Realized by the back reaction of the solid particles (pebbles/dust) to the gas drag, the streaming instability tends to drive axisymmetric filamentary structures in the dust component of a protoplanetary disk. In order to characterize the properties of these structures, we conducted computer simulations of this process in a laminar disk with the largest domain to date. The figure shows the top-down (radial-azimuthal) view of the solids in the disk in the nonlinear stage of the streaming instability. Multiple axisymmetric filaments (up to five in the figure) are simultaneously concentrated by the instability and coexist in the disk. A systematic study of the computational domain helped us obtain a convergent measurement of the properties of the filaments, most importantly the characteristic radial separation between adjacent filaments.
This work has several important implications in protoplanetary disks and planet formation. First, it demonstrated that an axisymmetric structure in the dust component of a protoplanetary disk can be readily driven by the dust particles themselves via the back reaction force to the gas, without the presence of any planetary object. Second, the well-defined characteristic separation implies a characteristic mass budget for the formation of planetesimals. It turned out that indeed the characteristic mass of newborn planetesimals correlates well with the mass budget of each filement. Finally, any chemical inhomogeneity down to this scale may have an imprint in the compositions of asteroids and Kuiper Belt objects in the Solar System.
Movie: top (radial-azimuthal) view of the disk solids, before gravitational collapse
For the streaming instability to be able to strongly concentrate solid materials and drive planetesimal formation, there exists a critical threshold in solid abundance (Z). This critical solid abundance may depend on several factors. In this work, we used computer simulations to investigate how it depends on the stopping time (τs), which is roughly equivalent to particle size. The figure shows a map of solid abundance against stopping time. The black solid line depicts our estimate of the critical solid abundance, above which (green region) and below which (red region) strong concentration of solids does and does not occur, respectively.
Most importantly, this work demonstrated that the inner region of a protoplanetary disk only requires a few percent of millimeter-sized dust particles (τs ∼ 10-3) for planetesimals to form, a value much lower than previously thought, as the blue dashed line indicates.
Reference: Yang, C.-C., Johansen, A., & Carrera, D. 2017, A&A, 606, A80.
This work represented the first study of how the streaming instability behaves in a disk with non-ideal MHD. We set up computer simulations modelling a layered accretion disk with a mid-plane (magnetically) dead zone, sandwiched by turbulent surface layers driven by the magneto-rotational instability (MRI). We studied how solid particles respond to the disturbances in the mid-plane driven by the surface layers and how the critical abundance for planetesimal formation differs in this environment.
The figure shows the side (radial-vertical) view of the distribution of the solids in the disk. We found that the perturbations in the gas are highly aniostropic, and the particles are significantly stirred up than the accretion stress would have suggested. In other words, the vertical diffusion of the gas and the particles is much stronger than the shear stress. We have quantified the diffusion coefficients and the shear stress as a function of vertical height from our models.
In contrast to the expectation that planetesimal formation should be much more difficult in such a disturbed environment, we found that the critical solid abundance remains similar to that in a laminar disk, namely, a few percent. The figure shows a dense axisymmetric filament of soilds results from a model with a solid abundance of 2%. This indicates that the criterion for planetesimal formation is not sensitive to the vertical sedimentation of the solid particles. Instead, it should be a combination of the soild abundance and the strength of radial diffusion, that is, the higher the solid abundance or the weaker the radial diffusion, the more easily planetesimals can form.
Reference: Yang, C.-C., Mac Low, M.-M., & Johansen, A. 2018, ApJ, 868, 27.
Movie: side (radial-vertical) and top (radial-azimuthal) views of the disk gas and solids in a dead zone for particles of dimensionless stopping time τs = 0.1 and solid abundance Z = 2%