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, Z crit . This threshold depends on the dimensionless stopping time, τ 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 ≤ τ s ≤ 1.0. Additionally, we study SI-driven concentration that is unique to 3D. We find that Z crit is as low as ≈0.002 at τ s = 0.1 and exceeds ≈0.03 at τ s = 10 −3 . Compared to 2D, our 3D results yield lower Z crit for τ s > 0.02, but higher for τ s ≤ 0.02, with a sharp transition between τ s = 0.02 and 0.03. This transition correlates with the midplane density ratio ( ϵ ): ϵ < 1 where 3D gives lower thresholds, and ϵ > 1 where 3D gives higher thresholds. We also find a filaments-in-filaments structure when ϵ < 1, which enhances clumping compared to 2D. By contrast, when ϵ > 1 and τ s ≤ 0.03, dust filaments in 3D do not drift inward, suppressing filament mergers and strong clumping. In 2D, filaments drift inward regardless of ϵ , 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.