Abstract

The demographics of Kepler planets provide a key testbed for models of planet formation and evolution, particularly for explaining the radius valley separating super-Earths and sub-Neptunes. A primordial interpretation based on differences in bulk densities-where rocky and water-rich planets form via migration pathways-offers an alternative to atmospheric loss scenarios. Updated interior structure models of water worlds with adiabatic steam atmospheres reproduce the observed valley near similar to 2 R-circle plus more accurately. Furthermore, migration models from our Genesis library suggest that these formation pathways can also account for the distinct period distributions of super-Earths and sub-Neptunes, as well as the emergence of the hot Neptune desert. Motivated by this, we develop a Bayesian hierarchical mixture model for close-in Kepler planets (P < 100 days), combining rocky planets and water worlds without H/He envelopes. The inferred mass distributions of rocky and water-rich planets peak at similar to 2.6 and similar to 7 M-circle plus, respectively, with the water mass fraction of water worlds peaking at similar to 41%. Water worlds provide a good representation of the Kepler sub-Neptune population, with the radius cliff emerging as a "waterfall"-a sharp decline in their occurrence. However, our mass-radius analysis shows that water worlds alone cannot explain planets with R greater than or similar to 3 R-circle plus, implying that at least similar to 20% of sub-Neptunes in the sample are enriched in H/He gas.