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1. Streaming instability with multiple dust species – I. Favourable conditions for the linear growth

   https://doi.org/10.1093/mnras/staa3628  

   Zhu; Yang (December 2020, Monthly Notices of the Royal Astronomical Society)

   null (Ed.)

   ABSTRACT A recent study suggests that the streaming instability, one of the leading mechanisms for driving the formation of planetesimals, may not be as efficient as previously thought. Under some disc conditions, the growth time-scale of the instability can be longer than the disc lifetime when multiple dust species are considered. To further explore this finding, we use both linear analysis and direct numerical simulations with gas fluid and dust particles to mutually validate and study the unstable modes of the instability in more detail. We extend the previously studied parameter space by one order of magnitude in both the range of the dust-size distribution [Ts, min, Ts, max] and the total solid-to-gas mass ratio ε and introduce a third dimension with the slope q of the size distribution. We find that the fast-growth regime and the slow-growth regime are distinctly separated in the ε–Ts, max space, while this boundary is not appreciably sensitive to q or Ts, min. With a wide range of dust sizes present in the disc (e.g. Ts, min ≲ 10−3), the growth rate in the slow-growth regime decreases as more dust species are considered. With a narrow range of dust sizes (e.g. Ts, max/Ts, min = 5), on the other hand, the growth rate in most of the ε–Ts, max space is converged with increasing dust species, but the fast and the slow growth regimes remain clearly separated. Moreover, it is not necessary that the largest dust species dominate the growth of the unstable modes, and the smaller dust species can affect the growth rate in a complicated way. In any case, we find that the fast-growth regime is bounded by ε ≳ 1 or Ts, max ≳ 1, which may represent the favourable conditions for planetesimal formation. 

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2. Dust–gas dynamics driven by the streaming instability with various pressure gradients

   https://doi.org/10.1093/mnras/stae272  

   Baronett, Stanley A; Yang, Chao-Chin; Zhu, Zhaohuan (February 2024, Monthly Notices of the Royal Astronomical Society)

   ABSTRACT The streaming instability, a promising mechanism to drive planetesimal formation in dusty protoplanetary discs, relies on aerodynamic drag naturally induced by the background radial pressure gradient. This gradient should vary in discs, but its effect on the streaming instability has not been sufficiently explored. For this purpose, we use numerical simulations of an unstratified disc to study the non-linear saturation of the streaming instability with mono-disperse dust particles and survey a wide range of gradients for two distinct combinations of the particle stopping time and the dust-to-gas mass ratio. As the gradient increases, we find most kinematic and morphological properties increase but not always in linear proportion. The density distributions of tightly coupled particles are insensitive to the gradient whereas marginally coupled particles tend to concentrate by more than an order of magnitude as the gradient decreases. Moreover, dust–gas vortices for tightly coupled particles shrink as the gradient decreases, and we note higher resolutions are required to trigger the instability in this case. In addition, we find various properties at saturation that depend on the gradient may be observable and may help reconstruct models of observed discs dominated by streaming turbulence. In general, increased dust diffusion from stronger gradients can lower the concentration of dust filaments and can explain the higher solid abundances needed to trigger strong particle clumping and the reduced planetesimal formation efficiency previously found in vertically stratified simulations. 

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3. Physical models of streaming instabilities in protoplanetary discs

   https://doi.org/10.1093/mnras/staa2311  

   Squire, Jonathan; Hopkins, Philip F (October 2020, Monthly Notices of the Royal Astronomical Society)

   null (Ed.)

