Thresholds for Particle Clumping by the Streaming Instability

Abstract

The streaming instability (SI) is a mechanism to aerodynamically concentrate solids in protoplanetary disks and trigger the formation of planetesimals. The SI produces strong particle clumping if the ratio of solid to gas surface density—an effective metallicity—exceeds a critical value. This critical value depends on particle sizes and disk conditions such as radial drift-inducing pressure gradients and levels of turbulence. To quantify these thresholds, we perform a suite of vertically stratified SI simulations over a range of dust sizes and metallicities. We find a critical metallicity as low as 0.4% for the optimum particle sizes and standard radial pressure gradients (normalized value of Π = 0.05). This subsolar metallicity is lower than previous results, due to improved numerical methods and computational effort. We discover a sharp increase in the critical metallicity for small solids, when the dimensionless stopping time (Stokes number) is ≤0.01. We provide simple fits to the size-dependent SI clumping threshold, including generalizations to different disk models and levels of turbulence. We also find that linear, unstratified SI growth rates are a surprisingly poor predictor of particle clumping in nonlinear, stratified simulations, especially when the finite resolution of simulations is considered. Our results widen the parameter space for the SI to trigger planetesimal formation.

Streaming Instability with Multiple Dust Species: II. Turbulence and Dust-Gas Dynamics at Nonlinear Saturation

“…These pieces of information could be used as a guide and predict the properties near the mid-plane of a vertically stratified disc, which helps isolate the effects of vertical sedimentation of the gas and the dust particles by comparison. We note that Li & Youdin (2021) recently found no apparent connection between the linear growth of the streaming instability in an unstratified disc and the strong clumping of solids in a vertically stratified one. Therefore, we believe it is even more imperative to further investigate the nonlinear saturation of the streaming instability before understanding its connection to vertically stratified discs.…”

“…For larger particles, the vertical diffusion coefficient shows some variation but generally is confined in between 10 −3 𝑐 s 𝐻 g and 10 −2 𝑐 s 𝐻 g , with the maximum at 𝜏 s 0.3, while the radial diffusion coefficient shows monotonic increase with increasing 𝜏 s until 𝜏 s ∼ 1, where 𝐷 p, 𝑥 ∼ 10 −3 𝑐 s 𝐻 g . We note that in contrary to 𝐷 p,𝑧 > 𝐷 p,𝑥 in our Model B, previous vertically stratified simulations with 𝜏 s,max = 1 showed that 𝐷 p,𝑧 𝐷 p, 𝑥 (Bai & Stone 2010b;Schaffer et al 2018; see also Li & Youdin 2021), and we discuss this further in Section 4.5.…”

“…11. except for 𝐷 p,𝑧 of small particles (Bai & Stone 2010b;Schaffer et al 2018; see also Section 4.5 as well as Li & Youdin 2021).…”

“…Otherwise, a statistically steady state of the dust layer is maintained without any appreciable local dust concentrations. This critical solid-to-gas ratio depends on the dust size (Carrera et al 2015;Yang et al 2017;Li & Youdin 2021), the background radial pressure gradient (Bai & Stone 2010c), as well as the external turbulence (Yang et al…”

Dynamical Implantation of Blue Binaries in the Cold Classical Kuiper Belt

“…First, the surface density of solids would be boosted near 45 au, including the contribution from the cold finger effect (Drazkowska & Alibert 2017). This could potentially produce, if grains stick and grow to become large enough (Birnstiel et al 2016), favorable conditions for the streaming instability (Carrera et al 2015, Yang et al 2017, Li & Youdin 2021. Second, for temperatures below 30 K, CO can be destroyed on grains (chemistry mediated by cosmic ray ionization), producing CO 2 , CH 3 OH (methanol), and other hydrocarbons (e.g., Bosman et al 2018), all of which have relatively high sublimation temperatures and can remain on a surface.…”