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

TL;DR

This study addresses how magma oceans influence the chemical makeup of sub-Neptune envelopes and their observable atmospheres. It develops a self-consistent interior–atmosphere model (Atmodeller) that couples magma–gas and gas–gas equilibria with real-gas equations of state for the H–He–C–N–O–Si system, applied to the canonical hot sub-Neptune TOI-421b. Key findings show that Si-bearing gases dominate the magma-envelope boundary and in the observable atmosphere at solar metallicity when the mantle is fully molten, whereas methane becomes dominant at high accreted-metallicity, high-melt cases; solubility in magma and non-ideal gas effects significantly modulate gas abundances, shifting the balance between SiH$_4$, SiO, CH$_4$, and H$_2$- and He-rich envelopes. The results yield concrete diagnostics—notably the SiH$_4$/CH$_4$ and Si/C ratios—that can reveal magma-ocean presence and mantle melt state in sub-Neptunes with equilibrium temperatures below ~1000 K, guiding future JWST/ARIEL retrievals and informing planetary formation and evolution theories.

Abstract

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.

Figures (16)

• Figure 1: Illustration of magma--envelope chemical coupling. Volatile element budgets are set by the metallicity of accreted gas, and the refractory element budgets are set by the sum of the metallicity of accreted gas and their budget in the bulk silicate Earth scaled by planet mass. Gas--gas reactions, magma--gas reactions, gas solubilities in magma and real gas behaviour are modelled using Atmodeller2025arXiv250700499B.
• Figure 2: Comparison of the compressibility factors ($Z$) modelled in Eq. \ref{['eq:Virial_SiH4']} with those observed in the shock experiments of 2018PhyB..541...89W. The data are colour-coded by temperature (in K). The derived coefficients, their associated uncertainties, and the reduced chi-squared ($\chi^2_r$) values are shown in the legend.
• Figure 3: Partial pressures of H$_2$, H$_2$O, SiO and SiH$_4$ at the magma--envelope boundary (MEB) of TOI-421b ($R_{\rm MEB} = 1.65 R_{\oplus}$, $R_P = 2.64 R_{\oplus}$, $M_P = 6.7 M_{\oplus}$, $T_{\rm MEB}=3000$ K with a fully molten mantle) in the H--O--Si chemical system. (a) Envelope composition with real gas behaviour and gas solubility. (b) Envelope composition with ideal gas behaviour and gas solubility. O$_2$ partial pressures are less than 10$^{-7}$ bar and not shown.
• Figure 4: Fugacity coefficients of the H--O--Si gases for the real gas case of Fig. \ref{['fig:HOSi_model']}.
• Figure 5: The solubility of H (in the form of H$_2$ and H$_2$O) as a function of the total H budget relative to the planet mass for real and ideal gas cases from Fig. \ref{['fig:HOSi_model']}.