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

Aritra Chakrabarty, Gijs D. Mulders, Artyom Aguichine, Natalie Batalha

TL;DR

The paper addresses the origin of Kepler's radius valley by testing a primordial dichotomy between rocky super-Earths and water-rich sub-Neptunes, using steam atmospheres and migration-driven formation to explain close-in planets without invoking atmospheric loss as the sole sculptor. It develops a Bayesian hierarchical, two-population model (rocky and water-rich steam worlds, both H/He-free) and constrains their period, mass, WMF, and occurrence distributions from $P<100$ days Kepler data, incorporating realistic completeness corrections. The results show mass peaks at $\sim 2.6~M_\oplus$ (rocky) and $\sim 7~M_\oplus$ (water worlds) with a WMF peak near $0.41$, and that water worlds naturally reproduce the radius valley as a sharp drop ('waterfall'), though $R\gtrsim 3~R_\oplus$ planets require a non-negligible fraction ($\sim 20\%$) of H/He-rich envelopes. This supports a formation-driven origin for much of the Kepler sub-Neptune population, highlights a mixed formation history, and provides quantitative constraints for future population synthesis and observational efforts.

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 $\sim2~R_\oplus$ 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 $\sim2.6~M_\oplus$ and $\sim7~M_\oplus$, respectively, with the water mass fraction of water worlds peaking at $\sim41\%$. 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 $R \gtrsim 3~R_\oplus$, implying that at least $\sim20\%$ of sub-Neptunes in the sample are enriched in H/He gas.

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

TL;DR

The paper addresses the origin of Kepler's radius valley by testing a primordial dichotomy between rocky super-Earths and water-rich sub-Neptunes, using steam atmospheres and migration-driven formation to explain close-in planets without invoking atmospheric loss as the sole sculptor. It develops a Bayesian hierarchical, two-population model (rocky and water-rich steam worlds, both H/He-free) and constrains their period, mass, WMF, and occurrence distributions from days Kepler data, incorporating realistic completeness corrections. The results show mass peaks at (rocky) and (water worlds) with a WMF peak near , and that water worlds naturally reproduce the radius valley as a sharp drop ('waterfall'), though planets require a non-negligible fraction () of H/He-rich envelopes. This supports a formation-driven origin for much of the Kepler sub-Neptune population, highlights a mixed formation history, and provides quantitative constraints for future population synthesis and observational efforts.

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 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 ( days), combining rocky planets and water worlds without H/He envelopes. The inferred mass distributions of rocky and water-rich planets peak at and , respectively, with the water mass fraction of water worlds peaking at . 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 , implying that at least of sub-Neptunes in the sample are enriched in H/He gas.
Paper Structure (12 sections, 12 equations, 3 figures)

This paper contains 12 sections, 12 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Method
  3. Distributions of Period, Mass, and Water Mass-Fraction in the Population Model
  4. Orbital period distributions
  5. Mass Distributions
  6. WMF Distributions
  7. Properties of the host stars
  8. Calculating Size of the Planets
  9. Calculation of Likelihood for Bayesian Inference
  10. Maximizing the posterior likelihood using MCMC
  11. Comparison of Predictive Performance of the Models
  12. Results and Discussion

Figures (3)

  • Figure 1: Mass–radius models for rocky planets zeng19 and water worlds with WMF $= 0.5$, having condensed-water layers zeng19 and steam atmospheres aguichine21.
  • Figure 2: Relative deviation of the log-likelihood values for different numbers of simulated planets with respect to the median log-likelihood obtained from 100,000 simulated planets. The green point denotes our chosen number of simulated planets, i.e., 10,000, with which we get $<$0.2% deviation while maintaining a manageable computational cost.
  • Figure 3: Top: Shaded regions indicate the 1-$\sigma$ range of WMF distributions from the different models. Bottom: ELPD values and their associated uncertainties for the different models. The ELPD values show significant overlap, with Model I slightly outperforming the others.