Coexistence of coagulation and streaming instabilities in protoplanetary discs

Abstract

The streaming instability is considered one of the leading candidates for the formation of planetesimals, due to its ability to overcome the bouncing and fragmentation barriers. The formation of dense dust clumps through this process, however, is possible provided it involves solids with dimensionless stopping times $\sim 0.1$ in standard discs, which typically corresponds to 1-10 cm-sized particles. This implies that dust coagulation is required for the SI to be an efficient process. Here, we employ unstratified, shearing-box simulations combined with a moment equation for solving the coagulation equation to examine the effect of dust growth on the SI. In dust-rich discs with a dust-to-gas ratio $\epsilon\gtrsim 1$, coagulation is found to have little impact on the SI; while in dust-poor discs with $\epsilon\sim 0.01$, we observe the formation of vertically extended filaments through the action of the coagulation instability (CI), which is triggered due to the dependence of coagulation efficiency on dust density. For moderate dust-to-gas ratios $\epsilon\sim 0.1$ and Stokes numbers $St \lesssim 0.1$, we find onset of the SI within these filaments, with a linear growth rate significantly higher compared to standard SI. We refer to this regime as coagulation-assisted SI. The synergy between both instabilities in that case leads to isotropic turbulence and dust concentrations that are increased by a factor of $30-40$. As dust continues to grow, SI tends to overcome the effect of the CI such that the nonlinear saturation phase is similar to pure SI. Our results suggest that coagulation, by simply increasing dust size, may facilitate the formation of dense clumps through the SI; even though it has only little effect on its nonlinear evolution.