Atmospheres of low-mass planets: the "boil-off"

We show that, for a low-mass planet that orbits its host star within a few tenths of an AU (like the majority of the {\it Kepler} planets), the atmosphere it was able to accumulate while embedded in the proto-planetary disk may not survive unscathed after the disk disperses. This gas envelope, if more massive than a few percent of the core (with a mass below $10 M_\oplus$), has a cooling time that is much longer than the time-scale on which the planet exits the disk. As such, it could not have contracted significantly from its original size, of order the Bondi radius. So a newly exposed proto-planet would be losing mass via a Parker wind that is catalyzed by the stellar continuum radiation. This represents an intermediate stage of mass-loss, occurring soon after the disc has dispersed, but before the EUV/X-ray driven photoevaporation becomes relevant. The surface mass-loss induces a mass movement within the envelope that advects internal heat outward. As a result, the planet atmosphere rapidly cools down and contracts, until it has reached a radius of order $0.1$ Bondi radius, at which time the mass-loss effectively shuts down. Within a million years after the disk disperses, we find a planet that has only about ten percent of its original envelope, and a Kelvin-Helmholtz time that is much longer than its actual age. We suggest that this "boil-off" process may be partially responsible for the lack of planets above a radius of $2.5 R_\oplus$ in the {\it Kepler} data, provided planet formation results in initial envelope masses of tens of percent.