Water enrichment of forming sub-Neptune envelopes limited by oxygen exhaustion

Abstract

The interaction between a magma ocean and a primordial atmosphere is increasingly recognized as a key process in shaping planetary envelope compositions. This coupling should strongly influence gas accretion, yet its role during the disk-embedded stage remains poorly constrained. We develop a time-dependent model that couples solid accretion, nebular-gas accretion, and water enrichment and partitioning through magma-atmosphere interactions, along with post-disk thermal evolution and escape. We find that, for super-Earth-mass planets, water production is generally limited by the magma oxygen budget and typically ceases before disk dispersal. Subsequent nebular-gas accretion dilutes the envelope toward hydrogen-dominated compositions, largely independent of the initial magma redox state. This establishes an upper bound on the envelope water fraction -- the oxygen exhaustion limit -- primarily set by the reactive-oxygen inventory and the planet mass. After disk dispersal, degassing increases the water fraction only in Earth-mass planets undergoing strong escape, while super-Earths exhibit little change because surface pressures are hardly affected by escape. Magma-atmosphere coupling alone therefore cannot maintain water-rich envelopes in sub-Neptunes and produces a strong mass-composition relation imposed by the oxygen exhaustion limit. Highly enriched sub-Neptunes would therefore imply additional mechanisms such as late volatile delivery or post-disk giant impacts. The relation between planetary radius and envelope composition offers a means to infer magma properties, providing a pathway to connect present-day observables with early formation histories.

Figures (9)

• Figure 1: Schematic structure of the planet in our model. From top to bottom, the planet consists of four layers: a nebular-composition envelope (pure H$_2$), a vapor-mixed envelope (H$_2$ + H$_2$O), a reactive magma layer, and a non-reactive (inert) magma layer. Only the vapor-mixed envelope and the reactive magma are assumed to interact. If the radiative–convective boundary (RCB) lies within the nebular-composition layer, its convective part is assumed to mix with the vapor-mixed layer. See text for details.
• Figure 2: Time evolution of planetary properties for the nominal case (see Table \ref{['tab:parameter']} for parameter values). Panel (a): Masses of the core (black), vapor-mixed envelope (blue), and nebular-composition envelope (magenta). Panel (b): Total planetary radius at 10 mbar (red) and core radius (black). Panel (c): Total (red) and H$_2$O partial (blue) pressures at the magma surface. Panel (d): Temperature at the bottom of the envelope. Panel (e): Water mass in the bulk planet (grey), magma (red), and vapor-mixed envelope (blue). Panel (f): Water mass fraction in the vapor-mixed envelope. Grey dotted and dashed lines indicate the termination of solid accretion and the time of disk dispersal, respectively.
• Figure 3: Time evolution of the envelope's pressure–temperature structure in the nominal case (see also Fig. \ref{['fig:MRPTWX_nominal']}). The grey region shows the nebular-composition layer and the colored region shows the vapor-mixed layer, color-coded by its H$_2$O mass fraction ($X_{\rm H_2O,mix}$). Thin and thick segments indicate radiative and convective regions, respectively. The outer boundary is fixed at 500 K, while the pressure decreases from 1 Pa as the disk dissipates.
• Figure 4: Time evolution of the water mass fraction in the vapor-mixed envelope ($X_{\rm H_2O,mix}$) for different initial values of $X_{\rm H_2O,eq}$. Other parameters are identical to those listed in Table \ref{['tab:parameter']}. Grey dotted and dashed lines indicate the termination of solid accretion and the time of disk dispersal, respectively.
• Figure 5: Time evolution of the water mass fraction in the vapor-mixed envelope ($X_{\rm H_2O,mix}$) for different isolation masses $M_{\rm iso}$, ranging from $1M_\oplus$ to $6M_\oplus$ in $1M_\oplus$ increments. Other parameters are the same as in Table \ref{['tab:parameter']}. The grey dashed line marks the time of disk dispersal.