How a Sub-Neptune Stores Hydrogen in Its Depths ✛
Context
Sub-Neptunes, planets with radii of 1.8–4 Earth radii and masses of 2–20 Earth masses, occupy an intermediate position between rocky super-Earths and gas giants. Their internal structure is usually described as a silicate core covered by a hydrogen–helium envelope, with some dissolution of gases into magma allowed at the boundary. However, first-principles calculations have shown that at temperatures above roughly 4000 K, silicate melt and hydrogen mix completely, forming a single supercritical fluid. This work incorporates miscibility into an evolutionary model of the planet, moving away from the idea of a fixed magma-ocean surface. Nearby in the archive are studies on how hydrogen interacts with magma and how giant planets store light elements, but this is the first time the dynamics of the binodal over time have been traced.
Methods
The authors built a one-dimensional, spherically symmetric model of a sub-Neptune in hydrostatic and thermochemical equilibrium. They used the phase diagram of the binary system H2–MgSiO3 obtained from DFT molecular dynamics and analytically approximated the binodal, the surface separating the region of complete miscibility from the region where gas and melt coexist. The planet is divided into an interior, where temperatures and pressures are above the binodal, and an envelope, where they are below. In the interior, full convection and a constant mass fraction of hydrogen are assumed; in the envelope, silicate vapor, melt droplet precipitation (rain), and possible suppression of convection by the mean molecular weight gradient are considered. The structure equations are solved by the shooting method with an adaptive Runge–Kutta integrator, and evolution is tracked through energy conservation with a time step, as the planet cools from 5 million to 10 billion years.
Results
A young sub-Neptune with a mass of 6 Earth masses and 3% hydrogen by mass stores about 75% of its total hydrogen in the interior; over billions of years, this fraction drops to 10%. The temperature at the binodal changes only slightly, from about 4000 K at the beginning to 3000 K at the end, and its radius shrinks as the planet cools. The density of the interior is lower than that of pure silicate, so the silicate material sits higher in the gravitational potential. Energy is lost mainly through gravitational contraction of the silicate part, not through cooling of the hydrogen envelope, as in the standard model. As a result, a mixed planet contracts more slowly, and at ages of 10–100 million years, its radius is tens of percent smaller than that of an unmixed model with the same parameters. After 5 billion years, the radii nearly coincide, but the internal distribution of hydrogen remains different.
Implications
This work introduces the binodal as a physically justified boundary between the interior and envelope of a sub-Neptune, instead of an arbitrary magma-ocean surface. This changes the interpretation of observed radii: the mass of hydrogen in the planet may be correct, but the envelope mass may be overestimated by several times, because some hydrogen is hidden in the interior. Unlike neighboring works that considered gas dissolution via Henry's law or static models, here the evolution of the binodal and its influence on thermal contraction are traced for the first time. This approach shows that extrapolating Henry's law to high temperatures misses the phase transition and leads to errors in estimating the interior composition.
Future development
The next step is to include iron, helium, and water in the model, for which new DFT calculations of phase equilibria are needed. It is also important to connect miscibility with gas accretion and atmospheric loss processes: if hydrogen escapes into the interior, the 'boiling' of the envelope after disk dispersal may proceed differently. Observational tests may emerge when comparing the radii of young sub-Neptunes in clusters with predictions from models with and without miscibility.
Impact
The results will affect the interpretation of mass–radius relations of exoplanets and models of planet formation with hydrogen envelopes.
Next steps
Build models with iron and helium, and run simulations of accretion and atmospheric loss that account for miscibility.
Key open problems
In planetary science, an open question remains how exactly sub-Neptunes lose their envelopes and why the 'radius valley' emerges. The miscibility of hydrogen with silicates changes the initial mass distribution and cooling rate, which directly affects predictions for this valley. Without accounting for the phase transition, models may systematically overestimate the envelope mass and incorrectly assess which planets become super-Earths.
The knowledge machine's view
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
The authors built an evolutionary model of a sub-Neptune that accounts for full miscibility of hydrogen and silicate melt at high temperatures, using the H2–MgSiO3 phase diagram and the binodal as the boundary between the interior and the envelope. They tracked the planet's cooling from 5 million to 10 billion years and showed that young sub-Neptunes store most of their hydrogen in the interior, and the radius shrinks more slowly than in immiscible models.
Where its strength is
The strength of this work is that it replaces the arbitrary magma ocean surface with a physically motivated binodal derived from first-principles calculations, and for the first time tracks its dynamics during evolution. This provides a new tool for interpreting observed radii of sub-Neptunes.
Where it could go next
- It might be interesting to see how this approach to storing hydrogen in the interior affects models of giant planets, where dissolution of light elements in deep envelopes is also discussed.based on: How Giant Planets Hide Hydrogen Inside arXiv:2606.30644
- Closely related is work on the interaction of hydrogen with magma and the formation of water; perhaps one should consider chemical reactions in the interior that could affect phase equilibrium.based on: How Hydrogen and Magma Create Water Deep Inside Planets arXiv:2511.06507
- It would be interesting to compare with models of planets with long-lived magma oceans: how the binodal behaves under prolonged high temperatures, for example due to tidal heating.based on: Worlds with Eternal Magma Oceans arXiv:2512.05816
Worth trying
- Test how the radius evolution changes when accounting for possible water formation in the interior and its effect on the phase diagram.
- Apply the model to planets with tidal heating to see whether the binodal can remain at great depth for a long time.
- Compare the model's predictions with the observed distribution of sub-Neptune radii as a function of age.
Why this may matter
If hydrogen-silicate miscibility is widespread, it could change estimates of the mass of hydrogen envelopes on sub-Neptunes and, consequently, our understanding of their formation and evolution.
Nearby works in our archive
- How Giant Planets Hide Hydrogen Insidesimilarity 0.63
- How Hydrogen and Magma Create Water Deep Inside Planetssimilarity 0.62
- Worlds with Eternal Magma Oceanssimilarity 0.60
- A Volcanic Planet Breathes Hydrogensimilarity 0.58
- A Waterfall of Planets: The Mystery of the Vanishing Water Worldssimilarity 0.57
The closest work in the archive sits at 0.63 by meaning — the usual level for our corpus.
Inside a young sub-Neptune, the temperature at the boundary between the interior and envelope reaches 4000 K, which is hotter than the surface of many M-type stars.
In Stanisław Lem's novel 'Solaris', the planet's ocean behaves as a single living system; here, the interior of a sub-Neptune also turns out not to be an inert core but an active, mixing medium that exchanges material with the envelope.
Key numbers
- temperature at the binodal: from ~4000 K to ~3000 K over evolution
- fraction of hydrogen in the interior of a young planet: ~75% of total hydrogen
- fraction of hydrogen in the interior of an old planet: ~10% of total hydrogen
- difference in radii of young models: tens of percent
- evolution time: from 5 million to 10 billion years