  In our previous work (Paper I), we demonstrated that coagulation instability
results in dust concentration against depletion due to the radial drift and
accelerates dust growth locally. In this work (Paper II), we perform numerical
simulations of coagulation instability taking into account effects of
backreaction to gas and collisional fragmentation of dust grains. We find that
the slowdown of the dust drift due to backreaction regulates dust concentration
in the nonlinear growth phase of coagulation instability. The dust-to-gas
surface density ratio increases from $10^{-3}$ up to $\sim10^{-2}$. Each
resulting dust ring tends to have mass of $\simeq0.5M_{\oplus}-1.5M_{\oplus}$
in our disk model. In contrast to Paper I, the dust surface density profile
shows a local plateau structure at each dust ring. In spite of the regulation
at the nonlinear growth, the efficient dust concentration reduces their
collision velocity. As a result, dust grains can grow beyond the fragmentation
barrier, and the dimensionless stopping time reaches unity as in Paper I. The
necessary condition for the efficient dust growth is (1) weak turbulence of
$\alpha<1\times10^{-3}$ and (2) a large critical velocity for dust
fragmentation ($> 1$ m/s). The efficient dust concentration in outer regions
will reduce the inward pebble flux and is expected to decelerate the planet
formation via the pebble accretion. We also find that the resulting rings can
be unstable to secular gravitational instability (GI). The subsequent secular
GI promotes planetesimal formation. We thus expect that a combination of these
instabilities is a promising mechanism for dust-ring and planetesimal
formation.
