Current Population Statistics Do Not Favor Photoevaporation over Core-powered Mass Loss as the Dominant Cause of the Exoplanet Radius Gap

We search for evidence of the cause of the exoplanet radius gap, i.e. the dearth of planets with radii near $1.8\ R_\oplus$. If the cause was photoevaporation, the radius gap should trend with proxies for the early-life high-energy emission of planet-hosting stars. If, alternatively, the cause was core-powered mass loss, no such trends should exist. Critically, spurious trends between the radius gap and stellar properties arise from an underlying correlation with instellation. After accounting for this underlying correlation, we find no trends remain between the radius gap and stellar mass or present-day stellar activity as measured by near-UV emission. We dismiss the nondetection of a radius gap trend with near-UV emission because present-day near-UV emission is unlikely to trace early-life high-energy emission, but we provide a catalog of GALEX near-UV and far-UV emission measurements for general use. We interpret the nondetection of a radius gap trend with stellar mass by simulating photoevaporation with mass-dependent evolution of stellar high-energy emission. The simulation produces an undetectable trend between the radius gap and stellar mass under realistic sources of error. We conclude that no evidence, from this analysis or others in the literature, currently exists that clearly favors either photoevaporation or core powered mass loss as the primary cause of the exoplanet radius gap. However, repeating this analysis once the body of well-characterized $< 4\ R_\oplus$ planets has roughly doubled could confirm or rule out photoevaporation.