The Role of Core Mass in Controlling Evaporation: the Kepler Radius Distribution and the Kepler-36 Density Dichotomy

We use models of coupled thermal evolution and photo-evaporative mass loss to understand the formation and evolution of the Kepler-36 system. We show that the large contrast in mean planetary density observed by Carter et al. (2012) can be explained as a natural consequence of photo-evaporation from planets that formed with similar initial compositions. However, rather than being due to differences in XUV irradiation between the planets, we find that this contrast is due to the difference in the masses of the planets' rock/iron cores and the impact that this has on mass loss evolution. We explore in detail how our coupled models depend on irradiation, mass, age, composition, and the efficiency of mass loss. Based on fits to large numbers of coupled evolution and mass loss runs, we provide analytic fits to understand threshold XUV fluxes for significant atmospheric loss, as a function of core mass and mass loss efficiency. Finally we discuss these results in the context of recent studies of the radius distribution of Kepler candidates. Using our parameter study, we make testable predictions for the frequency of sub-Neptune sized planets. We show that 1.8-4.0 R_earth planets should become significantly less common on orbits within 10 days and discuss the possibility of a narrow "occurrence valley" in the radius-flux distribution. Moreover, we describe how photo-evaporation provides a natural explanation for the recent observations of Ciardi et al. (2013) that inner planets are preferentially smaller within the systems.