Context : Kepler observations have revealed a class of short period exoplanets , of which Kepler-1520 b is the prototype , which have comet-like dust tails thought to be the result of small , rocky planets losing mass .
The shape and chromaticity of the transits constrain the properties of the dust particles originating from the planet ’ s surface , offering a unique opportunity to probe the composition and geophysics of rocky exoplanets .

Aims : We aim to approximate the average Kepler long-cadence light curve of Kepler-1520 b and investigate how the optical thickness and transit cross-section of a general dust tail can affect the observed wavelength dependence and depth of transit light curves .

Methods : We developed a new 3D model that ejects sublimating particles from the planet surface to build up a dust tail , assuming it to be optically thin , and used 3D radiative transfer computations that fully treat scattering using the distribution of hollow spheres ( DHS ) method , to generate transit light curves between 0.45 and 2.5 \mu m .

Results : We show that the transit depth is wavelength independent for optically thick tails , potentially explaining why only some observations indicate a wavelength dependence .
From the 3D nature of our simulated tails , we show that their transit cross-sections are related to the component of particle ejection velocity perpendicular to the planet’s orbital plane and use this to derive a minimum ejection velocity of 1.2 kms ^ { -1 } .
To fit the average transit depth of Kepler-1520 b of 0.87 % , we require a high dust mas-loss rate of 7 - 80 M _ { \oplus } Gyr ^ { -1 } which implies planet lifetimes that may be inconsistent with the observed sample .
Therefore , these mass-loss rates should be considered to be upper limits .

Conclusions :