Radial profiles of the dust disc surface density seen in Fig. 1. Radial profiles are given for the azimuthal average (indicated by the grey area, equivalent in both plots), as well as at cuts leading and trailing Earth (top) and Venus (bottom). The radial cuts located at azimuths of ±8° and ±20° from the planets illustrate the azimuthal asymmetry present in the rings (leading gap and trailing enhancement). Also shown are the locations of the semi-major axes of the inner planets. Other particle β are given in Figs. A.1 and A.2.