Gravitational instability in the dust layer of a protoplanetary disk : the case with a constant Richardson number

Abstract

The gravitational instability in the dust layer of a protoplanetary disk with a constant Richardson number is investigated. The linear analysis of the gravitational instability is performed. The following assumptions are used: (1) One fluid model is adopted, that is, difference of velocities between dust and gas are neglected. (2) The gas is incompressible. (3) The gas flow is axisymmetric with respect to the rotation axis of the disk. Numerical results show that the critical density at the midplane is 2.85 times as large as that for the uniform dust density distribution by Sekiya (1983). Our results give a new restriction on the planetesimal formation by the gravitational instability.