We perform nonlinear numerical simulations to investigate the density evolution in the dust layer of a protoplanetary disk due to gravitational instability and dust settling toward the midplane. We restrict our study to the region where the radial pressure equilibrium is negligible so that the shear-induced instability is avoided, and we also restrict our model to an axisymmetric perturbation as a first step of nonlinear numerical simulations of the gravitational instability. We find that there are two different evolutionary paths of the gravitational instability, depending on the nondimensional gas friction time, which is defined as the product of the gas friction time and the Keplerian angular velocity. If the nondimensional gas friction time is equal to 0.01, the gravitational instability grows faster than dust settling. On the other hand, if the nondimensional gas friction time is equal to 0.1, dust aggregates settle sufficiently before the gravitational instability grows. In the latter case, an approximate analytical calculation reveals that dust settling is faster than the growth of the gravitational instability, regardless of the dust density at the midplane. Thus, the dust layer becomes extremely thin and may reach a few tenths of the material density of the dust before the gravitational instability grows, as long as there is no turbulence.
All Science Journal Classification (ASJC) codes
- Astronomy and Astrophysics
- Space and Planetary Science