Coexistence of coagulation and streaming instabilities in protoplanetary disks

¹ Laboratoire d’astrophysique de Bordeaux, Univ. Bordeaux, CNRS, B18N, allée Geoffroy Saint-Hilaire, 33615 Pessac, France
² Institute of Astronomy and Astrophysics, Academia Sinica, Taipei 10617, Taiwan
³ Physics Division, National Center for Theoretical Sciences, Taipei City 10617, Taiwan

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 9 November 2025
Accepted: 12 December 2025

Abstract

The streaming instability is considered to be one of the leading candidates for the formation of planetesimals, given its ability to overcome the bouncing and fragmentation barriers. However, the formation of dense dust clumps through this process is possible provided it involves solids with dimensionless stopping times ~0.1 in standard disks, 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 disks with a dust-to-gas ratio ϵ ≳ 1, coagulation is found to have little impact on the SI. Meanwhile, in dust-poor disks with ϵ ~ 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 ϵ ~ 0.1 and Stokes numbers St ≲ 0.1, we find an 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, could facilitate the formation of dense clumps through the SI, although we note that it has only a slight effect on its nonlinear evolution.