Top panel: maximum solid density evolution as a function of time for single species runs with τ_s = 10⁻³, 10⁻², 10⁻¹, 10⁰ and 10¹. The metallicity is shown on the top axis. The horizontal black dashed line corresponds to ρ_p,max ∕ρ_g = 100, which represents our adopted metallicity threshold for filament formation. Middle and bottom panels: Effect of changes in N_p for τ_s = 10⁻¹ and 10⁻², respectively.Here, the solid lines show the relative maximum density for 10 vs. 20 particles per cell while the dashed lines show the relative maximum density for 10 vs. 100 particles per cell. In both cases, the level of deviation from unity is low, implying that the particle number does not have a significant effect on the maximum density of the single-species streaming instability. The colors correspond to the legend in the top panel.