Dust Rings as a Footprint of Planet Formation in a Protoplanetary Disk

Relatively large dust grains (referred to as pebbles) accumulate at the outer edge of the gap induced by a planet in a protoplanetary disk, and a ring structure with a high dust-to-gas ratio can be formed. Such a ring has been thought to be located right outside of the planet orbit. We examined the evolution of the dust ring formed by a migrating planet, by performing two-fluid (gas and dust) hydrodynamic simulations. We found that the initial dust ring does not follow the migrating planet and remains at the initial location of the planet in the cases with a low viscosity of $\alpha \sim 10^{-4}$. The initial ring is gradually deformed by viscous diffusion, and a new ring is formed in the vicinity of the migrating planet, which developes from the trap of the dust grains leaking from the initial ring. During this phase, two rings co-exist outside the planet orbit. This phase can continue over $\sim 1$~Myr for a planet migrating from 100~au. After the initial ring disappears, only the later ring remains. This change in the ring morphology can provide clues as to when and where the planet was formed, and is the footprint of the planet. We also carried out simulations with a mass-growing planet. These simulations show more complex asymmetric structures in the dust rings. The observed asymmetric structures in the protoplanetary disks may be related to a migrating and mass-growing planet.