Probing Conditions for Strong Clumping by the Streaming Instability: Small Dust Grains and Low Dust-to-gas Density Ratio

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 critical Z (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 of τ_s. These works found that, for τ_s ≤ 0.01, Z_crit was 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, when τ_s = 0.01, strong clumping occurs even at Z ≲ 0.01, lower than Z_crit found in all previous studies. Consequently, we revise a previously published fit to the Z_crit curve to account for this updated Z_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 as Z ≳ Z_crit. Our results demonstrate the efficiency of the SI in clumping small particles at Z ∼ 0.01, which is a significant refinement of the conditions for planetesimal formation by the SI.