Streaming instability

The streaming instability operates when solid particles in a protoplanetary disk experience aerodynamic drag from the surrounding gas. Because the gas is partially pressure-supported, it orbits at slightly less than the Keplerian speed, while particles, feeling no pressure, tend to orbit faster. This differential motion causes particles to drift inward and lose angular momentum to the gas. The instability feeds on this relative motion: a local concentration of particles reduces the local gas density, which increases the gas's orbital speed, thereby reducing the drag on the particles and allowing them to stay concentrated. This positive feedback amplifies density fluctuations, leading to the formation of dense particle clumps.

The linear growth of the streaming instability was first analyzed by Youdin and Goodman in 2005, and the nonlinear outcome was demonstrated by Johansen and Youdin in 2006 using numerical simulations. The instability requires a particle-to-gas mass ratio of order unity in the midplane, which is plausible in the inner regions of protoplanetary disks, especially after radial drift concentrates solids.

The streaming instability is widely regarded as the most promising mechanism to overcome the barriers to planetesimal formation. The classical growth by coagulation stalls at centimeter sizes due to bouncing and fragmentation, and radial drift removes particles inward too quickly. The streaming instability bypasses these issues by directly forming gravitationally bound clumps from small particles, which then collapse into planetesimals of sizes ranging from 100 km to 1000 km.

Simulations show that the clumps can reach densities high enough for gravitational collapse, producing planetesimals with a size distribution that matches the observed Kuiper Belt and asteroid belt populations. The efficiency of the process depends on the local disk conditions, such as turbulence level and particle size distribution. The instability is particularly effective for particles with Stokes numbers near unity, meaning they are marginally coupled to the gas.

Direct observational evidence for the streaming instability is challenging, but indirect support comes from the existence of planetesimals and the properties of dust in protoplanetary disks. The size distribution of Kuiper Belt objects, with a deficit of small bodies, is consistent with a formation by gravitational collapse rather than coagulation. Also, the presence of pebble-sized particles in disks, as inferred from millimeter observations, suggests that the conditions for the streaming instability are met.

The instability has implications for the formation of gas giants, as it can rapidly produce massive cores that accrete gas before the disk dissipates. It also influences the chemical composition of planetesimals, as the collapse process can trap volatiles. Recent studies have explored the role of the streaming instability in the formation of planetesimals in the outer solar system, including the building blocks of comets.

One lesser-known aspect is that the streaming instability can also operate in the presence of a magnetic field, leading to a hybrid instability that may be important in magnetized disks. Another is that the instability can produce a bimodal size distribution of planetesimals, with a population of small bodies and a population of large ones, which may explain the dichotomy in the asteroid belt.

The instability was originally discovered in the context of Saturn's rings, where similar drag instabilities were studied, but its application to planetesimal formation was a later development. Also, the nonlinear saturation of the instability can lead to the formation of particle streams that persist for long times, which may be observable as asymmetries in disk emission. Recent work has shown that the streaming instability can be triggered by the presence of a pressure bump, such as those created by a planet, which can concentrate particles and initiate the instability.

Planetesimal

A solid object formed during the early solar system, ranging in size from meters to hundreds of kilometers, that can accrete to form planets.

Aerodynamic drag

The force exerted by a gas on a solid particle moving relative to it, which causes the particle to lose or gain angular momentum.

Protoplanetary disk

A rotating disk of gas and dust around a young star, from which planets form.

Stokes number

A dimensionless number characterizing the coupling between a particle and the gas; a Stokes number near unity means the particle is marginally coupled.