Silane/Methane Ratio as a Magma Ocean Signature of Sub-Neptunes

The James Webb Space Telescope is opening a new window into the atmospheres of sub‑Neptunes, a class of planets where magma oceans may play a central role in shaping their atmospheric composition. At the magma ocean-envelope boundary (MEB; pressures >10 kbar), gas behaviour departs strongly from ideality, yet the consequences of real‑gas effects for chemical equilibria remain poorly quantified.

We model coupled magma-gas and gas-gas equilibrium chemistry for TOI‑421b, a hot sub‑Neptune, using real‑gas equations of state in the H–He–C–N–O–Si system. Our results show that H and N are the most soluble species in magma, followed by He and C. Using new real gas fits to experimental SiH₄ data, we find that SiH₄ dominates the MEB composition for a fully molten mantle at solar metallicity, but CH₄ becomes favoured at 100× solar. Reducing the mantle melt fraction suppresses both Si transfer from the magma ocean and the solubility of H and He, producing more H₂‑ and He‑rich envelopes.

Extending equilibrium chemistry through the observable atmosphere (1 mbar-100 bar), we find that Si‑bearing condensate clouds efficiently remove Si‑bearing gases, though SiH₄ remains a key species when solar‑metallicity gas is accreted. Both the SiH₄/CH₄ ratio and the Si/C ratio increase with mantle melt fraction and decrease with gas metallicity.

These trends identify the competition between SiH₄ and CH₄ as a diagnostic of both metallicity and the presence of magma oceans on sub‑Neptunes with equilibrium temperatures below 1000 K. Conversely, H₂‑ and He‑rich atmospheres that are SiH₄‑poor yet CH₄‑bearing may suggest a limited or absent role for magma oceans.