   ABSTRACT We develop simple, physically motivated models for drag-induced dust–gas streaming instabilities, which are thought to be crucial for clumping grains to form planetesimals in protoplanetary discs. The models explain, based on the physics of gaseous epicyclic motion and dust–gas drag forces, the most important features of the streaming instability and its simple generalization, the disc settling instability. Some of the key properties explained by our models include the sudden change in the growth rate of the streaming instability when the dust-to-gas mass ratio surpasses one, the slow growth rate of the streaming instability compared to the settling instability for smaller grains, and the main physical processes underlying the growth of the most unstable modes in different regimes. As well as providing helpful simplified pictures for understanding the operation of an interesting and fundamental astrophysical fluid instability, our models may prove useful for analysing simulations and developing non-linear theories of planetesimal growth in discs. 

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4. Dust concentration via coupled vertical settling and radial migration in substructured non-ideal MHD discs and early planet formation

   https://doi.org/10.1093/mnras/staf798  

   Hsu, Chun-Yen; Li, Zhi-Yun; Tu, Yisheng; Hu, Xiao; Lin, Min-Kai (May 2025, Monthly Notices of the Royal Astronomical Society)

   ABSTRACT We investigate the dynamics of dust concentration in actively accreting, substructured, non-ideal magnetohydrodynamic wind-launching discs using two-dimensional and three-dimensional (3D) simulations incorporating pressureless dust fluids of various grain sizes and their aerodynamic feedback on gas dynamics. Our results reveal that mm/cm-sized grains are preferentially concentrated within the inner 5–10 au of the disc, where the dust-to-gas surface density ratio (local metallicity Z) significantly exceeds the canonical 0.01, reaching values up to 0.25. This enhancement arises from the interplay of dust settling and complex gas flows in the meridional plane, including mid-plane accretion streams at early times, mid-plane expansion driven by magnetically braked surface accretion at later times, and vigorous meridional circulation in spontaneously formed gas rings. The resulting size-dependent dust distribution has a strong spatial variation, with large grains preferentially accumulating in dense rings, particularly in the inner disc, while being depleted in low-density gas gaps. In 3D, these rings and gaps are unstable to Rossby wave instability, generating arc-shaped vortices that stand out more prominently than their gas counterparts in the inner disc because of preferential dust concentration at small radii. The substantial local enhancement of the dust relative to the gas could promote planetesimal formation via streaming instability, potentially aided by the ‘azimuthal drift’ streaming instability that operates efficiently in accreting discs and a lower Toomre Q expected in younger discs. Our findings suggest that actively accreting young discs may provide favourable conditions for early planetesimal formation, which warrants further investigation. 

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5. Positive feedback: How a synergy between the streaming instability and dust coagulation forms planetesimals

   https://doi.org/10.1051/0004-6361/202554100  

   Carrera, Daniel; Lim, Jeonghoon; Eriksson, Linn_E J; Lyra, Wladimir; Simon, Jacob B (April 2025, Astronomy & Astrophysics)

   Context.One of the most important open questions in planet formation is how dust grains in a protoplanetary disk manage to overcome growth barriers and form the ∼100 km planet building blocks that we call planetesimals. There appears to be a gap between the largest grains that can be produce by coagulation, and the smallest grains that are needed for the streaming instability (SI) to form planetesimals. Aims.Here we explore the novel hypothesis that dust coagulation and the SI work in tandem; in other words, they form a feedback loop where each one boosts the action of the other to bridge the gap between dust grains and planetesimals. Methods.We developed a semi-analytical model of dust concentration due to the SI, and an analytic model of how the SI affects the fragmentation and radial drift barriers. We then combined them to model our proposed feedback loop. Results.In the fragmentation-limited regime, we find a powerful synergy between the SI and dust growth that drastically increases both grain sizes and densities. We find that a midplane dust-to-gas ratio ofϵ ≥ 0.3 is a sufficient condition for the feedback loop to reach the planetesimal-forming region for turbulence values 10⁻⁴ ≤ α ≤ 10⁻³and grain sizes 0.01 ≤ St ≤ 0.1. In contrast, the drift-limited regime only shows grain growth without significant dust accumulation. In other words, planetesimal formation remains challenging in the drift-dominated regime and dust traps may be required to allow planet formation at wide orbital distances. 

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