Planetesimal Formation without Thresholds. II: Gravitational Instability of Solids in Turbulent Protoplanetary Disks

Abstract

We show that small solids in low mass, turbulent protoplanetary disks collect into self-gravitating rings. Growth is faster than disk lifetimes and radial drift times for moderately strong turbulence, characterized by dimensionless diffusivities, $α_g < 10^{-6} -- 10^{-3}$ when particles are mm-sized. This range reflects a strong dependance on disk models. Growth is faster for higher particle surface densities. Lower gas densities and larger solids also give faster growth, as long as aerodynamic coupling is tight. In simple power law models, growth is slowest around ~0.3 AU, where drag coupling is strongest for mm-sized solids. Growth is much faster close to the star where orbital times are short, with implications for in situ formation of short period extrasolar planets. Growth times also decrease toward the outer disk where lower gas densities allow greater particle settling. Beyond roughly Kuiper Belt distances however, solids are sufficiently decoupled from gas that dissipative gravitational instabilities are less effective. Turbulence not only slows growth, but also increases radial wavelengths. The initial solid mass in an unstable ring can be ~0.01 M_Earth or greater, huge compared to km-sized planetesimals. Nonlinear fragmentation, which has not been studied in detail, will lower the final planetesimal mass. We consider applications to the asteroid belt and discuss the alternate hypothesis of collisional agglomeration.