Pressure Bumps and Dust Traps: Where Planets Get Their Building Blocks

What a pressure bump is and why dust cares about pressure

In a smooth disk, gas is partially supported outward by its own pressure gradient (pressure falls with radius), so the gas orbits slightly slower than the Keplerian speed — sub-Keplerian by a factor set by η ≈ (c_s/v_K)² × |d ln P / d ln r| / 2, typically η ≈ 0.001–0.005. Solid particles feel no pressure; they want to orbit at the full Keplerian speed. Moving faster than the gas, they feel a persistent headwind, lose angular momentum, and spiral inward.

The crucial insight is that dust drifts toward higher pressure. Wherever the radial pressure profile P(r) has a local maximum — a pressure bump — the gas there orbits at exactly the Keplerian speed (because locally dP/dr = 0), so the headwind vanishes. On the inner flank of the bump gas is super-Keplerian and pushes dust outward; on the outer flank it is sub-Keplerian and drags dust inward. Both flows converge on the peak. The bump therefore behaves as a dust trap, collecting solids from a wide swath of the disk into a narrow ring.

• Gas: pressure-supported, sub-Keplerian, smooth.
• Dust: no pressure support, drifts up ∇P toward the maximum.

The mechanism: radial drift and the drift-velocity law

The workhorse relation, derived by Weidenschilling (1977) and Nakagawa, Sekiya & Hayashi (1986), gives a particle's radial drift velocity as:

v_drift = −(2 η v_K) / (St + 1/St),

where St is the Stokes number — the ratio of the grain's aerodynamic stopping time to the local orbital time — and v_K is the Keplerian speed. The 1/(St + 1/St) factor peaks at St = 1, where drift is fastest and equals roughly η v_K.

• St ≪ 1 (small grains): tightly coupled to gas, drift ∝ St, very slow.
• St ≫ 1 (boulders): decoupled, drift ∝ 1/St, slow again.
• St ≈ 1: worst case — the notorious radial-drift / metre-size barrier.

A pressure bump defeats this because η is proportional to the local pressure gradient d ln P/d ln r. At the peak that gradient goes to zero and can even reverse sign, so v_drift → 0 and then reverses, pushing dust back toward the peak. The trap does not merely slow drift; it creates a stable equilibrium point where solids accumulate. The width of the accumulated dust ring is set by the balance between this trapping and turbulent diffusion, giving a Gaussian-like ring of width w ≈ H √(α/(α + St)), where H is the gas scale height and α the turbulence parameter.

Characteristic numbers and a worked example

Consider a disk around a 1 M_sun star with η ≈ 0.002 at 10 AU, where v_K ≈ 9.4 km/s. A centimetre pebble there has St ≈ 0.1, so:

v_drift ≈ 2 × 0.002 × 9400 m/s / (0.1 + 10) ≈ 3.7 m/s.

Over one orbital period (~30 yr, or ~10⁹ s) it moves ~3.7 × 10⁹ m ≈ 0.025 AU inward — meaning it crosses the whole 10 AU in only a few thousand orbits, well under 1 Myr. For St ≈ 1 the drift jumps to ~19 m/s, and the grain reaches the star in a few hundred orbits. This is why unaided growth stalls.

• Enrichment factor: a trap can raise the local dust-to-gas ratio Z = Σ_d/Σ_g from the interstellar ~0.01 to well above 0.1.
• Trigger for gravity: once Z locally exceeds the streaming-instability threshold Z_crit ≈ 0.01–0.02 (Carrera, Johansen & Davies 2015; Li & Youdin 2021), pebbles clump and collapse into 100 km planetesimals in a handful of orbits.
• Ring masses: observed dust rings hold tens to hundreds of Earth masses of solids — ample raw material for planetary cores.

How pressure bumps are observed — the ALMA ring revolution

The most famous demonstration came in 2014, when ALMA imaged the disk around HL Tau (~140 pc away, only ~1 Myr old) at ~5 AU resolution and revealed a stunning set of concentric bright dust rings separated by dark gaps. Surveys such as DSHARP (2018) then showed that such rings and gaps are ubiquitous, not exotic.

