Strong clumping in global streaming instability simulations with a dusty fluid

Context. The process of planet formation in protoplanetary disks and the drivers behind the formation of their seeds are still major unknowns. It is a broadly accepted theory that multiple processes can trap dusty material in radially narrow rings or vortex-like structures, preventing the dust from drifting inwards. However, it is still necessary to identify the relevant process behind the clumping of this dusty material, which can result in its collapse under gravity. One promising candidate is the streaming instability arising from the aerodynamic interaction between dust and gas once their densities are similar. Aims. We used a global disk model based on recent observational constraints to investigate the capacity of the streaming instability to form dust clumps, which would then undergo gravitational collapse. Furthermore, our goal is to verify the observability of the produced structures using Atacama Large Millimeter/submillimeter Array (ALMA) or Next Generation Very Large Array (ngVLA). Methods. For the first time, we present global 2D (R, z) hydrodynamic simulations using the FARGO3D code, where the dust is treated as a pressureless fluid. The disk model assumes stratification, realistic boundary conditions, and meaningful resolution to resolve the fast-growing modes. We chose two values for the total dust-to-gas mass ratio Z = 0.01 and Z = 0.02. We then compared the maximum clump density to the local Hill density and computed the optical depth of the dust disk. Results. With a dust-to-gas mass ratio of Z = 0.01, we confirm previous streaming instability simulations, which did not indicate any ability to form strong concentrations of dust clumps. With Z = 0.02, dense clumps form within 20 orbits; however, they reached only 30% of the Hill density, even when applying disk parameters from the massive protoplanetary disks GM Aur, HD 163296, IM Lup, MWC 480, and TW Hya, which all share astonishingly similar surface density profiles. Conclusions. Our results show that clumping by the streaming instability to trigger self-gravity is less efficient than previously thought, especially when more realistic density profiles are applied. By extrapolating our results, we estimated the gravitational collapse of concentrated pebbles earliest at 480 orbits; whereas for more frequent, less massive, or more compact disks, this time frame can reach up to 1000 orbits. Our results predict that substructures caused by streaming instability can vary between optical thin and optical thick at ALMA Band 1 wavelength for less massive disks. However, the average clump separation is 0.03 au at 10 au distance to the star, which is far too small to be observable with ALMA and even ngVLA. For the currently observed disks and best-fit surface density profiles, we predict efficient planetesimal formation outside 10 au, where the ratio of Hill- and gas midplane density is sufficiently small. Our results suggest that even for massive Class II disks, the critical Hill density can be reached in dust concentrations within 480–1000 orbits, corresponding to tens or hundreds of thousands of years, depending on the radial position.