Streaming Instability and Turbulence: Conditions for Planetesimal Formation

The streaming instability (SI) is a leading candidate for planetesimal formation, which can concentrate solids through two-way aerodynamic interactions with the gas. The resulting concentrations can become sufficiently dense to collapse under particle self-gravity, forming planetesimals. Previous studies have carried out large parameter surveys to establish the critical particle to gas surface density ratio ( Z ), above which SI-induced concentration triggers planetesimal formation. The threshold Z depends on the dimensionless stopping time ( τ _s , a proxy for dust size). However, these studies neglected both particle self-gravity and external turbulence. Here, we perform 3D stratified shearing box simulations with both particle self-gravity and turbulent forcing, which we characterize via a turbulent diffusion parameter, α _D . We find that forced turbulence, at amplitudes plausibly present in some protoplanetary disks, can increase the threshold Z by up to an order of magnitude. For example, for τ _s = 0.01, planetesimal formation occurs when Z ≳ 0.06, ≳0.1, and ≳0.2 at α _D = 10 ^−4 , 10 ^−3.5 , and 10 ^−3 , respectively. We provide a single fit to the critical Z required for the SI to work as a function of α _D and τ _s (although limited to the range τ _s = 0.01–0.1). Our simulations also show that planetesimal formation requires a mid-plane particle-to-gas density ratio that exceeds unity, with the critical value being largely insensitive to α _D . Finally, we provide an estimation of particle scale height that accounts for both particle feedback and external turbulence.