospheric compositions, bulk properties, and vertical chemical profiles for each case are compared directly to recent JWST transmission spectroscopy retrieval results for well-characterized sub-Neptunes (e.g., K2-18 b, TOI-270 d). Observables used for comparison are volume mixing ratios of CH4, H2O, and the atmospheric mean molecular weight. The diagnostic power of the CH4/H2O ratio combined with MMW is emphasized as a two-dimensional discriminator of formation environment. Variation of photochemical assumptions and condensation (e.g., water condensation) are discussed, as well as implications of vertical mixing strength for upper atmosphere composition.

7. Reproducibility: The chemical equilibrium model and atmospheric codes used (FastChem, HELIOS, VULCAN) are open source, but the paper does not indicate if all scripts or frozen model weights are publicly released. Some input datasets such as soot molecular formula and chondritic rock abundances are drawn from prior publications.

End-to-end example: For a 6 M⊕ planet formed with soot-water-rock composition and 5% accreted H2 primordial gas, GCE computes gas abundances at AMOI—yielding a methane-dominated atmosphere with CH4 mixing ratio ~10^-1, metal mass fraction near unity, and MMW > 17 g/mol. This is input to FastChem and HELIOS-K to generate opacities, HELIOS to produce P-T profile, and VULCAN to obtain vertical mixing ratio profiles under photochemistry and vertical transport. The final observable atmosphere retains strong methane signatures under strong mixing, matching patterns seen in JWST spectra of methane-rich sub-Neptunes.

Technical innovations

• Integration of global chemical equilibrium modeling coupling metal, silicate, and gas phases to simulate interior–atmosphere chemical equilibration of sub-Neptunes.
• Incorporation of refractory carbon (soot) composition as a key planetary building block and its effect on atmospheric methane abundance and bulk properties.
• Coupled simulation framework linking deep interior chemistry with photochemical-kinetic atmospheric models (FastChem, HELIOS, VULCAN) for end-to-end prediction of atmosphere observable signatures.
• Identification of the joint H2O/CH4 ratio and atmospheric mean molecular weight (MMW) as a robust two-dimensional diagnostic to infer exoplanet formation location regarding the water ice line.

Datasets

• Synthetic planetary interior and atmosphere compositions generated via global chemical equilibrium model, N≈4 core composition scenarios with varying mass fractions of rock, water, and soot.
• JWST transmission spectroscopy retrieval data for sub-Neptunes (K2-18 b, TOI-270 d, TOI-421 b, GJ3470 b, GJ9827 d, LP791-18 c, TOI-732 c) from multiple literature sources.

Baselines vs proposed

• Rock-only core (case 1): Atmospheric CH4 molar fraction < 10^-7 vs soot-water-rock core (case 3): CH4 molar fraction ~ 0.1 to 1, implying >10^6× enhancement in methane.
• Water-rock core (case 4): Atmospheric MMW < 7.5 vs soot-water-rock core (case 3): MMW > 17.
• Volatile-poor cores (cases 1 and 2): Atmospheric metal mass fraction Z < 0.3 vs volatile-rich core (case 3): Z approaches unity.
• Accreted primordial gas fraction variation (1% to 9%): atmospheric gas composition and bulk properties vary only marginally, demonstrating weak sensitivity.

Figures from the paper

Figures are reproduced from the source paper for academic discussion. Original copyright: the paper authors. See arXiv:2606.20464.

Fig 5: Molar mixing ratios of CH4/H2O versus mean molecular weight (MMW) as a diagnostic of sub-Neptune formation location

Limitations

• Assumption of global, full chemical equilibrium between interior and atmosphere may be idealized; real planets may have limited equilibration due to convection barriers or molecular weight gradients.
• Soot composition is fixed and simplified, ignoring nitrogen and sulfur chemistry, and does not account for variation in soot molecular formulas.
• Atmospheric models do not include refractory condensation effects (e.g., silicates) which might alter upper atmosphere composition and thermal structure.
• Photochemistry and vertical mixing are modeled with parameterized eddy diffusion coefficients with inherent uncertainties, allowing some degeneracy in predictions especially between cases 3 and 4 at low mixing.
• Choice of magma ocean interface temperature (TAMOI) influences absolute atmospheric mass fractions and compositions; explored only two values (2000 K and 3000 K).
• Comparisons to JWST data rely mostly on CH4 and H2O abundances; CO and CO2 retrievals are model dependent and less constrained.
• No explicit modeling of atmosphere escape processes beyond qualitative discussion, though they impact evolved atmospheric compositions.

Open questions / follow-ons

• How interior–atmosphere chemical equilibration is physically regulated over time by dynamical mixing barriers and phase separation in sub-Neptunes remains to be quantified.
• What are the effects of a variable and more realistic soot molecular composition including nitrogen and sulfur on atmospheric chemistry and observables?
• How do non-equilibrium processes such as condensation clouds and photochemical hazes modify the atmospheric signatures and the robustness of the H2O/CH4-MMW diagnostic?
• Can atmospheric escape and fractionated mass loss histories be integrated quantitatively with formation and interior chemistry models to explain observed diversity?

Why it matters for bot defense

For bot-defense and CAPTCHA practitioners, this study exemplifies how detailed compositional and chemical equilibrium modeling can link intrinsic system components to observable signatures, analogous to tracing the properties of user interactions or network traffic back to underlying behavioral or environmental factors. Although the domain is astrophysical, the approach of building interpretable, physics-based models that generate multi-parameter diagnostics (here H2O/CH4 ratio and mean molecular weight) offers an instructive example relevant to designing bot detection features that combine orthogonal signal dimensions. Careful coupling of deep internal states (e.g., user intent or device characteristics) informs predictions about surface-level observables (network requests), paralleling the interior–atmosphere coupling studied here. Practitioners can appreciate that indirect, bulk composition diagnostics allow inference of formation or provenance environments which might otherwise be unobservable, a principle with broad applicability in anomaly detection. However, uncertainties from unmodeled processes and mixing strength highlight the importance of accounting for physical constraints and environmental factors when interpreting observational data in security contexts.

Cite

@article{arxiv2606_20464,
  title={ Atmospheric diversity of sub-Neptunes from formation with rock, water, and soot },
  author={ Caroline Dorn and Aaron Werlen and Sean Jordan },
  journal={arXiv preprint arXiv:2606.20464},
  year={ 2026 },
  url={https://arxiv.org/abs/2606.20464}
}

Read the full paper

• arXiv:2606.20464 (abstract)
• arXiv:2606.20464 (PDF)