Vertically integrated dust density distribution after 1 (left) and 5 (right) Myr of evolution, when a massive planet (1, 5, and 15 MJup, from top to bottom) is embedded in the disk at 20 AU (vertical dash-dotted line). At the location of the snow line (vertical dashed line at ~ 0.4 AU), the fragmentation velocity changes from 1 m s-1 to 10 m s-1 within a range of ~ 2 AU. The solid white line corresponds to St = 1, which is proportional to Σg. The solid blue line corresponds to the maximum grain size due to fragmentation (Eq. (3)), while the dotted green line represents the drift barrier (Eq. (4)).
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