Dynamics of Porous Dust Aggregates and Gravitational Instability of Their Disk

We consider the dynamics of porous icy dust aggregates in a turbulent gas disk and investigate the stability of the disk. We evaluate the random velocity of porous dust aggregates by considering their self-gravity, collisions, aerodynamic drag, turbulent stirring and scattering due to gas. We extend our previous work by introducing the anisotropic velocity dispersion and the relaxation time of the random velocity. We find the minimum mass solar nebular model to be gravitationally unstable if the turbulent viscosity parameter $\alpha$ is less than about $4 \times 10^{-3}$. The upper limit of $\alpha$ for the onset of gravitational instability is derived as a function of the disk parameters. We discuss the implications of the gravitational instability for planetesimal formation.