Comparison of different toy models with dust initially only present outside of 15 AU. Panel A: initial dust distribution. The white lines correspond to Stokes numbers of St = {10⁻³,10⁻²,10⁻¹,10⁰}; the bold white line corresponds to St = 1. All other panels show snapshots of models at 1 Myr. Panel B: fiducial toy model with a Saturn-mass planet at 5 AU and a fragmentation velocity of 10 m s⁻¹. Panel C: Model without a planet. The vertical dashed lines are the location at which the dust flux is measured in Fig. 2. Panel D: model without fragmentation. Panel E: model with a reduced fragmentation velocity of 1 m s⁻¹. Bottom right: model with bouncing instead of fragmentation.