Stabilization of the Shear Instability in a Dust Layer of a Protoplanetary Disk and Possible Formation of Planetesimals due to Gravitational Fragmentation of the Dust Layer

We show that the planetesimal formation due to the gravitational fragmentation of a dust layer in a protoplanetary disk is possible. The dust density distribution in the dust layer would approach the constant Richardson number distribution due to the dust stirring by the shear instability and dust settling. We perform the analysis of the shear instability of dust layer in a protoplanetary disk with the constant Richardson number density distribution. Our study revealed that this distribution is stable against the shear instability even if the dust density at the midplane reaches the critical density of the gravitational instability, and the planetesimal formation through the gravitational fragmentation of the dust layer can occur even for the dust to gas surface density ratio with the solar composition.