# Streaming Instability for Particle-Size Distributions

## TL;DR

This study investigates how a distribution of particle sizes affects the growth and efficiency of the streaming instability, a key process in planetesimal formation, revealing that multi-species systems grow more slowly than single-species ones.

## Contribution

First analysis of the linear streaming instability considering a particle-size distribution, showing slower growth rates and implications for planet formation models.

## Key findings

- Multi-species streaming instability grows on longer timescales than single-species.
- High dust-to-gas ratios can lead to growth times comparable to secular instabilities.
- Particle segregation may enhance instability growth.

## Abstract

The streaming instability is thought to play a central role in the early stages of planet formation by enabling the efficient bypass of a number of barriers hindering the formation of planetesimals. We present the first study exploring the efficiency of the linear streaming instability when a particle-size distribution is considered. We find that, for a given dust-to-gas mass ratio, the multi-species streaming instability grows on timescales much longer than those expected when only one dust species is involved. In particular, distributions that contain close-to-order-unity dust-to-gas mass ratios lead to unstable modes that can grow on timescales comparable, or larger, with those of secular instabilities. We anticipate that processes leading to particle segregation and/or concentration can create favourable conditions for the instability to grow fast. Our findings may have important implications for a large number of processes in protoplanetary disks that rely on the streaming instability as usually envisioned for a unique dust species. Our results suggest that the growth rates of other resonant-drag-instabilities may also decrease considerably when multiple species are considered.