Catastrophic evaporation of rocky planets

Short-period exoplanets can have dayside surface temperatures surpassing 2000 K, hot enough to vaporize rock and drive a thermal wind. Small enough planets evaporate completely. We construct a radiative hydrodynamic model of atmospheric escape from strongly irradiated, low-mass rocky planets, accounting for dust-gas energy exchange in the wind. Rocky planets with masses ≲ 0.1 M_⊕ (less than twice the mass of Mercury) and surface temperatures ≳2000 K are found to disintegrate entirely in ≲10 Gyr. When our model is applied to Kepler planet candidate KIC 12557548b - which is believed to be a rocky body evaporating at a rate of dot{M} ≳ 0.1 M_{{{oplus }}} Gyr^-1 - our model yields a present-day planet mass of ≲ 0.02 M_⊕ or less than about twice the mass of the Moon. Mass-loss rates depend so strongly on planet mass that bodies can reside on close-in orbits for Gyr with initial masses comparable to or less than that of Mercury, before entering a final short-lived phase of catastrophic mass-loss (which KIC 12557548b has entered). Because this catastrophic stage lasts only up to a few per cent of the planet's life, we estimate that for every object like KIC 12557548b, there should be 10-100 close-in quiescent progenitors with sub-day periods whose hard-surface transits may be detectable by Kepler - if the progenitors are as large as their maximal, Mercury-like sizes (alternatively, the progenitors could be smaller and more numerous). According to our calculations, KIC 12557548b may have lost ∼70 per cent of its formation mass; today we may be observing its naked iron core.