The Radius Cliff is a Waterfall: Explaining Sub-Neptune Exoplanets with Steam Worlds

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 ∼2​​​​​​ R ⊕ 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 ∼2.6 and ∼7 M ⊕ , respectively, with the water mass fraction of water worlds peaking at ∼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 ≳ 3 R ⊕ , implying that at least ∼20% of sub-Neptunes in the sample are enriched in H/He gas.