Water-rich sub-Neptunes and rocky super-Earths around different stars: Radii shaped by volatile partitioning, formation, and evolution

Despite precise characterization measurements, the nature of planets with radii between 2 and 4 Earth radii -- sub-Neptunes -- remains unknown due to degeneracies in interior models. Nevertheless, the field has compiled an impressive ensemble of small planets with measured masses and radii orbiting different stars. This dataset can be used to test the prediction of large water reservoirs on sub-Neptunes, as proposed by planet formation theory with orbital migration. We aim to determine whether this water reservoir is included in photoevaporative winds and how much of it can partition into the rocky and metallic interior. We coupled the results of a planetary formation model with planetesimal and gas accretion as well as orbital migration with evolution models that assume either perfect mixing of water with H/He in the envelope or complete segregation. For the mixed envelopes, we also included an analytic treatment of fractionation during photoevaporative mass loss. Furthermore, we studied the effect of equilibrium dissolution of water into an assumed magma ocean and metallic core for the first time in coupled formation-evolution models. Out of the tested scenarios, the mass-radius relation of exoplanets is relatively well matched by all scenarios where the atmosphere is of mixed composition. The agreement depends on mass, with better consistency for the model without dissolution below 3 Earth masses and hints of the opposite at higher masses. Fractionation is not found to significantly alter the properties of the planets for our initial conditions due to initially massive envelopes on all planets. For all scenarios, we quantified the radius valley location and its scaling with stellar mass. The mass--radius relations for water-rich sub-Neptunes are broadly consistent with observations. However, statistical surveys in both mass and radius are required to distinguish between the scenarios. The mixed-composition loss of different volatiles, their dissolution into the planetary interior, and the solidification of the magma ocean are natural next steps toward a comprehensive atmosphere-interior evolution model.