The Streaming Instability with Multiple Dust Species in Protoplanetary Disks

The streaming instability is a fundamental process that can drive dust-gas dynamics and ultimately planetesimal formation in protoplanetary disks. However, it has recently been shown that the instability with a distribution of dust sizes may not operate efficiently under certain conditions, hence a revisit to the instability becomes necessary.

Using linear analysis, we systematically explore an unprecedentedly large parameter space spanned by the limits and slope of the dust-size distribution and the total dust-to-gas density ratio. We show that the growth of the instability can be classified into two distinct regimes — fast- and slow-growth — depending mainly on the leading dust size τ_s,max and the total dust-to-gas density ratio ε. The regime of fast growth requires either large τ_s,max or large ε, and the two regimes are distinctly separated by a sharp boundary in the τ_s,max–ε space, while this boundary is not appreciably sensitive to the slope or the lower end of the dust-size distribution. We further conduct numerical simulations of an unstratified disk into nonlinear saturation of the instability. For the fast-growth regime, the one system with small τ_s,max but large ε drives turbulent vertical dust-gas vortices, while the other with large τ_s,max leads to radial traffic jams and filamentary concentrations of dust particles. By contrast, a system in the slow-growth regime results in a virtually quiescent state.

Although the saturation states in the fast-growth regime are similar to their single-species counterparts, a wealth of information can be found with the multi-species streaming instability. We find that the dust density distribution driven by turbulent vortices is flat in low densities, while the one undergoing traffic jams has a low-end cutoff. Moreover, we find that in the fast-growth regime, significant dust segregation by size occurs, with large particles moving towards dense regions while small particles remain in the diffuse regions, and the mean radial drift of each dust species is appreciably altered from the (initial) drag-force equilibrium. The former effect may skew the spectral index derived from multi-wavelength observations and change the initial size distribution of a pebble cloud for planetesimal formation. The latter effect along with turbulent diffusion may influence the radial transport and mixing of solid materials in young protoplanetary disks.