--- title: "How pebbles collect in a planet-forming disk" description: "Gas can make pebbles drift inward, trap them at a pressure maximum and respond to their push. Follow the steps before gravitational collapse." canonical_url: "https://sandboxphysics.com/stories/dust-gas/pebbles-in-a-headwind/" language: "en" page_type: "story" alternate_languages: zh-CN: "https://sandboxphysics.com/zh/stories/dust-gas/pebbles-in-a-headwind/" last_modified: "2026-10-28" --- [Gas, drifting pebbles and the first concentrations](https://sandboxphysics.com/stories/dust-gas/) AC14 · L1 # How pebbles collect in a planet-forming disk Sandbox Physics · 2026-10-28 A gas pressure maximum can collect drifting solids because the gas pushes them toward it from both sides. Once enough dust gathers, its drag also changes the gas. These processes help material stay together long enough for later growth. ## Before you begin A qualitative idea of orbital motion and pressure. The next chapters introduce stopping time, force balance and linear growth. ## 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 ## Exercises and explanations 1. Why do particles on opposite sides of a pressure maximum drift toward the same location? Read the explanation The sign of the pressure gradient changes. Inside the maximum the faster gas adds angular momentum to solids, moving them outward; outside it the slower gas removes angular momentum, moving them inward. ## Try the prediction ### [Prepare a pressure trap](https://sandboxphysics.com/labs/protoplanetary-dust-traps/) 1. Watch the default amber concentration, then drag the pressure marker sideways. The new gas profile is prepared first and the dust is evolved afterward. 2. Compare Tightly tied grains with Rapidly drifting pebbles. Keep the prepared gas contrast fixed and explain the different concentration. 3. Choose A linear streaming wave. Notice the changed radial–vertical orientation and the small-amplitude stopping rule. [Next: Derive the drift and the gas response](https://sandboxphysics.com/stories/dust-gas/drift-and-feedback/) ## Sources and calculation scope 1. [Youdin & Goodman 2005, Streaming Instabilities, arXiv v1](https://arxiv.org/pdf/astro-ph/0409263v1) 10 September 2004 version 1; ApJ 620,459–469(2005). Full text read, Section 2 equations 1–7/12–17/24–31, Figures 1–3 and Section 4 mode geometry; Section 5 equation 39 and its restricted terminal-velocity domain; Section 6 distinguishes arbitrary linear amplitude from subsequent collapse. The PDF itself prints a later Draft Modified July 5, 2018 header; the archive version is explicitly frozen. 2. [Youdin & Johansen 2007, Linear Evolution and Numerical Methods, v1](https://arxiv.org/pdf/astro-ph/0702625v1) 23 February 2007 version 1; ApJ 662,613–626. Sections 2.1–2.3 equations 1–14, Table 1 and Section 4/Figures 4–5. Fixed stopping time, two-way drag, three velocity components with radial–vertical dependence, finite-resolution eigenmode tests and weakly compressible published roots. Section 2.3 explicitly explains why steady radial traffic-jam arguments alone do not produce linear SI growth. 3. [Li & Youdin 2021, Thresholds for Particle Clumping, v2](https://arxiv.org/pdf/2105.06042v2) 14 October 2021 version 2; DOI 10.3847/1538-4357/ac0e9f. Full-text Sections 2,3.1–3.5 and 4: stratified simulation setup, surface metallicity versus volume loading, threshold map Figure 1, linear-growth maps Figure 7 and clumping comparison Figure 8. Equation 21 diffusion diagnostic fails to predict all nonlinear stratified clumping, explicitly cautioning against universal linear thresholds. 4. [ALMA DSHARP official data release and revised radial profiles](https://almascience.eso.org/almadata/lp/DSHARP/) Project2016.1.00484.L, release snapshot28October2026. Exact Elias24 ASCII profile last-modified5August2019, all300rows/eight columns; original README updated5February2020; exact8640-byte FITS primary header bounded-range fetched, no image pixels. Hashes, units, source terms and observing/header metadata are retained in the public package. 5. [Huang et al.2018, DSHARP II Annular Substructures, v1](https://arxiv.org/pdf/1812.04041v1) 10December2018 version 1; ApJL869,L42. Full-text Section 3.1 radial-profile construction and Section 5 interpretations; annular emission can have multiple origins. The real Elias24 brightness profile is read separately from the synthetic gas/dust calculations. DSHARP I, ApJL869,L41, is also cited by the official release for calibration/beam provenance.