Saturation Level of the Streaming Instability
Abstract
In proto-planetary disks, gas turbulence can cluster dust grains and catalyze the formation of planetesimals. This process depends on the strength of the turbulence. Here, we evaluate the turbulence strength that is induced by the streaming instability. Based on the amount of free energy available, we estimate the viscous parameter to be alpha ~ St Pi^2 f(epsilon), where St (< 1) is the Stokes number of the streaming grains, Pi is the dimensionless pressure gradient, and f (epsilon) is an explicit function of epsilon, the local dust-to-gas density ratio. This estimate explains the results of many previous studies, and is also supported by our additional tailor-made simulations. We discuss two easy applications of our result, one is a self-consistent dust scale height, one is the astrophysical relevance of a pressure bump. Lastly, while this work allows one to characterize the streaming turbulence, we emphasize our current inability to connect the strength of turbulence to the formation of planetesimals.
Related
- A comparison of particle and fluid approaches for modeling the streaming instability in global patch simulations
- Saturation Mechanism of Cosmic Ray Streaming Instabilities with a Shell Distribution
- Streaming instabilities in weakly ionized protoplanetary discs: The ambipolar streaming instability
- Importance of the Resonant Cosmic-Ray Streaming Instability Upstream of Collisionless Shocks
- Closing the Gap: A Test of the Streaming Instability Using Simulations and Observations of the Cold-Classical Kuiper Belt Size Distribution
BibTeX
@misc{wu2026saturation,
title = {{Saturation Level of the Streaming Instability}},
author = {Yanqin Wu and Xuqi Chen and Joshua Bromley},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28736},
eprint = {2610.28736},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28736},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Saturation Level of the Streaming Instability
AU - Yanqin Wu
AU - Xuqi Chen
AU - Joshua Bromley
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.28736
UR - https://arxiv.org/abs/2610.28736
AB - In proto-planetary disks, gas turbulence can cluster dust grains and catalyze the formation of planetesimals. This process depends on the strength of the turbulence. Here, we evaluate the turbulence strength that is induced by the streaming instability. Based on the amount of free energy available, we estimate the viscous parameter to be alpha ~ St Pi^2 f(epsilon), where St (< 1) is the Stokes number of the streaming grains, Pi is the dimensionless pressure gradient, and f (epsilon) is an explicit function of epsilon, the local dust-to-gas density ratio. This estimate explains the results of many previous studies, and is also supported by our additional tailor-made simulations. We discuss two easy applications of our result, one is a self-consistent dust scale height, one is the astrophysical relevance of a pressure bump. Lastly, while this work allows one to characterize the streaming turbulence, we emphasize our current inability to connect the strength of turbulence to the formation of planetesimals.
ER -