On the Formation of Planetesimals Via Secular Gravitational Instabilities with Turbulent Stirring

We study the gravitational instability (GI) of small solids in a gas disk as a mechanism to form planetesimals. Dissipation from gas drag introduces secular GI, which proceeds even when standard GI criteria for a critical density or Toomre's Q predict stability. We include the stabilizing effects of turbulent diffusion, which suppresses small-scale GI. The radially wide rings that do collapse contain up to ~0.1 Earth masses of solids. Subsequent fragmentation of the ring (not modeled here) would produce a clan of chemically homogenous planetesimals. Particle radial drift time scales (and, to a lesser extent, disk lifetimes and sizes) restrict the viability of secular GI to disks with weak turbulent diffusion, characterized by α <~ 10^-4. Thus, midplane dead zones are a preferred environment. Large solids with radii gsim10 cm collapse most rapidly because they partially decouple from the gas disk. Smaller solids, even below ~ mm sizes, could collapse if particle-driven turbulence is weakened by either localized pressure maxima or super-solar metallicity. Comparison with simulations that include particle clumping by the streaming instability shows that our linear model underpredicts rapid, small-scale gravitational collapse. Thus, the inclusion of more detailed gas dynamics promotes the formation of planetesimals. We discuss relevant constraints from solar system and accretion disk observations.