A Unified Treatment of Kepler Occurrence to Trace Planet Evolution II: The Radius Cliff Formed by Atmospheric Escape

The Kepler mission enabled us to look at the intrinsic population of exoplanets within our galaxy. In period-radius space, the distribution of the intrinsic population of planets contains structure that can trace planet formation and evolution history. The most distinctive feature in period-radius space is the radius cliff, a steep drop-off in occurrence between $2.5-4$R$_\oplus$ across all period ranges, separating the sub-Neptune population from the rarer Neptunes orbiting within 1 au. Following our earlier work to measure the occurrence rate of the Kepler population, we characterize the shape of the radius cliff as a function of orbital period ($10-300$ days) as well as insolation flux (9500S$_\oplus$ -- 10S$_\oplus$). The shape of the cliff flattens at longer orbital periods, tracking the rising population of Neptune-sized planets. In insolation, however, the radius cliff is both less dramatic and the slope is more uniform. The difference in this feature between period- and insolation-space can be linked to the effect of EUV/X-ray versus bolometric flux in the planet's evolution. Models of atmospheric mass loss processes that predict the location and shape of the radius valley also predict the radius cliff. We compare our measured occurrence rate distribution to population synthesis models of photoevaporation and core-powered mass-loss in order to constrain formation and evolution pathways. We find that the models do not statistically agree with our occurrence distributions of the radius cliff in period- or insolation-space. Atmospheric mass loss that shapes the radius valley cannot fully explain the shape of the radius cliff.