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

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