On the likely magnesium-iron silicate dusty tails of catastrophically e vaporating rock y planets

Catastrophically e v aporating rocky planets provide a unique opportunity to study the composition of small planets. The surface composition of these planets can be constrained via modelling their comet-like tails of dust. In this work, we present a new self-consistent model of the dusty tails: we physically model the trajectory of the dust grains after the y hav e left the gaseous outflow, including an on-The-fly calculation of the dust cloud s optical depth. We model two catastrophically e v aporating planets: KIC 1255 b and K2-22 b. For both planets, we find the dust is likely composed of magnesium-iron silicates (olivine and pyroxene), consistent with an Earth-like composition. We constrain the initial dust grain sizes to be ∼1.25-1.75 μm and the average (dusty) planetary mass-loss rate to be ∼3 M Gyr -1 . Our model shows that the origin of the leading tail of dust of K2-22 b is likely a combination of the geometry of the outflow and a low radiation pressure force to stellar gravitational force ratio. We find the optical depth of the dust cloud to be a factor of a few in the vicinity of the planet. Our composition constraint supports the recently suggested idea that the dusty outflows of these planets go through a greenhouse effect-nuclear winter cycle, which gives origin to the observed transit depth time variability. Magnesium-iron silicates have the necessary visible-To-infrared opacity ratio to give origin to this cycle in the high mass-loss state.