The two-fluid analysis of the Kelvin-Helmholtz instability in dusty layer of a protoplanetary disk: A possible path toward the planetesimal formation through the gravitational instability

We analyze the stability of dust layer in protoplanetary disk to understand the effect of the relative motion between gas and dust. The previous analyses not including the effect of relative motion between gas and dust show that the shear-induced turbulence may prevent the dust grains from settling sufficiently to be gravitationally unstable. We determine the growth rate of Kelvin-Helmholtz instability in wide range of parameter space, and propose a possible path toward the planetesimal formation through the gravitational instability. We expect the density of dust layer becomes ${\rho }_{\mathrm{d}}\mathrm{/}{\rho }_{\mathrm{g}}\sim 200$ if the dust grains can grow up to 5m.