The Streaming Instability in 3D: Conditions for Strong Clumping

Abstract: The streaming instability (SI) is a leading mechanism for planetesimal formation, driving the aerodynamic concentration of solids in protoplanetary disks. The SI triggers strong clumping (i.e., strong enough for clumps to collapse) when the solid-to-gas column density ratio, $Z$, exceeds a threshold, $\Zcrit$. This threshold depends on the dimensionless stopping time, $\tau_s$. Although the strong-clumping threshold has been explored over the last decade, it has been determined largely through 2D axisymmetric simulations. In this work, we perform a suite of 3D, vertically stratified simulations to establish a clumping threshold across $10^{-3} \leq \tau_s \leq 1.0$. Additionally, we study SI-driven concentration that is unique to 3D. We find that $\Zcrit$ is as low as $\approx 0.002$ at $\tau_s=0.1$ and exceeds $\approx 0.03$ at $\tau_s=10^{-3}$. Compared to 2D, our 3D results yield lower $\Zcrit$ for $\tau_s > 0.02$, but higher for $\tau_s \leq 0.02$, with a sharp transition between $\tau_s = 0.02$ and 0.03. This transition correlates with midplane density ratio ($\epsilon$): $\epsilon < 1$ where 3D gives lower thresholds, and $\epsilon > 1$ where 3D gives higher thresholds. We also find a filaments-in-filaments structure when $\epsilon < 1$, which enhances clumping compared to 2D. By contrast, when $\epsilon > 1$ and $\tau_s \leq 0.03$, dust filaments in 3D do not drift inward, suppressing filament mergers and strong clumping. In 2D, filaments drift inward regardless of $\epsilon$, triggering strong clumping easier in this regime. Our results underscore the necessity of 3D simulations for accurately capturing SI-driven concentration and building the strong-clumping threshold.