Sculpting the sub-Saturn Occurrence Rate via Atmospheric Mass Loss

Abstract

The sub-Saturn ($\sim$4--8$R_{\oplus }$) occurrence rate rises with orbital period out to at least $\sim$300 days. In this work we adopt and test the hypothesis that the decrease in their occurrence towards the star is a result of atmospheric mass loss, which can transform sub-Saturns into sub-Neptunes ($\lesssim$4$R_{\oplus }$) more efficiently at shorter periods. We show that under the mass loss hypothesis, the sub-Saturn occurrence rate can be leveraged to infer their underlying core mass function, and by extension that of gas giants. We determine that lognormal core mass functions peaked near $\sim$10--20$M_{\oplus }$ are compatible with the sub-Saturn period distribution, the distribution of observationally-inferred sub-Saturn cores, and gas accretion theories. Our theory predicts that close-in sub-Saturns should be $\sim$50\% less common and $\sim$30\% more massive around rapidly rotating stars; this should be directly testable for stars younger than $\lesssim$500 Myr. We also predict that the sub-Jovian desert becomes less pronounced and opens up at smaller orbital periods around M stars compared to solar-type stars ($\sim$0.7 days vs.~$\sim$3 days). We demonstrate that exceptionally low-density sub-Saturns, "Super-Puffs", can survive intense hydrodynamic escape to the present day if they are born with even larger atmospheres than they currently harbor; in this picture, Kepler 223 d began with an envelope $\sim$1.5$\times$ the mass of its core and is currently losing its envelope at a rate $\sim$2$\times 10^{-3}{M}_{\oplus }{\mathrm{Myr}}^{-1}$. If the predictions from our theory are confirmed by observations, the core mass function we predict can also serve to constrain core formation theories of gas-rich planets.

Accepted to ApJ

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• The mass-radius relation of intermediate-mass planets outlined by hydrodynamic escape and thermal evolution
• Evidence for Primordial Alignment: Insights from Stellar Obliquity Measurements for Compact Sub-Saturn Systems
• Trapping (sub-)Neptunes similar to TOI-216b at the inner disk rim: Implications for the disk viscosity and the Neptunian desert
• Helium in Exoplanet Exospheres: Orbital and Stellar Influences
• Sub-Jovian desert of exoplanets at its boundaries. Parameter dependence along the main sequence
• Small and Close-In Planets are Uncommon Around A-type Stars
• Discovery and characterization of a dense sub-Saturn TOI-6651b
• Confirmation of the hot super-Neptune TOI-672 b with NIRPS and HARPS and Insights into the Neptunian desert around M dwarfs
• A Multi-Planet System's Sole Super-Puff: Exploring Allowable Physical Parameters for the Cold Super-Puff HIP 41378 f
• Refining the Masses and Radii of the Star Kepler-33 and its Five Transiting Planets