Most Rocky Sub-Neptunes are Molten: Mapping the Solidification Shoreline for Gas Dwarf Exoplanets

TL;DR

This work uses the PROTEUS interior-climate model to map a solidification shoreline in the $T_{eff}$–$F_{ins}$ plane, delineating where gas dwarfs maintain permanent magma oceans versus solidified mantles. By coupling mantle dynamics, radiative-convective climate, and volatile exchange, the authors show that 98% of detected sub-Neptunes would reside in the molten regime if they are gas dwarfs, with envelope mass fraction and instellation flux as the dominant controls. Secondary factors like envelope oxidation state and bulk C/H ratio influence the shoreline, but high mean molecular weight atmospheres from oxidising or carbon-rich interiors can push planets out of the sub-Neptune radius regime, complicating simple classifications. The results motivate observational searches for magma-ocean–atmosphere interactions (e.g., via JWST) and propose the shoreline as a framework for assessing interior states across the sub-Neptune population, while highlighting areas for model enhancement (escape, high-pressure solubility, broader mass range).

Abstract

Sub-Neptunes are the most common type of detected exoplanet, yet their observed masses and radii are degenerate with several interior structures. One possibility is that sub-Neptunes have silicate/iron interiors and H$_2$-dominated atmospheres, i.e., they are `gas dwarfs'. If gas dwarfs have molten interiors, interactions between their magma oceans and atmospheres will produce distinct observational signatures. These signatures may break the degeneracy in interior structure, while providing insight into their interior processes, history, and population trends. We expect all such planets are born molten, but under what conditions do they remain molten today? We use the coupled interior-climate evolution model, PROTEUS, to estimate the `solidification shoreline': the instellation flux boundary (as a function of stellar $T_{\rm eff}$) that separates molten gas dwarfs from solidified ones. Our results show that 98\% of detected sub-Neptunes occupy a region of parameter space consistent with their having permanent magma oceans, if they are gas dwarfs. While mantle $f{\rm O}_2$ and bulk volatile C/H ratio both influence magma ocean lifetimes, planets with oxidising mantles and carbon-rich atmospheres are unlikely to have radii consistent with the sub-Neptune classification. Therefore, most detected sub-Neptunes (if they are gas dwarfs) have permanent magma oceans. This result motivates further research into the interactions between molten interiors and overlying atmospheres, and campaigns to identify unambiguous signatures of these interactions.

Figures (11)

• Figure 1: Left: Instellation flux at which the thermal steady state of a gas dwarf transitions from a permanent magma ocean to a solidified mantle: the 'solidification shoreline'. Planets in the region of the parameter space to the left of the shoreline will have permanent magma oceans, and any planets to the right of the shoreline will have solidified mantles. The solidification shoreline is shown for envelope mass fractions of 0.1%, 0.3% and 1%. The positions of all detected sub-Neptunes in this parameter space are shown as scatter points; their colour corresponds to the EMF calculated using equation 2 from Lopez2014. Right: Ratio of the observed instellation flux of detected sub-Neptunes ($F_{\text{observed}}$) to the instellation flux required for them to be on their appropriate solidification shoreline ($F_{\text{boundary}}$) as a function of host star effective temperature. Errors in $F_{\text{observed}}$/$F_{\text{boundary}}$ are propagated from observed masses, host star effective temperature and planet masses. A ratio of F$_{\text{observed}}$/F$_{\text{boundary}}$=1, corresponding to a planet located on the solidification shoreline, is shown. Sub-Neptunes for which there exist published JWST transmission spectra as well as those in the solidified mantle region are shown in blue, and those without JWST transmission spectra are shown in maroon.
• Figure 2: Absorption cross-sections of key species as a function of wavelength for $P=10^{3}$ bar and $T=1500$ K (i.e., the pressure and temperature expected near the base of the atmosphere of a gas dwarf). The cross-section due to H$_2$-H$_2$ collisionally induced absorption is also shown. The blackbody spectrum corresponding to an effective temperature of $T=4500$ K (i.e., an effective temperature typical of a K-type star) is shown. Absorption cross-sections are taken from the DACE database Grimm2015Grimm2021 and cross-sections for H$_2$-H$_2$ collisionally induced absorption are taken from the HITRAN database Gordon2022.
• Figure 3: Left: Global melt fraction of the mantle (red dots) as well as the net atmospheric flux at the end of the planet's thermal evolution (blue crosses) as a function of oxygen fugacity of the magma ocean. All simulations with $\Delta{\rm IW} < -2$ achieve mantle solidification, and all simulations with $\Delta{\rm IW} > -2$ end their evolution with a permanent magma ocean. The stellar effective temperature, instellation flux, planet mass and metallicity used in these simulations are also shown. The instellation flux was chosen such that the planet was located at the transition from a permanent magma ocean to a solidified mantle in the $T_{\text{eff,*}}$-$F_{\text{ins}}$ parameter space. Right: Volume mixing ratios of key species in the atmosphere as a function of mantle oxygen fugacity ($\Delta$IW). The downward longwave radiative flux at the base of the atmosphere, which quantifies the rate of surface heating due to the greenhouse effect of the atmosphere, as a function of mantle oxygen fugacity is also shown.
• Figure 4: Global melt fraction of the mantle (red dots) as well as the net atmospheric flux at the end of the planet's thermal evolution (blue crosses) as a function of the C/H ratio of the bulk volatile inventory. Results are shown for simulations with a mantle oxygen fugacity of $\Delta{\rm IW}=-4$ (left panel) as well as $\Delta{\rm IW}=4$ (right panel). All of the simulations corresponding to a mantle oxygen fugacity of $\Delta{\rm IW}=-4$ end their evolution with a solidified mantle, and all of the simulations corresponding to a mantle oxygen fugacity of $\Delta{\rm IW}=4$ end their evolution with a permanent magma ocean. The stellar effective temperature, instellation flux and planet mass used in these simulations are also listed in the upper corners. The instellation flux was chosen such that the planet was located at the transition from a permanent magma ocean to a solidified mantle in the $T_{\text{eff}}$-$F_{\text{ins}}$ parameter space.
• Figure 5: Volume mixing ratios of key species in the atmosphere as a function of the C/H ratio of the bulk volatile inventory. The left and right panels show the results for simulations with mantle oxygen fugacities of $\Delta{\rm IW} = -4$ and 4 respectively. The downward longwave radiative flux at the base of the atmosphere, which quantifies the rate of surface heating due to the greenhouse effect of the atmosphere, as a function of the C/H ratio of the bulk volatile inventory is also shown.