The Effects of Non-ideal Mixing in Planetary Magma Oceans and Atmospheres

TL;DR

This paper develops a comprehensive thermodynamic model to study how non-ideal mixing affects volatile exchange between magma oceans and atmospheres on sub-Neptunes and super-Earths, with implications for interpreting observations.

Contribution

It introduces a fully coupled model incorporating activity and fugacity coefficients across melt, metal, and gas phases, advancing understanding of planetary interior and atmospheric interactions.

Findings

Non-ideality causes modest corrections at planetary embryo conditions.

At higher temperatures and pressures, non-ideal effects are more significant but still within 20-50%.

Global treatment of non-ideality is essential for accurate planetary modeling.

Abstract

Sub-Neptunes with hydrogen-rich envelopes are expected to sustain long-lived magma oceans that continuously exchange volatiles with their overlying atmospheres. Capturing these interactions is key to understanding the chemical evolution and present-day diversity of sub-Neptunes, super-Earths, and terrestrial planets, particularly in light of new JWST observations and upcoming missions. Recent advances in both geochemistry and astrophysics now allow the integration of experimental constraints and thermodynamic models across melt, metal, and gas phases. Here we extend a global chemical equilibrium model to include non-ideal behavior in all three phases. Our framework combines fugacity corrections for gas species with activity coefficients for silicate and metal species, enabling a fully coupled description of volatile partitioning. We show that for planetary embryos (0.5 M$_\oplus$ at 2350 K), non-ideality introduces only modest corrections to atmosphere-magma ocean interface (AMOI) pressures, volatile inventories, and interior compositions. In contrast, for sub-Neptunes with higher temperatures ($\approx$ 3000 K) and pressures, non-ideal effects are more pronounced, though still modest in absolute terms$-$typically within 20% and at most a factor of two. Including activity and fugacity coefficients simultaneously increases the AMOI pressure, enhances water retention in the mantle and the envelope. Our results demonstrate that non-ideality must be treated globally: applying corrections to only one phase leads to incomplete or even misleading trends. These findings highlight the importance of self-consistent global thermodynamic treatments for interpreting atmospheric spectra and interior structures of sub-Neptunes and super-Earths.