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

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.