The Streaming Instability Cannot Form Planetesimals from mm-size Grains in Pressure Bumps

Abstract

We present evidence that it is unlikely that the streaming instability (SI) can form planetesimals from mm grains inside axisymmetric pressure bumps. We conducted the largest simulation of the SI so far (7 million CPU hours), consisting of a large slice of the disk with mm grains, a solar-like dust-to-gas ratio ($Z = 0.01$), and the largest pressure bump that does not cause gravitational instability (GI) in the particle layer. We used a high resolution of $1000/H$ to resolve as many SI unstable modes as possible. The simulation produced a long-lived particle over-density far exceeding the SI criteria (i.e., a critical solid abundance to headwind parameter ratio $Z/\Pi$) where strong clumping would occur if these conditions were present over an extended region of the disk; yet we observed none. The likely reason is that the time it takes particles to cross the high-$Z/\Pi$ region ($t_{\rm cross}$) is shorter than the growth timescale of the SI ($t_{\rm grow}$). We propose an added criterion for planetesimal formation by the SI -- that $t_{\rm cross} > t_{\rm grow}$. We show that any bump larger than the one in this run would form planetesimals by the GI instead of the SI. Our results significantly restrict the pathways to planet formation: Either protoplanetary disks regularly form grains larger than 1~mm, or planetesimals do not form by the SI in axisymmetric pressure bumps. Since bumps large enough to induce the GI are likely Rossby-wave unstable, we propose that mm grains may only form planetesimals in vortices.