Primordial Radius Gap and Potentially Broad Core Mass Distributions of Super-Earths and Sub-Neptunes

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Abstract The observed radii distribution of Kepler exoplanets reveals two distinct populations: those that are more likely to be terrestrials (≲1.7R ⊕) and those that are more likely to be gas-enveloped (≳2R ⊕). There exists a clear gap in the distribution of radii that separates these two kinds of planets. Mass-loss processes like photoevaporation by high-energy photons from the host star have been proposed as natural mechanisms to carve out this radius valley. These models favor underlying core mass function of sub-Neptunes that is sharply peaked at ∼4–8M ⊕, but the radial-velocity follow-up of these small planets hints at a more bottom-heavy mass function. By taking into account the initial gas accretion in gas-poor (but not gas-empty) nebula, we demonstrate that (1) the observed radius valley is a robust feature that is initially carved out at formation during late-time gas accretion; and (2) that it can be reconciled with core mass functions that are broad extending well into the sub-Earth regime. The maximally cooled isothermal limit prohibits cores lighter than ∼1–2M ⊕ from accreting enough mass to appear gas-enveloped. The rocky-to-enveloped transition established at formation produces a gap in the radius distribution that shifts to smaller radii farther from the star, similar to that observed. For the best agreement with the data, our late-time gas accretion model favors dust-free accretion in hotter disks with cores slightly less dense than the Earth (∼0.8ρ ⊕) drawn from a mass function that is as broad as .