Mapping the transition from liquid to supercritical water on sub-Neptunes

“Water worlds” - planets with rocky cores overlain by water-rich envelopes - may make up a significant proportion of the sub-Neptune population and their atmospheric characterisation with JWST can offer insights into planetary formation and migration (e.g., Benneke et al. 2024). Whereas colder water worlds may be able to form liquid water oceans and have hydrogen-rich upper atmospheres, warmer planets would contain water in a supercritical state. In this case, hydrogen in the envelope mixes with the supercritical water and the observable upper atmosphere would have a high mean molecular weight with a smaller scale height. In intermediate regimes, a supercritical water layer will lie below a condensing cloud deck and hydrogen-dominated upper atmosphere. In this work, we aim to define the boundary between these three regimes using a 1D radiative-convective model. Our model uses the SOCRATES radiative transfer code coupled to a radiative-convective driver to solve for equilibrium temperature-pressure profiles in a water world atmosphere. We account for the effects of convective inhibition in the condensing layers and the non-idealness of supercritical water at high temperatures and pressures, both of which can dramatically affect the structure of the atmosphere. The resulting framework allows us to demarcate the transition between ocean worlds and sub-Neptunes with a mixed envelope as a function of instellation, interior flux and envelope composition. In the case where water is supercritical, the level at which condensation occurs (and the cold-trapping of water vapour) determines whether the observable atmosphere is hydrogen or water-dominated. We discuss whether the change in composition of the upper atmosphere accompanied by this transition would be observable.