# Interpretation of the resonant drag instability of dust settling in protoplanetary disc

## TL;DR

This paper analyzes the resonant drag instability in protoplanetary discs, showing how dust settling and mode coupling lead to dust clumping, with growth rates depending on dust velocity and mixture parameters.

## Contribution

It introduces a mode coupling framework between inertial waves and settling dust waves, explaining the instability mechanism in dust-gas mixtures.

## Key findings

- Instability growth rate scales with the square root of the coupling term.
- Higher dust settling velocities lead to faster dust clumping.
- Mode coupling enables dust aggregation in protoplanetary discs.

## Abstract

The recently discovered resonant drag instability of dust settling in protoplanetary disc is considered as the mode coupling of subsonic gas-dust mixture perturbations. This mode coupling is coalescence of two modes with nearly equal phase velocities: the first mode is inertial wave having positive energy, while the second mode is a settling dust wave (SDW) having negative energy as measured in the frame of gas environment being at rest in vertical hydrostatic equilibrium. SDW is a trivial mode produced by the bulk settling of dust, which transports perturbations of dust density. The phase velocity of SDW is equal to the bulk settling velocity times the cosine of the angle formed by the wave vector and the rotation axis. In this way, the bulk settling of dust makes possible the coupling of SDW with the inertial wave and the onset of the instability. In accordance with the concept of the mode coupling, the instability growth rate is proportional to the square root of the dispersion equation coupling term, which itself contains the small mass fraction of dust in gas-dust mixture, the squared radial wavenumber of the modes, and the squared bulk settling velocity. Thus, the higher is the bulk settling velocity, the heavier clumps of dust can be aggregated by the instability of the same rate.