Streaming Instability and Turbulence: Conditions for Planetesimal Formation

TL;DR

This study investigates how external turbulence influences the conditions for streaming instability-driven planetesimal formation, revealing that turbulence raises the critical solid-to-gas ratio needed for collapse, with implications for protoplanetary disk models.

Contribution

The paper introduces 3D simulations including particle self-gravity and turbulence, providing a quantitative fit for the critical solid-to-gas ratio as a function of turbulence and particle size.

Findings

Turbulence increases the threshold solid-to-gas ratio for planetesimal formation.

Planetesimal formation requires a mid-plane particle-to-gas density ratio exceeding unity.

Provided a model for particle scale height considering feedback and turbulence.

Abstract

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 ($\tau_s$, 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 $\alpha_D$ that measures turbulent diffusion. 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 $\tau_s = 0.01$, planetesimal formation occurs when $Z \gtrsim 0.06$, $\gtrsim 0.1$, and $\gtrsim 0.2$ at $\alpha_D = 10^{-4}$, $10^{-3.5}$, and $10^{-3}$, respectively. We provide a single fit to the critical $Z$ as a function of $\alpha_D$ and $\tau_s$ required for the SI to work (though limited to the range $\tau_s = 0.01$--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 independent of $\alpha_D$. Finally, we provide the estimation of particle scale height that accounts for both particle feedback and external turbulence.