Silane-Methane Competition in Sub-Neptune Atmospheres as a Diagnostic of Metallicity and Magma Oceans

The James Webb Space Telescope is characterising the atmospheres of sub-Neptunes. The presence of magma oceans on sub-Neptunes is expected to strongly alter the chemistry of their envelopes and observable atmospheres. At the magma ocean-envelope boundary (MEB, $>$10 kbar), gas properties deviate from ideality, yet the effects of real gas behaviour on chemical equilibria remain underexplored. Here, we compute equilibrium between magma-gas and gas-gas reactions using real gas equations of state in the H-He-C-N-O-Si system for TOI-421b, a canonical hot sub-Neptune potentially hosting a magma ocean. We find that H and N are the most soluble in magma, followed by He and C. We fit real gas equations of state to experimental data on SiH$_4$, and show that, for a fully molten mantle, SiH$_4$ dominates at the MEB under accreted gas metallicity of 1$\times$ solar, but is supplanted by CH$_4$ at 100$\times$ solar. Lower mantle melt fractions lower both magma-derived Si abundances in the envelope and the solubility of H and He in magma, yielding H$_2$- and He-rich envelopes. Projecting equilibrium chemistry through the observable atmosphere (1 mbar-100 bar), we find that `clouds’ of Si-bearing condensates strongly deplete Si-bearing gases, although SiH$_4$ remains key, especially when a solar gas is accreted. SiH$_4$/CH$_4$ and Si/C ratios increase with mantle melt fraction and decrease with accreted gas metallicity. The competition between SiH$_4$ and CH$_4$ is therefore diagnostic of metallicity and presence of magma oceans on sub-Neptunes with equilibrium temperatures below 1000 K. The corollary is that H$_2$- and He-rich, SiH$_4$-deficient and CH$_4$-bearing observable atmospheres may indicate a limited role or absence of magma oceans on sub-Neptunes.

💡 Research Summary

This paper investigates how the competition between silane (SiH₄) and methane (CH₄) can be used to diagnose both the atmospheric metallicity and the presence of a deep magma ocean in sub‑Neptune exoplanets, focusing on the hot sub‑Neptune TOI‑421b as a case study. The authors recognize that at the magma‑envelope boundary (MEB), pressures exceed 10 kbar and temperatures are around 3000 K, conditions under which gases deviate markedly from ideal‑gas behavior. To capture this, they develop real‑gas equations of state (EOS) for SiO and SiH₄. SiO is modeled using the Redlich‑Kwong EOS combined with the law of corresponding states, yielding a compressibility factor Z₍c₎≈0.33 that matches experimental data. For SiH₄, where high‑pressure data were previously lacking, the authors fit a quadratic Virial EOS (Z = 1 + A(T)P + B(T)P²) to shock‑compression measurements spanning 44–138 GPa and 1200–4100 K, deriving temperature‑dependent coefficients (A₀≈3.86 GPa⁻¹, B₀≈‑0.019 GPa⁻², etc.) with quantified uncertainties.

The chemical equilibrium calculations are performed with the open‑source Python package Atmodeller, which simultaneously treats gas‑gas reactions, magma‑gas exchange, gas solubility in melt, and the real‑gas corrections. The model is parameterized by three key variables: (1) the mass fraction of accreted hydrogen (0.1–1 wt % of the planet’s mass), (2) the metallicity of the accreted nebular gas (1× or 100× solar), and (3) the mantle melt fraction (1 %–100 %). Elemental budgets are set using solar abundances (Lodders 2009) and bulk‑silicate‑Earth SiO₂ composition, scaled according to the chosen metallicity and melt fraction. TOI‑421b’s bulk properties (R = 2.64 R⊕, M = 6.7 M⊕, T_eq ≈ 920 K) and a fixed MEB temperature of 3000 K are adopted.

Key results include:

1. Hydrogen and nitrogen are the most soluble species in the magma, followed by helium and carbon.
2. For a fully molten mantle (100 % melt) and solar metallicity, SiH₄ dominates the Si‑bearing gas phase at the MEB, out‑competing CH₄.
3. When the metallicity is increased to 100× solar, carbon and nitrogen abundances rise dramatically, causing CH₄ (and NH₃) to supplant SiH₄ as the dominant reduced carbon‑bearing gas.
4. Reducing the melt fraction sharply lowers the total Si and O budgets (by factors of 10–100) and diminishes H and He solubility, leading to H₂‑ and He‑rich envelopes with very low SiH₄.
5. Extending the equilibrium calculation upward through the observable atmosphere (1 mbar–100 bar) shows that Si‑bearing condensates (e.g., SiO₂, SiC clouds) efficiently remove SiH₄ and SiO from the gas phase. Nonetheless, under low metallicity and high melt fraction, SiH₄ can remain at detectable mixing ratios (∼10⁻⁶–10⁻⁵ bar).

The authors identify two diagnostic ratios: SiH₄/CH₄ and Si/C. Both increase with higher mantle melt fraction and decrease with higher gas metallicity. Consequently, measuring these ratios in JWST transmission or emission spectra of sub‑Neptunes with equilibrium temperatures below ~1000 K can simultaneously constrain (a) the bulk metallicity of the atmosphere (1–100× solar) and (b) whether a global magma ocean is present.

The paper’s major contributions are (i) providing the first high‑pressure, high‑temperature EOS for SiH₄ based on experimental data, (ii) integrating magma‑envelope coupling with real‑gas thermodynamics in a self‑consistent mass‑budget framework, and (iii) demonstrating that SiH₄–CH₄ competition offers a robust, observable signature of interior state. The authors suggest future work should incorporate additional Si‑O gas species (e.g., SiO₂(g), Si₂O₃), detailed cloud microphysics, and three‑dimensional atmospheric dynamics to refine the predicted spectral signatures and enable quantitative comparison with forthcoming JWST observations.