--- title: "Gas, drifting pebbles and the first concentrations" description: "Derive gas–dust drift, evolve pressure traps, reproduce streaming growth rates and read real DSHARP rings beside nonlinear clumping thresholds." canonical_url: "https://sandboxphysics.com/stories/dust-gas/" language: "en" page_type: "story" alternate_languages: zh-CN: "https://sandboxphysics.com/zh/stories/dust-gas/" last_modified: "2026-10-28" --- AC14 # Gas, drifting pebbles and the first concentrations Sandbox Physics · 2026-10-28 Pressure changes the gas orbit; drag changes the pebbles. Follow a drifting mixture into a pressure trap, test a separate growing wave, and read an observed dust ring with its physical assumptions. 1. L1 ## [How pebbles collect in a planet-forming disk](https://sandboxphysics.com/stories/dust-gas/pebbles-in-a-headwind/) Gas can make pebbles drift inward, trap them at a pressure maximum and respond to their push. Follow the steps before gravitational collapse. 2. L2 ## [Derive the drift and the gas response](https://sandboxphysics.com/stories/dust-gas/drift-and-feedback/) Solve the four local force-balance equations for gas and dust, recover test-particle drift and follow mass-conserving trapping in a finite patch. 3. L3 ## [Give a streaming wave two directions to grow](https://sandboxphysics.com/stories/dust-gas/two-directions-to-grow/) Linearize coupled gas and dust around their drifting equilibrium, retain radial–vertical modes and derive a six-state growth problem. 4. L3 ## [Reproduce a streaming growth rate and a bounded patch](https://sandboxphysics.com/stories/dust-gas/streaming-replay/) Run independent six-root, eight-root, ODE and two-dimensional grid benchmarks with frozen inputs, then inspect numerical diffusion and failed limits. 5. L4 ## [Read dust rings and clumping thresholds without skipping a step](https://sandboxphysics.com/stories/dust-gas/rings-and-thresholds/) Read a real DSHARP brightness profile alongside fixed primary streaming papers, separating emission, linear growth, turbulent mixing and nonlinear clumping. [Move a pressure peak](https://sandboxphysics.com/labs/protoplanetary-dust-traps/) ## 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. [Benítez-Llambay, Krapp & Pessah 2019, FARGO3D multifluid tests, v3](https://arxiv.org/pdf/1811.07925v3) Version 3, 10 June 2019; ApJS 241, 25. Read Sections 3.4–3.5, Table 4, equation 86 and Appendix E. The temporal exponential uses the negative of the paper's eigenvalue; the complex growth eigenvalue used here has the opposite sign. Table 4 gives the full eight-state LinA growth rate as 0.4190091323 and LinB as 0.0154862262, matching the independent matrix. Section 3.5.3 attributes the small difference from the 2007 table to gas-density drag-feedback terms; this distinction is already established in that paper. 4. [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. 5. [Umurhan, Estrada & Cuzzi 2020, Streaming Instability in Turbulent Disks, v4](https://arxiv.org/pdf/1906.05371v4) 25 May 2020 version 4, PDF header 26 May. Sections 3.1–3.3, equations 4–18 and Appendix A: explicit viscosity, dust diffusion/pressure and equilibrium forcing; Section 5 interprets growth with a turbulent dilution model. The Lab’s equal damping of all linear fields is a much simpler declared teaching closure, not a reproduction of this alpha-disk model. 6. [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. 7. [DSHARP radial-profile original README](https://almascience.eso.org/almadata/lp/DSHARP/profiles/README_profiles) All eight column definitions, Jy/beam intensity/errors, Rayleigh–Jeans and full-Planck temperature conversions, negative-intensity NaNs and the August2019 radius correction propagated in February2020. Pointwise uncertainties are not an independent-bin covariance matrix. 8. [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. 9. [Andrews et al.2018, DSHARP I Motivation, Sample, Calibration and Overview](https://arxiv.org/abs/1812.04040) Published ApJL869,L41; the official public release requests this calibration/survey citation together with DSHARP II. Survey abstract, official release description and original Elias24 FITS header were consulted. We reuse the released profile and header, not its CASA calibration pipeline or visibilities.