Concentrating small particles in protoplanetary disks through the streaming instability (1611.07014v3)

Abstract: Laboratory experiments indicate that direct growth of silicate grains via mutual collisions can only produce particles up to roughly millimeters in size. On the other hand, recent simulations of the streaming instability have shown that mm/cm-sized particles require an excessively high metallicity for dense filaments to emerge. Using a numerical algorithm for stiff mutual drag force, we perform simulations of small particles with significantly higher resolutions and longer simulation times than in previous investigations. We find that particles of dimensionless stopping time $\tau_\mathrm{s} = 10^{-2}$ and $10^{-3}$ -- representing mm- and cm-sized particles interior of the water ice line -- concentrate themselves via the streaming instability at a solid abundance of a few percent. We thus revise a previously published critical solid abundance curve for the regime of $\tau_\mathrm{s} \ll 1$. The solid density in the concentrated regions reaches values higher than the Roche density, indicating that direct collapse of particles down to mm sizes into planetesimals is possible. Our results hence bridge the gap in particle size between direct dust growth limited by bouncing and the streaming instability.

Concentrating Small Particles in Protoplanetary Disks through the Streaming Instability: A Numerical Investigation

The research paper addresses the problem of solid material accumulation in protoplanetary disks, focusing on particles limited by direct growth barriers, specifically in the mm and cm size range. Laboratory experiments have showcased that direct growth of silicate grains through collisions is restricted to about millimeters in scale. The streaming instability, a mechanism that may overcome this size limit, has been examined, but previous simulation attempts suggested it required unrealistically high metallicities to be effective.

In this paper, the authors test the streaming instability's efficacy with small particles under conditions more closely aligned with typical disk environments. They employ a high-resolution numerical approach combined with longer simulation times, which allows them to capture the dynamics of small particles more effectively than previous studies. Specifically, they focus on particles with dimensionless stopping times, $\tau_\mathrm{s}=10^{-2}$ and $\tau_\mathrm{s}=10^{-3}$, correlating to millimeter and sub-millimeter sizes, respectively.

Key Findings and Numerical Insights

• The results demonstrate that particles with $\tau_\mathrm{s}=10^{-2}$ and $\tau_\mathrm{s}=10^{-3}$ can self-concentrate into high-density regions via the streaming instability at solid-to-gas ratios of just a few percent, specifically within $0.01 < Z_\mathrm{c} < 0.02$ for $\tau_\mathrm{s}=10^{-2}$ and $0.03 < Z_\mathrm{c} < 0.04$ for $\tau_\mathrm{s}=10^{-3}$. This is significantly lower than earlier reported requirements, showcasing the viability of planetesimal formation through this mechanism in typical disk conditions without necessitating high metallicities.
• The paper reveals that, akin to the smaller stopping time particles, larger stopping time particles achieve comparable concentration levels, albeit requiring lower solid abundances to do so. For larger $\tau_\mathrm{s}$ particles, the radial drift barrier is effectively overcome, narrowing the gap between dust coagulation thresholds and particle concentration ability inside the disk’s ice line.

Implications and Future Developments

The paper contributes a revised critical solid abundance curve, adjusting the threshold conditions under which the streaming instability operates. This revision is crucial because it positions the streaming instability as a plausible mechanism for bridging the size gap between dust aggregates and planetesimals within protoplanetary disks, especially where direct growth mechanisms stall due to bouncing and fragmentation.

From a theoretical perspective, this research establishes a robust simulation framework capable of capturing complex dynamics in particle-gas systems, capable of further exploration into varying particle properties, size distributions, and interactions within magnetized environments—a condition reflective of more realistic protoplanetary disk scenarios.

Potential future work could examine the concentricity dynamic in multi-sized particle distributions and explore downstream processes, such as gravitational collapse within high-density filaments. Given that particles of widely varied sizes are likely to interact within a protoplanetary disk, this aspect will provide deeper insights into how small-scale instabilities contribute to large-scale planetary formation.

This research mitigates previous concerns about the high metallicity prerequisites and demonstrates a natural pathway where planetesimal formation becomes a viable process under reasonable disk conditions. Future development will undoubtedly include magnetohydrodynamic models and extended simulations that encompass a more considerable portion of the disk within the temporal and spatial dimensions.