2021ApJ...908...32L

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 dN/dM_core∝M_core^–0.7.