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Abstract The streaming instability (SI) is a leading mechanism for concentrating solid particles into regions dense enough to form planetesimals. Its efficiency in clumping particles depends primarily on the dimensionless stopping time (τ_s, a proxy for particle size) and dust-to-gas surface density ratio (Z). Previous simulations identified a criticalZ(Z_crit) above which strong clumping occurs, where particle densities exceed the Hill density (thus satisfying a condition for gravitational collapse), over a wide range ofτ_s. These works found that, forτ_s≤ 0.01,Z_critwas above the interstellar medium value (∼0.01). In this work, we reexamine the clumping threshold using 2D axisymmetric, stratified simulations at high resolution and with relatively large (compared to many previous simulations) domain sizes. Our main results are as follows: First, whenτ_s = 0.01, strong clumping occurs even atZ ≲ 0.01, lower thanZ_critfound in all previous studies. Consequently, we revise a previously published fit to theZ_critcurve to account for this updatedZ_crit. Second, higher resolution results in a thicker dust layer, which may result from other instabilities manifesting, such as the vertically shearing SI. Third, despite this thicker layer, higher resolution can lead to strong clumping even with a lower midplane dust-to-gas density ratios (which results from the thicker particle layer) so long asZ ≳ Z_crit. Our results demonstrate the efficiency of the SI in clumping small particles atZ ∼ 0.01, which is a significant refinement of the conditions for planetesimal formation by the SI. 

ABSTRACT The streaming instability, a promising mechanism to drive planetesimal formation in dusty protoplanetary discs, relies on aerodynamic drag naturally induced by the background radial pressure gradient. This gradient should vary in discs, but its effect on the streaming instability has not been sufficiently explored. For this purpose, we use numerical simulations of an unstratified disc to study the non-linear saturation of the streaming instability with mono-disperse dust particles and survey a wide range of gradients for two distinct combinations of the particle stopping time and the dust-to-gas mass ratio. As the gradient increases, we find most kinematic and morphological properties increase but not always in linear proportion. The density distributions of tightly coupled particles are insensitive to the gradient whereas marginally coupled particles tend to concentrate by more than an order of magnitude as the gradient decreases. Moreover, dust–gas vortices for tightly coupled particles shrink as the gradient decreases, and we note higher resolutions are required to trigger the instability in this case. In addition, we find various properties at saturation that depend on the gradient may be observable and may help reconstruct models of observed discs dominated by streaming turbulence. In general, increased dust diffusion from stronger gradients can lower the concentration of dust filaments and can explain the higher solid abundances needed to trigger strong particle clumping and the reduced planetesimal formation efficiency previously found in vertically stratified simulations.