Creating the Radius Gap without Mass Loss

The observed exoplanet population features a gap in the radius distribution that separates the smaller super-Earths ($\lesssim$1.7$R_\oplus$) from the larger sub-Neptunes ($\sim$1.7--4$R_\oplus$). While mass loss theories can explain many of the observed features of this radius valley, it is difficult to reconcile them with a potentially rising population of terrestrials beyond orbital periods of ~30 days. We investigate the ability of initial gas accretion to reproduce both the location of the observed radius gap and the existence of long-period terrestrials. We first update the analytic scalings of gas accretion rate accounting for the shrinking of the bound radius by hydrodynamic effects. From the cooling evolution of planetary envelope with realistic opacity and equation of state, we find that the envelope mass fraction depends only weakly with the radius shrinking factor ($M_{\rm gas}/M_{\rm core} \propto f_R^{0.31}$). Co-evolving planetary masses and disk structures, focussing on dust-free opacity, we find that gas accretion alone is able to carve out the observed radius gap, with slopes $R_{\rm gap} \propto P^{-0.11}$ and $R_{\rm gap} \propto M_\star^{0.24}$ for top-heavy; and $R_{\rm gap} \propto P^{-0.10}$ and $R_{\rm gap} \propto M_\star^{0.21}$ for bottom-heavy core mass distributions, in good agreement with observations. Our model reconciles the location of the radius gap with the existence of long period terrestrials. The peaks and valleys in the radius distribution were likely set in place primordially while post-formation processes further tune the exoplanetary population. We provide potential observational tests that may be possible with PLATO and Roman Space Telescope.