Diagram to illustrate for what part of the tail the assumption of an optically thin dust cloud is valid. The solid line shows h_{τ = 1}, the dust cloud half-height for which the radial optical depth equals unity. The dashed lines give the heights above the planet’s orbital plane reached by dust grains that are launched vertically from the planet with different initial vertical speeds v_z,0. Distances on the bottom axis are measured along the planet’s orbit. All curves are drawn for a typical model realisation. The shaded regions in the lower left indicate upper limits on the planet’s radius based on (1) the absence of transits in part of the Kepler data (light grey; R_p< 1.15R_⊕(1σ); Brogi et al. 2012) and (2) the planet-mass-dependent mass loss rate (dark grey; R_p ≲ 0.3R_⊕, model-dependent; Perez-Becker & Chiang 2013).