The gas has another way to support itself
A pebble orbiting a young star mainly balances gravity with its orbital motion. Gas also feels pressure. Where pressure decreases outward, its outward pressure force supplies part of the support against gravity, and it can orbit a little more slowly than a solid body.
The pebble then feels a headwind. Drag removes orbital angular momentum, and the pebble spirals inward. This drift can carry growing solids toward the star before they assemble into much larger bodies. There is a broad range of particle sizes: tiny grains closely follow the gas, while larger pebbles can move appreciably through it.
Reading: Youdin & Goodman 2005, Streaming Instabilities, arXiv v1 · Youdin & Johansen 2007, Linear Evolution and Numerical Methods, v1
A pressure maximum reverses the push
Inside a local pressure maximum, pressure rises outward. The gas can orbit faster than a freely orbiting solid there. Drag acts as a tailwind, adding angular momentum and moving the solid outward. Outside the maximum, the usual headwind moves it inward. The two directions bring material toward the same region.
The pressure structure must come from somewhere. A planet can produce one, but so can other disk processes. Preparing a gas bump is a useful way to ask how solids respond after it exists. The motion and continuity of the solids then determine how much dust collects.
A trapped pile is not automatically permanent. Mixing can spread material, the gas structure can change, and the amount delivered depends on particle coupling. A useful experiment follows both the growing concentration and the gas that holds it.
Reading: Youdin & Johansen 2007, Linear Evolution and Numerical Methods, v1 · Huang et al.2018, DSHARP II Annular Substructures, v1
The dust can push back
Drag is mutual. As gas slows a pebble, that pebble pushes the gas the other way. The effect is small when solids carry little mass. It becomes important when the local dust density approaches or exceeds the gas density. The gas changes its orbital and radial motion, altering the drift of the next solids that arrive.
This feedback also permits a collective instability. A small density and velocity disturbance can draw energy from the relative gas–dust drift and grow. It is called streaming instability. Its simplest linear model has variation in both the radial and vertical directions and keeps all three velocity components. A purely radial traffic-jam picture leaves out motions needed for that growth.
The first growing waves are small perturbations. Following them into dense clumps requires a nonlinear calculation; deciding whether those clumps collapse requires self-gravity as well. A calculation of linear growth supplies one stage in this sequence.
Reading: Youdin & Goodman 2005, Streaming Instabilities, arXiv v1 · Youdin & Johansen 2007, Linear Evolution and Numerical Methods, v1 · Li & Youdin 2021, Thresholds for Particle Clumping, v2
What a bright ring tells us
ALMA can map millimeter-wave emission from young disks with narrow bright rings and dark gaps. A ring is a measured brightness structure. Converting it into a dust amount also requires temperature, opacity and optical-depth assumptions; measuring the gas pressure is a further step.
The public DSHARP Elias24 profile provides a concrete example. Its ring is visible in the measured radial intensity and remains separate from the synthetic gas and dust experiment. A similar-looking band in a model helps us form questions about trapping. To identify its origin in a real disk, we compare more than its appearance.
The later source guide follows this distinction through observed brightness, linear waves and thresholds for nonlinear clumping. Each stage brings in another piece of physics and another way to test it.
Reading: ALMA DSHARP official data release and revised radial profiles · Huang et al.2018, DSHARP II Annular Substructures, v1 · Li & Youdin 2021, Thresholds for Particle Clumping, v2