Sub-Neptune Memories I: Implications of Inefficient Mantle Cooling and Silicate Rain

TL;DR

This study demonstrates that inefficient mantle cooling and silicate rain can sustain inflated radii of sub-Neptunes over gigayear timescales, challenging the notion that interiors quickly become adiabatic. By upgrading the APPLE code to couple thermal and compositional evolution with stable stratification and silicate–hydrogen phase separation, the authors show that hot, liquid mantles and a bifurcated envelope can explain observed radii and densities without invoking water-worlds for several planets. The work highlights that bulk composition inferences from mean densities must account for internal thermal state and historical mixing, and that post-formation entropies may be constrained through evolution modeling combined with improved atmospheric measurements. These insights have implications for interpreting exoplanet demographics, informing formation scenarios, and guiding future JWST and Habitable Worlds Observatory observations to probe interior conditions of sub-Neptunes.

Abstract

We explore the evolution of sub-Neptune (radii between $\sim$1.5 and 4 R$_\oplus$) exoplanet interior structures using our upgraded planetary evolution code, \texttt{APPLE}, which self-consistently couples the thermal and compositional evolution of the whole structure. We incorporate stably stratified regions with convective mixing and, for the first time, ab initio results on the phase separation of silicate-hydrogen mixtures to model silicate rain in sub-Neptune envelopes. We demonstrate that inefficient mantle cooling can retain sufficient heat to Gyr ages: inefficient heat transport from mantle to envelope alone keeps radii $\sim$10\% larger than predicted by adiabatic models at late times. Silicate rain can contribute an additional $\sim$5\% to the radius, depending on envelope mass and initial metal abundance. The silicate-hydrogen immiscibility region may lie in the middle or even upper envelope, far above the envelope-mantle boundary layer, and bifurcates the envelope into two an upper, hydrogen-rich region and a lower, metal-rich region above the mantle. If silicate rain occurs, atmospheres should appear depleted of silicates while radii remain inflated at late ages. To demonstrate this, we present interior evolution models for GJ 1214 b, K2-18 b, TOI-270 d, and TOI-1801 b, showing that hot, liquid silicate mantles with thin envelopes reproduce their radii and mean densities, providing an alternative to water-world interpretations. These results imply that bulk compositions inferred from mean density must account for mantle thermal state and envelope mixing/phase separation history; such thermal ``memories'' may constrain formation entropies and temperatures when metallicities are better measured.

Figures (12)

• Figure 1: Interior structure schematic for the interior composition of sub-Neptune models presented in this work. Color is an approximate indicator of temperature (specific values depend on the model). The envelope ($\sim$5% by mass) is a mixture of hydrogen, helium, and heavy elements ($Z$) represented by either water (Section \ref{['subsec:entropy']}) or silicates (Sections \ref{['subsec:stratification']}, \ref{['subsec:miscibility']}). The mantle composition is MgSiO$_3$, and the core composition is Fe$_{16}$Si. We maintain a 2:1 mass ratio between the core and the mantle. For this work, the EMB represents a steep compositional gradient and thus controls mantle cooling by transferring heat to the envelope via conduction. Since conductive flux alone is insufficient to transport the entire interior heat to the envelope, a steep temperature gradient forms at the EMB, as seen in all models in this work.
• Figure 2: Example isotherms of Fe$_{16}$Si EOS from Fischer2012, and the liquid iron EOSes of Ichikawa2014 and Dorogokupets2017Thermodynamics6000K, at a temperature of 10,000 K. The density differences (top panel) above 200 GPa range between 7% and 10%, and the isobaric heat capacity, C$_P$ (bottom panel), differs by nearly 50%. Present models of Earth's interior indicate that its liquid outer core may be composed of iron alloys. For simplicity, we apply the Fe$_{16}$Si EOS of Fischer2012 in the cores throughout this work.
• Figure 3: The thermal conductivity of MgSiO$_3$(top) implemented in the mantle, which governs non-convective heat transport. The electronic and phonon (lattice or vibrational) components are included Stamenkovic2011PengDeng2024. The electronic component dominates at higher temperatures. The Rosseland mean opacities (bottom) at 100 times solar abundance control the radiative heat transport in the envelope Sharp2007LacyBurrows2023. All of these quantities are density- and temperature-dependent. The thermal conductivities of French2019 control the conductive heat transport in the envelope if water is used.
• Figure 4: Coexistence (binodal) curve temperature curve fits of StixrudeGilmore2025 are shown in the left and center panel as a function of silicate mass fraction and H$_2$ mole fraction, respectively. In the left panel, a given local temperature (e.g., the dashed red line) can intersect the coexistence curve at two equilibrium abundances, these being $Z_{\rm low}$ and $Z_{\rm high}$. The diffusion-advection method described by Eq. \ref{['eq:misc']} uses $Z_{\rm low}$ and $Z_{\rm high}$ to drive the local metal fraction to $Z_{\rm low}$ and $Z_{\rm high}$. In the center panel, for any given coexistence curve, temperatures above the critical temperature (shown in black dashed) are always miscible (or mixed). The right panel shows the miscibility temperatures at a constant silicate fraction of 0.5 compared with the melting curve of Fei2021, shown in red. Higher pressures of each coexistence curve correspond to lower miscibility temperatures, yielding a minimum pressure of 35 GPa according to the SG25 fits. The critical temperatures above 10 GPa lie at or below the melting temperatures of MgSiO$_3$, as shown on the right panel in dashed blue.
• Figure 5: Impact of initial mantle thermal state on the evolution of 3 and 10 M$_\oplus$ sub-Neptunes. Hotter initial mantles retain heat, maintaining significantly inflated radii even at late ages. These effects are more significant for more massive sub-Neptunes. Models assume an equilibrium temperature of 400 K, an envelope mass fraction of 5%, envelope metal mass fraction of $0.5$ (water), and a 1:2 core-to-mantle ratio. The top panel shows the radius evolution of models initialized with hot mantle temperatures of 9,000 K and 16,000 K for the 3 and 10 M$_\oplus$ models, respectively, compared with models initialized at mantle temperatures of 5,000 K and 7,000 K, respectively. Solid lines in the top row show the 1-bar radius; dashed colored lines mark the envelope–mantle boundary. The gray dotted line tracks the fractional radius difference ($\Delta R/R$). The bottom row shows pressure-temperature profiles at 0 Gyr (solid) and 10 Gyr (dashed). Overplotted are miscibility curves for hydrogen-silicates (green; StixrudeGilmore2025) and hydrogen-water (orange; Gupta2025), alongside melting curves for MgSiO$3$ (black dashed; Fei2021) and Fe$_{17}$Si (black dotted; Ezenwa2024).