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

The observed radii distribution of Kepler exoplanets reveal two distinct populations: those that are more likely to be bare rocks ($\lesssim1.7R_\oplus$) and those that are more likely to be gas-enveloped ($\gtrsim2R_\oplus$). 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 $\sim$6--8$M_\oplus$ but the radial-velocity follow-up of these small planets hint 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 the observed radius valley can be reconciled with core mass functions that are broad extending well into sub-Earth regime. The maximally cooled isothermal limit prohibits cores lighter than $\sim$1--2$M_\oplus$ 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 followed by photoevaporative mass loss favors dust-free accretion in hotter disks with a core mass function that is as broad as $dN/dM_{\rm core} \propto M_{\rm core}^{-0.7}$.