Does the Streaming Instability exist within the Terminal Velocity Approximation?

TL;DR

This paper examines whether the resonant Streaming Instability can be accurately modeled within the terminal velocity approximation, concluding that the instability's physical origin lies beyond this approximation's validity.

Contribution

It clarifies that the resonant Streaming Instability cannot be captured within the terminal velocity approximation, refining the understanding of gas-dust dynamics.

Findings

The linearised equations used previously exceed the approximation's accuracy.

The dispersion relation reveals the instability's long wavelength branch is beyond the approximation.

Refined equations show the instability does not occur within the terminal velocity approximation.

Abstract

Terminal velocity approximation is appropriate to study the dynamics of gas-dust mixture with solids tightly coupled to the gas. This work reconsiders its compatibility with physical processes giving rise to the resonant Streaming Instability in the low dust density limit. It is shown that the linearised equations have been commonly used to study the Streaming Instability within the terminal velocity approximation actually exceed the accuracy of this approximation. For that reason, the corresponding dispersion equation recovers the long wavelength branch of the resonant Streaming Instability caused by the stationary azimuthal drift of the dust. However, the latter must remain beyond the terminal velocity approximation by its physical definition. The refined equations for gas-dust dynamics in the terminal velocity approximation does not lead to the resonant Streaming Instability. The work additionally elucidates the physical processes responsible for the instability.