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 μm.
Results: We show that the transit depth is wavelength independent of 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 planets orbital plane and use this to derive a minimum ejection velocity of 1.2 km s$^-1$. To fit the average transit depth of Kepler-1520 b of 0.87%, we require a high dust mass-loss rate of 7-80 M$_øplus$ 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.