• Continuum rings: bright millimetre emission marks where large grains have piled up — the trap itself.
• Gas–dust size mismatch: the millimetre-dust disk is often far more compact and ring-like than the gas or the small-grain (scattered-light) disk, a smoking gun for radial trapping.
• Kinematic 'kinks': velocity perturbations in CO line data reveal the pressure-gradient changes and, in cases like HD 142527, dust trapping in an azimuthal vortex.
• Grain-size sorting: longer-wavelength (larger-grain) emission is narrower and better centred on the pressure peak than shorter-wavelength emission.

These signatures let observers infer where P(r) peaks and estimate how efficiently each ring concentrates solids.

What makes a bump — related mechanisms and cousins

Pressure bumps are an outcome; several distinct physical processes can create them, and it matters which one is acting:

• Planet-carved gaps: an embedded planet clears an annular gap; the gas pressure peaks just outside its orbit, trapping dust. This is the leading explanation for HL Tau-like rings, though it risks circular reasoning (you need a planet to make the trap that makes planets).
• Dead-zone edges: where the magnetorotational instability switches on/off, the change in turbulent viscosity α piles up gas and creates a bump.
• Ice lines (snow lines): across the water or CO condensation front, the sudden change in grain stickiness and gas surface density can seed a bump.
• Vortices: the Rossby-wave instability spins up anticyclonic vortices that trap dust both radially and azimuthally — 2D traps, seen as horseshoe-shaped asymmetries (e.g. IRS 48, Oph IRS 48).

Distinguish the dust trap from the broader radial-drift barrier (the problem it solves) and from the streaming instability (the gravity-collapse step it enables). The bump concentrates; the instability collapses.

Significance, famous cases, and open questions

Pressure bumps reframe planet formation: rather than solids growing uniformly everywhere, planet building is localized at a few special radii where traps live. This naturally explains why disks show a small number of well-defined rings, and it supplies the concentrated pebble reservoirs that feed rapid pebble accretion onto growing cores.

• Famous cases: HL Tau (the archetype), TW Hya (nested rings around a nearby ~10 Myr disk), HD 163296, and IRS 48 (an extreme azimuthal vortex trap).
• Open questions: Are most rings really carved by planets, or by ice lines and dead zones? How do bumps stay 'leaky' enough to let some dust through to inner planets, yet retentive enough to build planetesimals? What sets the lifetime and multiplicity of traps?
• Debate: whether streaming instability alone suffices inside traps, or whether self-gravity and turbulence set the true clumping threshold Z_crit — and how dust back-reaction (the drag dust exerts on gas) reshapes the bump.

The trap is now the standard bridge across the metre-size barrier, but the details of who digs the trap, and how efficiently it converts pebbles to planetesimals, remain frontier research.

Radial drift regimes by Stokes number St (ratio of a grain's aerodynamic stopping time to the orbital time), for a typical disk with η ≈ 0.002 and v_K ≈ 9.4 km/s at ~10 AU.

Grain / regime	Stokes number St	Coupling to gas	Approx. radial drift speed	Fate without a trap
Micron dust (ISM-like)	~1e-6 – 1e-4	Perfectly coupled	≪ 1 cm/s	Drifts negligibly; grows slowly
Millimetre grains	~1e-3 – 1e-2	Well coupled	~1–10 m/s	Slow inward drift over Myr
Centimetre–decimetre pebbles	~0.1 – 1	Marginally coupled	tens of m/s (peaks near St=1)	Lost to star in 100s–1000s of orbits
'Metre-size' boulders	~1 – 10	Decoupling	maximal, ~19 m/s at St=1	Fastest drift + destructive collisions
Trapped pebbles in a bump	~0.01 – 1	Coupled to gas peak	→ 0 at the pressure maximum	Accumulate → planetesimals