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Catastrophically evaporating rocky planets provide a unique opportunity tostudy the composition of small planets. The surface composition of theseplanets can be constrained via modelling their comet-like tails of dust. Inthis work, we present a new self-consistent model of the dusty tails: wephysically model the trajectory of the dust grains after they have left thegaseous outflow, including an on-the-fly calculation of the dust cloud'soptical depth. We model two catastrophically evaporating planets: KIC 1255b andK2-22b. For both planets, we find the dust is likely composed of magnesium-ironsilicates (olivine and pyroxene), consistent with an Earth-like composition. Weconstrain the initial dust grain sizes to be $\sim$ 1.25-1.75 $\mu$m and theaverage (dusty) planetary mass-loss rate to be $\sim$ 3$M_\oplus\mathrm{Gyr^{-1}}$. Our model shows the origin of the leading tail of dust ofK2-22b is likely a combination of the geometry of the outflow and a lowradiation pressure force to stellar gravitational force ratio. We find theoptical depth of the dust cloud to be a factor of a few in the vicinity of theplanet. Our composition constraint supports the recently suggested idea thatthe dusty outflows of these planets go through a greenhouse effect-nuclearwinter cycle, which gives origin to the observed transit depth timevariability. Magnesium-iron silicates have the necessary visible-to-infraredopacity ratio to give origin to this cycle in the high mass-loss state.

On the likely magnesium-iron silicate dusty tails of catastrophically evaporating rocky planets