2022ApJ...924....9H

The sub-Saturn (∼4-8 R_⊕) occurrence rate rises with orbital period out to at least ∼300 days. In this work we adopt and test the hypothesis that the decrease in their occurrence toward the star is a result of atmospheric mass loss, which can transform sub-Saturns into sub-Neptunes (<=4 R_⊕) 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 ∼10-20 M_⊕ 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 ∼50% less common and ∼30% more massive around rapidly rotating stars; this should be directly testable for stars younger than <=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 (∼0.7 days versus ∼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 ∼1.5x the mass of its core and is currently losing its envelope at a rate of ∼2 x 10^–3 M_⊕ 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.