  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.
