Streaming instability with multiple dust species – I. Favourable conditions for the linear growth

Recent study suggests that the streaming instability, one of the leading mechanisms for driving the formation of planetesimals, may not be as efficient as previously thought. Under some disc conditions, the linear growth rate of the instability decreases significantly when multiple dust species are considered, and the instability growth timescale can be longer than the disc lifetime. To further explore this finding, we use both linear analysis and direct numerical simulations with gas fluid and dust particles to mutually validate and study the unstable modes of the instability in more detail. We extend the previously studied parameter space by one order of magnitude in both the range of the dust-size distribution $[T_{s,min}, T_{s,max}]$ and the total solid-to-gas mass ratio $\varepsilon$ and introduce a third dimension with the slope $q$ of the size distribution. We find that the converged fast-growth regime and the non-converged slow-growth regime are distinctly separated by a sharp boundary in the $\varepsilon$-$T_{s,max}$ space, while this boundary is not appreciably sensitive to $q$ or $T_{s,min}$. Moreover, it is not necessary that the largest dust species dominate the growth of the unstable modes, and the smaller dust species can either increase or decrease the growth rate significantly. In any case, we find that the converged fast-growth regime is bounded by $\varepsilon\gtrsim1$ or $T_{s,max}\gtrsim1$, which may represent the favourable conditions for planetesimal formation.