  Secular gravitational instability (GI) is one of the promising mechanisms for
creating annular substructures and planetesimals in protoplanetary disks. We
perform numerical simulations of the secular GI in a radially extended disk
with inward drifting dust grains. The results show that, even in the presence
of the dust diffusion, the dust rings form via the secular GI while the dust
grains are moving inward, and the dust surface density increases by a factor of
ten. Once the secular GI develops into a nonlinear regime, the total mass of
the resultant rings can be a significant fraction of the dust disk mass. In
this way, a large amount of drifting dust grains can be collected in the dusty
rings and stored for planetesimal formation. In contrast to the emergence of
remarkable dust substructures, the secular GI does not create significant gas
substructures. This result indicates that observations of a gas density profile
near the disk midplane enable us to distinguish the mechanisms for creating the
annular substructures in the observed disks. The resultant rings start decaying
once they enter the inner region stable to the secular GI. Since the ring-gap
contrast smoothly decreases, it seems possible that the rings are observed even
in the stable region. We also discuss the likely outcome of the non-linear
growth and indicate the possibility that a significantly developed region of
the secular GI may appear as a gap-like substructure in dust continuum emission
since dust growth into larger solid bodies and planetesimal formation reduce
the total emissivity.
