The initial physical conditions of Kepler-36 b & c

The Kepler planetary system consists of two exoplanets at similar separations (0.115 & 0.128 AU), which have dramatically different densities. The inner planet has a density consistent with an Earth-like composition, while the outer planet is extremely low-density, such that it must contain a voluminous H/He envelope. Such a density difference would pose a problem for any formation mechanism if their current densities were representative of their composition at formation. However, both planets are at close enough separations to have undergone significant evaporation in the past. We constrain the core-mass, core composition, initial envelope-mass, and initial cooling-time of each planet using evaporation models conditioned on their present-day masses and radii, as inferred from Kepler photometry and transit timing analysis. The inner planet is consistent with being an evaporatively stripped core, while the outer planet has retained some of its initial envelope due to its higher core-mass. Therefore, both planets could have had a similar formation pathway, with the inner planet having an initial envelope-mass fraction of $\lesssim 10\%$ and core-mass of $\sim4.4$ M$_\oplus$, while the outer had an initial envelope-mass fraction of order 15-30\% and core-mass $\sim7.3$ M$_\oplus$. Finally, our results indicate that the outer planet had a long ($\gtrsim30$ Myr) initial cooling-time, much longer than would naively be predicted from simple timescale arguments. The long initial cooling-time could be evidence for a dramatic early cooling episode such as the recently proposed "boil-off" process.
Comment: Accepted version in ApJL, 6 pages, 3 figures