Redefining interiors and envelopes: hydrogen-silicate miscibility and its consequences for the structure and evolution of sub-Neptunes

TL;DR

This work introduces an evolving 1‑D interior‑structure model for sub‑Neptunes that explicitly accounts for hydrogen–silicate miscibility using the H2–MgSiO3 phase diagram. By defining the interior–envelope boundary with a binodal surface, the model self‑consistently tracks hydrogen distribution, silicate vapour, and mean molecular weight gradients, yielding a slower contraction and notable hydrogen storage in the interior at young ages. Across parameter studies, miscible planets exhibit radii smaller by tens of percent early on and converging toward standard models after ~Gyr, while retaining distinct internal chemical distributions. The framework highlights the need to move beyond solubility at a magma ocean surface and toward phase‑equilibria‑driven interiors to interpret sub‑Neptune structure, with implications for observations of young planetary populations and the interpretation of mass–radius relations.

Abstract

We present the first evolving interior structure model for sub-Neptunes that accounts for the miscibility between silicate magma and hydrogen. Silicate and hydrogen are miscible above $\sim 4000$K at pressures relevant to sub-Neptune interiors. Using the H$_2$-MgSiO$_3$ phase diagram, we self-consistently couple physics and chemistry to determine the radial extent of the fully miscible interior. Above this region lies the envelope, where hydrogen and silicates are immiscible and exist in both gaseous and melt phases. The binodal surface, representing a phase transition, provides a physically/chemically informed boundary between a planet's "interior" and "envelope". We find that young sub-Neptunes can store several tens of per cent of their hydrogen mass within their interiors. As the planet cools, its radius and the binodal surface contract, and the temperature at the binodal drops from $\sim 4000$K to $\sim 3000$K. Since the planet's interior stores hydrogen, its density is lower than that of pure-silicate. Gravitational contraction and thermal evolution lead to hydrogen exsolving from the interior into the envelope. This process slows planetary contraction compared to models without miscibility, potentially producing observable signatures in young sub-Neptune populations. At early times ($\sim 10$-$100$Myr), the high temperature at the binodal surface results in more silicate vapour in the envelope, increasing its mean molecular weight and enabling convection inhibition. After $\sim$Gyr of evolution, most hydrogen has exsolved, and the radii of miscible and immiscible models converge. However, the internal distribution of hydrogen and silicates remains distinct, with some hydrogen retained in the interior.

Figures (11)

• Figure 1: Upper panel: The change in Gibbs free energy of mixing, $\Delta \hat{G}_\text{mix}$, at $3975$ K and $1$ GPa for a binary, non-ideal mixture of hydrogen and MgSiO$_3$ (Equation \ref{['eq:DeltaG_mix']}) as a function of H$_2$ mole fraction. Conditions for co-existence of hydrogen in the gas and melt phases exist where the gradient of $\Delta \hat{G}_\text{mix}$ (equivalent to the chemical potential, as shown in the second panel) are equal and positive, as highlighted by the blue dashed line. The hydrogen mole fractions in the melt, $x_{\text{H}_2}^\text{melt}$, and gas phases, $x_{\text{H}_2}^\text{gas}$, are highlighted by blue dot-dashed lines. Lower panel: the binodal, also known as a co-existence curve, demarcates the boundary between miscible and immiscible regions of parameter space. This is shown at $1$ GPa. For temperatures above the binodal, hydrogen and MgSiO$_3$ melt form a homogenous miscible fluid. For temperatures below the binodal, hydrogen and MgSiO$_3$ exist in two phases: gas, including H$_2$, SiO, Mg and O$_2$, and silicate melt (rain) with hydrogen dissolved inside.
• Figure 2: A schematic for the interior structure of sub-Neptunes. Moving radially outwards from the planetary centre: the "interior" is defined as the region interior to the binodal surface. At the binodal, a phase change occurs as the convective, miscible, hydrogen-silicate fluid speciates into gas and melt phases. The region above the binodal is defined as the "envelope". The silicate vapour introduces a mean molecular weight gradient, which can inhibit convection. In this case, heat is transported via conduction and radiative diffusion. Silicate-rich melt droplets rain-out to rejoin the interior. Continuing to move radially outward, the envelope becomes unstable to convection and the gas become progressively more hydrogen-rich. The very upper region of the envelope is almost pure hydrogen gas, and heat is transported by radiative diffusion. Radiative-convective boundaries (RCBs) are shown as white dashed lines.
• Figure 3: Schematic showing the evolution of two interpretations of sub-Neptune interiors. In the standard model, a silicate interior is distinct from a hydrogen-rich envelope. As the planet contracts, the interior-envelope boundary does not significantly contract with time. The temperature at this interface can reach of order $\sim 10,000$ K at early ages. In the miscible model, the interior-envelope boundary is defined by a binodal surface, which delineates regions in which hydrogen and silicate are miscible or immiscible. The temperature at the binodal surface does not change significantly with time. The radial position of the binodal surface contracts with time.
• Figure 4: The interior structure profile for a $6 M_\oplus$ sub-Neptune with equilibrium temperature of $1000$ K and global hydrogen mass fraction of $5$% is shown as a black line in pressure-temperature-hydrogen mole fraction space. The blue surface represents the binodal, demarcating regions of parameter space where hydrogen and silicate melt are miscible or immiscible. In the interior of the planet, the temperatures and pressures are higher than the binodal, hence, hydrogen and silicate melt are miscible and form a homogenous supercritical mixture. In the envelope, temperatures and pressures are below the binodal, meaning the chemical components speciate into melt and gas phases, with the respective hydrogen mole fractions represented by individual black lines. As pressure and temperature drop, silicate-rich melt rains out, decreasing the hydrogen mole fraction in the melt phase, and increasing the hydrogen mole fraction in the gas phase. Projections of the profile in the pressure-temperature plane and hydrogen mole fraction-temperature plane are shown on the left (yellow projection) and right-hand-side (pink projection), respectively.
• Figure 5: The evolution of a $6 M_\oplus$ sub-Neptune with equilibrium temperature of $1000$ K and global hydrogen mass fraction of $3$% for two model classes. A standard model, shown in black, represents a simple case in which silicate melt and hydrogen cannot become miscible. The interior is a pure-silicate sphere of fixed mass. Similarly, the envelope is pure hydrogen and fixed in mass fraction at $3\%$. A miscible model, shown in blue, allows for miscibility between silicate and hydrogen. The interior-envelope boundary is now defined by a binodal. Upper panels show the evolution of each planet's photospheric radius, envelope mass fraction, fraction of total hydrogen mass stored in the planet's interior, and mass-averaged envelope mean molecular weight. Lower panels show the binodal surface in radius, temperature and pressure-space, as well as the interior density. Note that the binodal surface does not exist for the standard model, as it assumes an inert core, hence we show the interior-envelope boundary.