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

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.