Dust Radial Drift: Why Millimeter Grains Spiral Into the Star

What radial drift is and why gas is the culprit

Radial drift is the steady inward loss of solid particles from a protoplanetary disk — the flattened cloud of gas and dust that swaddles a newborn star. The gas dominates the mass (roughly 99% gas, 1% dust by the interstellar ratio), and it is the gas that sets the trap.

Gas in the disk is supported against the star's gravity by two forces: the outward centrifugal effect of its orbital motion and its own outward-pointing radial pressure gradient. Because pressure decreases outward, it lends the gas a little extra support, so the gas can orbit slightly slower than a free-falling body would — it is sub-Keplerian.

Solid grains feel no pressure. Left alone, a dust particle wants to travel at the full Keplerian velocity v_K = √(GM/r). It therefore orbits faster than the surrounding gas and runs headlong into a persistent headwind. Aerodynamic drag against that headwind removes the grain's orbital angular momentum, so it cannot maintain its orbit and spirals in. The dust is not falling because gravity increased — it is falling because friction is bleeding away the very motion that held it up.

The mechanism: headwind, drag, and the Stokes number

Quantify the headwind with the dimensionless factor η (eta), the fractional sub-Keplerian lag: η = −(1/2)(H/r)² · (d ln P / d ln r), where H/r is the disk's aspect ratio (typically 0.03–0.1). The headwind speed is Δv = η·v_K, and remarkably, in a Minimum Mass Solar Nebula it stays nearly constant at Δv ≈ 50–53 m/s across the disk.

How a grain responds depends on the Stokes number, St = t_stop · Ω_K — the aerodynamic stopping time measured in orbits. The drift velocity is:

• v_drift ≈ −2·St / (1 + St²) · η·v_K (for the dust, ignoring gas inflow)

This function peaks sharply at St = 1, where v_drift ≈ −η·v_K ≈ −50 m/s. Tiny grains (St << 1) are glued to the gas and barely drift; huge bodies (St >> 1) decouple and orbit almost Keplerian, so drift fades again. The danger zone is the crossover — roughly centimeter-to-meter sizes at a few AU — exactly the sizes a growing planet must pass through.

Characteristic numbers and a worked example

Take a 1 M_sun star and a marginally coupled grain (St = 1) at r = 1 AU. The Keplerian speed is v_K ≈ 30 km/s. With η ≈ 1.6×10⁻³, the headwind is Δv ≈ 50 m/s, and the peak drift speed is also ≈ 50 m/s.

The inspiral time is roughly the radius divided by the drift speed:

• t_drift ≈ r / |v_drift| = (1.5×10¹¹ m) / (50 m/s) ≈ 3×10⁹ s ≈ 100 years.

Equivalently, that is only about ~100 orbits. Compare this to:

• The disk gas lifetime: ~1–10 million years.
• The time to grow a grain from meter to kilometer size by sticking collisions: far longer than 100 orbits in most models.

The mismatch is brutal. A meter-sized boulder at 1 AU is removed some ten thousand times faster than the disk itself disperses, and faster than collisional growth can lift it out of the drift-prone size range. This is the essence of the meter-size barrier (or 'drift barrier'): solids are swept into the star before they can become planetesimals.

How it's observed: ALMA rings and the size problem

Radial drift was theoretical for decades, but the Atacama Large Millimeter/submillimeter Array (ALMA) made its consequences visible. Millimeter-wave continuum emission traces exactly the mm-to-cm grains most vulnerable to drift.

Two lines of evidence stand out:

• Compact dust vs. extended gas. In many disks the mm-dust disk is much smaller in radius than the gas disk (traced by CO). This size dichotomy is a smoking gun for inward drift concentrating the large grains.
• Bright rings. The landmark 2014 ALMA image of HL Tau revealed a series of concentric bright and dark rings. The bright rings are interpreted as pressure bumps — local maxima in gas pressure where dP/dr flips sign, halting drift and trapping grains. Disks like TW Hya, HD 163296, and DS Tau show the same structures.

Multi-wavelength spectral index measurements (comparing flux at, say, 1.3 mm and 3 mm) constrain grain size: values near α ≈ 2 in the rings indicate grains grown to millimeters or larger, precisely where they should have drifted away — evidence that traps are actively retaining them.

Related regimes and how drift differs from its cousins

Radial drift is one of several ways a disk loses or redistributes solids, and it is easy to confuse with its relatives:

• Vertical settling. Grains also sink toward the disk midplane as the vertical component of gravity overcomes weak drag. Settling concentrates dust into a thin layer; drift then moves that layer inward. Settling is vertical, drift is horizontal.
• Gas viscous accretion. The gas itself spirals onto the star via turbulent viscosity, but on the ~Myr disk timescale — far slower than the ~100-yr dust drift. Well-coupled small grains partly ride this slow gas flow.
• Fragmentation / bouncing barriers. These limit growth by collisional destruction rather than transport. The drift barrier removes material; the fragmentation barrier shatters it. Together they form the broader 'meter-size barrier.'
• Type I/II planet migration. That is a fully formed planet exchanging angular momentum with the disk gravitationally — a different physical channel entirely, though it shares the theme of inward drift.

Proposed escapes from drift include pressure traps at bump/gap edges, snow lines, and the streaming instability, which lets locally over-dense dust collapse gravitationally into ~100-km planetesimals in a few orbits — outrunning the drift clock.

Significance, famous cases, and open questions

Radial drift reframed the central puzzle of planet formation. Weidenschilling's 1977 analysis (building on Adachi, Hayashi & Nakazawa 1976) showed that the standard growth-by-sticking scenario has a fatal bottleneck: solids vanish into the star before reaching planetesimal size. Every modern theory must explain how nature beats the clock.

Landmark cases and lines of attack include:

• HL Tau (2014): the ALMA image that turned drift from equation to picture, launching a decade of dust-trapping studies.
• Pebble accretion: the same drifting pebbles that threaten to be lost can, if a planetary embryo already exists, be efficiently captured — turning the drift problem into a delivery mechanism (Ormel & Klahr 2010; Lambrechts & Johansen 2012).
• Streaming instability and pressure traps as the leading routes past the barrier.

Open questions remain sharp: What creates the pressure bumps — embedded planets, snow lines, or magnetized dead zones? How much does turbulence stir grains out of the peak-drift regime? And does the streaming instability need pre-concentrated dust that only traps can supply? Radial drift is settled physics; how planets survive it is very much unsolved.

Radial drift regimes by particle size, indexed to Stokes number (St) for a Sun-like star near 1 AU. St = t_stop × Ω_K couples aerodynamic stopping time to orbital frequency; drift peaks at St ≈ 1.

Particle size	Stokes number St	Coupling to gas	Radial drift behavior
Sub-micron to ~10 μm	St << 1 (10⁻⁶–10⁻⁴)	Perfectly entrained	Moves with gas; negligible drift
~0.1–1 mm	St ~ 10⁻³–10⁻²	Well coupled	Slow inward drift over Myr
~1 mm–1 cm	St ~ 10⁻²–0.1	Marginally coupled	Drift becomes significant; rings form
~10 cm–1 m	St ≈ 1	Marginally coupled — peak drag	Maximum drift, ~50 m/s; ~100 yr inspiral
~10 m–1 km	St >> 1	Decoupled from gas	Nearly Keplerian; drift slows again