In the depths of sub-Neptunes, the most common type of planet in the Galaxy, though not one you could stand on, silicate magma and hydrogen mix into a single supercritical cocktail. Previously, it was thought that beneath the dense hydrogen atmosphere lay a sharp boundary with molten silicate, like oil on water. Now, calculations show that at the pressures and temperatures of these interiors, the two layers fully dissolve into each other. Instead of a layered cake, you get a homogeneous drink, where hydrogen is not a passive diluent but an active ingredient that changes the very recipe of the silicate cocktail.

To describe the properties of this cocktail, the researchers simulated a cell of 243 atoms: 27 magnesium, 27 silicon, 81 oxygen, and 108 hydrogen. This corresponds to the composition MgSiO3H4, with hydrogen making up 3.86% of the mass. First, they melted crystalline silicate, then added hydrogen. The calculations were performed at temperatures of 4000, 6000, and 8000 K and pressures up to ~600 GPa, which is roughly six million times atmospheric pressure. The resulting data were fitted to a single thermodynamic surface, from which they extracted density, entropy, heat capacity, thermal expansion, bulk modulus, and the Grüneisen parameter.

The result was surprising: the supercritical fluid MgSiO3H4 turned out to be less dense than the dry silicate melt under all conditions studied. The deviation from ideal mixing of the volumes of MgSiO3 and H2 reaches several percent and grows with pressure. Structural analysis showed that as pressure increases, the Si–H coordination number increases, while the number of stable H–H bonds drops sharply. At 4000 K and a pressure of about 340 GPa, only one in ten hydrogen atoms retains a bond with another hydrogen for longer than 100 femtoseconds; the rest are already integrated into the silicate network. This is a transition from molecular hydrogen to a more atomic form embedded in the silicate framework.

Applying the equation of state to models of sub-Neptunes with a mass of 6 Earth masses and a total hydrogen inventory of 4% showed that everything depends on the pressure at the atmosphere–interior boundary. If this boundary is at a depth with a pressure of 1 GPa, the planet's radius is one value. If it is 5 GPa, the radius changes by 5.7%. This is not trivial: for a planet with a radius of 20,000 km, the difference amounts to more than 1000 km. The distribution of hydrogen between the atmosphere and the interior directly affects the planet's radius and its thermal state.

Before this work, it was unclear how strongly dissolved hydrogen changes the density and thermal properties of silicate magma in sub-Neptune interiors. Now there is a quantitative equation of state showing that the density drops by several percent compared to dry silicate, and the mixing is highly non-ideal. Already today, this equation of state can be incorporated into models of sub-Neptune internal structure for more accurate interpretation of observed masses and radii. Hydrogen turned out to be not a passive diluent but an active ingredient that changes the very recipe of the silicate cocktail.