Testing the prevalence of hydrogen-silicate miscibility in young sub-Neptunes

Hydrogen-silicate miscibility can significantly alter the interior structure and thermal evolution of sub-Neptunes. We consider the interplay between this miscibility and stellar-driven atmospheric escape. We find that, for the first about 100 Myrs, sub-Neptunes store most of their hydrogen content within their miscible interiors, protecting it from escape. As hydrogen is removed from the top of the atmosphere, more hydrogen is exsolved from the miscible interior, resupplying the envelope mass and delaying the planet's contraction when compared with models that do not account for miscibility. Regardless of miscibility, atmospheric escape reproduces the young planet observations from TESS, and we highlight the emergence of the primordial Neptune desert at short orbital periods. We construct a population-level test for the prevalence of miscible sub-Neptunes which exploits their slower radial contraction. We find that about 70-100 observed young sub-Neptunes with ages 100 Myrs are required to answer this question.