Revisiting planetesimal formation from mm-sized grains in pressure bumps
We present evidence that the streaming instability (SI) can form planetesimals from millimeter grains inside axisymmetric pressure bumps, provided the bump is not too strongly reinforced. We conducted three-dimensional local shearing-box simulations of millimeter grains in a Gaussian pressure bump of amplitude $A = 0.6$, at a resolution of $160/H$. We varied only the Newtonian reinforcement timescale $t_{\rm reinf}$, the timescale on which the imposed bump is restored against particle back-reaction. Our reference run T1 uses $t_{\rm reinf} = 1\,Ω^{-1}$. Particles pile up in a narrow axisymmetric band at the minimum-headwind point, cross the Roche density, and collapse through direct gravitational instability (GI). In our weakly reinforced run T100 with $t_{\rm reinf} = 100\,Ω^{-1}$, the outcome is different. Particles drift through the bump roughly three times more slowly, and dense SI-like filaments develop across a wide radial region well before the Roche density is reached. These results are consistent with a residence-time criterion, which states that for the SI to grow, $t_{\rm cross} > t_{\rm grow}$, where $t_{\rm cross}$ is the time a particle spends inside the region where the ratio $Z/Π$ of the solid abundance $Z = Σ_p/Σ_g$ to the headwind parameter $Π= Δv/c_{\rm s}$ is high enough for strong clumping, and $t_{\rm grow}$ is the SI growth time. T1 violates this criterion, and T100 satisfies it. Our results suggest that the reinforcement timescale matters for millimeter grains because it helps set the crossing time, and therefore whether the SI has time to grow. We caution, however, that our reinforcement scheme is an idealised numerical construction rather than a physical bump-forming mechanism such as a planet, and a more definitive test of this picture will require simulations with a more physically motivated bump.