AC14 · Gas pushes back

Protoplanetary Dust Traps

How can drifting pebbles collect before they fall toward the star? Pressure changes the gas's orbital speed. Drag can then remove or add angular momentum, drawing solids toward a pressure peak. Concentrated dust pushes back on the gas and changes the drift. Trapping can feed further growth. Streaming instability is a separate collective instability requiring two-way drag and radial and vertical motion; gravitational collapse needs additional physics.

Prepare a gas pressure peak, move it through a dusty patch and watch mutual drag reshape both fluids. Then follow a separately labeled linear streaming mode.

Elapsed inverse angular frequency $8.00$

Dust peak / initial mean $1.74$

Largest gas radial speed · sound speed $0.00508$

Peak dust / gas density $0.356$

Move the pressure peak

Stopping time

0.3

\mathrm{St}=\Omega t_{\rm stop}

Initial dust / gas mean density

0.3

\epsilon_0

Prepared gas log-density contrast

0.6

A

Drag the pressure marker sideways to prepare a new gas peak. Warmed-up gas and dust then evolve together.

Initial position and physical limits

Prepared peak radial position

0

x_{\rm peak}/H

The radial gas pressure follows its evolved isothermal density; the prepared peak is not continually forced. Numerical fluxes smooth sharp structures. This one-velocity dust fluid covers early drift/trapping, not crossing particle streams or gravitational collapse. The separate linear mode has both radial and vertical dependence, no vertical stratification, and a declared small-amplitude stop.

Follow the drift and streaming course

Model assumptions

Synthetic bounded models. The default is an evolving one-dimensional radial isothermal-gas/pressureless-dust finite-volume patch with periodic boundaries and actual two-way drag. Moving the pressure marker prepares a new gas initial condition; the gas peak subsequently evolves freely. This radial trap is not streaming instability. The separate radial–vertical preset integrates the full linear incompressible two-fluid Fourier mode and stops at a small density contrast; it does not model nonlinear saturation or gravitational collapse. Stopping time is fixed, dust has one velocity per point and steep multistream states are outside the interpretation. Isothermality removes heat; numerical diffusion is measured separately from physical turbulence. No observed disk image, planet formation or ALMA inference is computed in this Lab.

Evolving radial pressure trap; this model does not contain streaming-instability modes.

Cyan marks gas and amber marks dust. Dots sample the saved fluid densities; short trails use local velocities. They are density tracers, not resolved grains or an observed ALMA image. The linear view instead shows an actual radial–vertical density perturbation with a fixed enlarged color scale.

Density profiles

Radial motion

Conservation, resolution and boundaries

The radial patch has128 cells and periodic boundaries. Its default dust-density relative L1 difference from a1024-cell reference is2.92percent at eight inverse angular frequencies; peak height differs by about6.1percent. These are numerical resolution differences, not physical error bars. The linear experiment retains one periodic mode with three velocity components per phase, stops at ten percent dust contrast or ten inverse angular frequencies, and uses a simple equal diffusion on perturbations rather than a complete turbulent disk model.

Start with the essentials

Focus question: Which way do solids drift on each side of a pressure maximum?
One-sentence intuition: Drag feeds back on the gas; a linear instability also needs the right spatial modes.

Core mathematical model

Stopping time

\mathrm{St}=\Omega t_{\rm stop}

Compare drag relaxation with orbital angular time. The Stokes number does not by itself specify a grain radius.

Test-particle radial drift

v_{{\rm d},x}=-\frac{2\mathrm{St}}{1+\mathrm{St}^2}\eta v_{\rm K}

Without feedback, drift is fastest near a stopping time of one inverse angular frequency. The pressure-gradient sign reverses at a maximum.

Equal and opposite momentum exchange

\rho_{\rm g}\mathbf a_{{\rm g},D}+\rho_{\rm d}\mathbf a_{{\rm d},D}=0

Drag is internal to the mixture and conserves its total momentum.

Common difficulties

A trap is a different experiment

Typical misconceptionAny growing dust peak is streaming instability.

Better mental modelA radial trap can collect material through a prepared gas structure. The separate streaming mode retains radial and vertical motions and tests a linear eigenvalue.

Run the experiment

01
Move the pressure structure
Drag the pressure marker sideways and watch the warmed-up density band.
What to observe: The gas initial condition moves; dust accumulates through the subsequent computed flow.
02
Change coupling
Compare Tightly tied grains and Rapidly drifting pebbles at the same pressure contrast.
What to observe: Different stopping times change relative motion and the amount collected in the same time.
03
Let the gas respond
Select Dust pushes the gas. Compare both density and velocity curves.
What to observe: More dust changes the gas motion and reduces radial drift; the gas is evolved rather than held as an unchanged background.
04
Test a separate wave
Choose A linear streaming wave, then Diffusion damps the wave. Read the orientation and unit changes.
What to observe: The small-amplitude radial–vertical mode grows or damps according to the integrated two-fluid equations.

Protoplanetary Dust Traps

Follow the gas as well as the dust

Core mathematical model

Stopping time

Test-particle radial drift

Equal and opposite momentum exchange

Common difficulties

A trap is a different experiment

Run the experiment

Move the pressure structure

Change coupling

Let the gas respond

Test a separate wave

Related experiments and articles

Gas, drifting pebbles and the first concentrations