Planetary population synthesis coupled with atmospheric escape: a statistical view of evaporation

We apply hydrodynamic evaporation models to different synthetic planet populations that were obtained from a planet formation code based on a core-accretion paradigm. We investigated the evolution of the planet populations using several evaporation models, which are distinguished by the driving force of the escape flow (X-ray or EUV), the heating efficiency in energy-limited evaporation regimes, or both. Although the mass distribution of the planet populations is barely affected by evaporation, the radius distribution clearly shows a break at approximately 2 $R_{\oplus}$. We find that evaporation can lead to a bimodal distribution of planetary sizes (Owen & Wu 2013) and to an "evaporation valley" running diagonally downwards in the orbital distance - planetary radius plane, separating bare cores from low-mass planet that have kept some primordial H/He. Furthermore, this bimodal distribution is related to the initial characteristics of the planetary populations because low-mass planetary cores can only accrete small primordial H/He envelopes and their envelope masses are proportional to their core masses. We also find that the population-wide effect of evaporation is not sensitive to the heating efficiency of energy-limited description. However, in two extreme cases, namely without evaporation or with a 100\% heating efficiency in an evaporation model, the final size distributions show significant differences; these two scenarios can be ruled out from the size distribution of $Kepler$ candidates.