Planet formation works by dust collapsing on its own, not by gas turbulence
Purely hydrodynamic instabilities like VSI and COS stir dust back into the atmosphere and cannot make planetesimals; only letting dust feed back actively, or even letting gas accrete, can compress dust to collapse densities.
The argument · tap a timestamp to hear it
1% dust gets stirred back into the atmosphere by VSI
At the standard interstellar-medium dust-to-gas ratio of 1%, dust grains settle to the midplane and are quickly remixed back into the atmosphere by VSI, with no hope of forming planets. But raise the metallicity by a few times and the dust's feedback on the gas brings extra inertia, producing dust-induced buoyancy that lets a dust layer form. The key is that you do not need to reach a dust-to-gas ratio of 1, because the vertical shear itself is weak, so only a modest increase in metallicity makes the feedback important.
— Min-Kai LinVortices can catch dust, but not hard enough
Vortices appear ubiquitously in 3D VSI simulations, and they do collect dust, but the concentration falls far short of what direct gravitational collapse requires. In 2D axisymmetric simulations, as the dust content rises from 1% to 10%, the morphology shifts from non-axisymmetric vortices to a more axisymmetric ring-like disk. The author thinks this is worth exploring: connecting the large-scale morphology seen in the sky to underlying properties like the disk's dust-to-gas mass ratio.
— Min-Kai LinThe dust layer grows its own new vertical shear
If dust does settle to the midplane, the story is not over: the dense dust layer orbits at Keplerian speed while the pure gas above and below orbits sub-Keplerian, producing very strong vertical shear between the dust layer and the gas layers. Using Dedalus for a global eigenvalue analysis, the author finds a family of extremely unstable modes with growth rates on the orbital timescale, but with scales of only 10 to the minus three H, requiring very high resolution to capture. The author notes that spectral simulations a decade ago already found that this dust version of the vertical shear instability destroys the dust layer, but those were early simulations and deserve revisiting with modern codes.
— Min-Kai LinCollect too much dust and the zonal flow disappears
Simulations coupling Boussinesq gas with pressureless dust show that after the instability saturates, a pressure ring slowly forms and dust collects in the ring. But interestingly, once the dust grains become quite concentrated, the pressure ring instead disappears. Raising the background dust-to-gas ratio from 1% to 10%, nothing happens — no zonal flow forms at all. The author does not explain this rigorously, but the best guess is that the dust fluid's angular momentum flux is always more positive than the gas's, making the total angular momentum flux less negative than in the pure-gas case, thereby weakening the toy model of zonal flow formation.
— Min-Kai LinVortices form, but no pressure bumps appear
In the "local global" approach, the author stuffs a global disk into a box, controls the N² profile precisely, and makes N² negative only near X=0. Running 3D simulations of a 2×6 cube, each for about 2000 orbits, the author finds the disk must be unstable over a sufficiently large region to form vortices; below an empirical line it only saturates into an axisymmetric state, and doing 3D is pointless. But the most critical finding is that even when vortices form, no vortex signature can be identified in the pressure field at all — there is no pressure bump to act as a dust trap. More worrying still, merely changing the vertical boundary condition from periodic to fixed top and bottom lids makes the vortices disappear.
— Min-Kai LinGas accretion flows can push weak clumping into strong clumping
A protoplanetary disk is fundamentally an accretion disk, so accretion should be in the model. In Fargo simulations the author applies a torque to the gas so that it accretes toward the star, with no pressure gradient imposed; the system is then intrinsically unstable, forming dense filamentary structures with dust-to-gas ratios approaching or even exceeding 100, enough to expect gravitational collapse. At a parameter point with Stokes number 0.1 and very low metallicity, strong clumping was not expected, but adding the accretion flow lifts the system into the strong-clumping regime. The author attributes this to the accretion flow lowering the turbulence level, letting dust settle. And the effect is not monotonic: turn the accretion parameter up too far and you go back to the non-strong-clumping state.
— Min-Kai LinIdeal MHD simply erases the traditional SI
Extending the standard linear theory of magnetohydrodynamic flow instabilities from pure hydrodynamics to ideal MHD, adding the Lorentz force and the induction equation, the picture changes completely. MRI appearing is no surprise, and a new branch where Alfvén waves resonate with the dust-gas drift is no surprise either; what is genuinely surprising is that the original flow instability disappears entirely. If SI existed independently, it should survive even if not dominant, but it is actively suppressed by the Lorentz force (very likely magnetic tension). However, protoplanetary disks are far from ideal MHD, so the author turns to non-ideal MHD with kinetic dust.
— Min-Kai LinHall MHD lets even dust-poor disks clump strongly
Doing linear calculations in the Hall-effect anti-parallel case, besides the conventional flow instability and MHD waves, the author finds a new mode that can be reproduced with the standard Hall MHD equations plus an extra term representing the B field drifting through the dust-gas mixture. A new postdoc, Remis Actor, is running simulations with thermal diffusion: with no MHD almost nothing happens; under fully developed MRI turbulence, highly concentrated dust is obtained even without feedback; under Hall MHD, quite strong dust concentration is also obtained. The key is that the starting dust-to-gas ratio is only 0.2, very poor, yet dust feedback plus Hall MHD can still produce strong clumping.
— Min-Kai LinIn their own words · checked verbatim
in the standard case, particles get remixed into the atmosphere and there's no hope for planet formation.
Min-Kai Lin10:27
Do they trap particles? They do, but not very impressively.
Min-Kai Lin12:29
you create these zonal flows that collect dust particles, but if you collect too much dust particles, the zonal flows disappear.
Min-Kai Lin26:38
you cannot actually identify any vortex in the bottom plot. So there's there's no signature of a pressure extreme or a pressure bump in the pressure field.
Min-Kai Lin38:45
the presence of an accretion flow through the disk appears to promote clumping. That's the basic message.
Min-Kai Lin48:57
What is a little bit surprising is the complete lack of the original streaming instability as it goes from hydro to ideal MHD.
Min-Kai Lin54:01
even starting with such a dust poor condition, combination of dust feedback and Hall MHD appears to be able to give you very strong clumping.
Min-Kai Lin57:02
Figures
| Standard interstellar-medium dust-to-gas ratio | 1% | 10:27 |
| Scale of the dust version of the vertical shear instability | 10 to the minus three H | 14:29 |
| Dust-to-gas ratio in the simulations | from 1% to 10% | 12:29 |
| Dust-to-gas ratio in the accretion-flow simulations | approaching or even exceeding 100 | 47:56 |
| Plasma beta in the ideal MHD calculations | about 10 to the 5th power | 59:04 |
| Starting dust-to-gas ratio in the Hall MHD simulations | 0.2 | 56:02 |
Glossary
- VSI (vertical shear instability)
- A hydrodynamic instability driven by vertical shear arising from a radial temperature gradient, essentially inertial waves being destabilised.
- COS (convective overstability)
- A hydrodynamic instability in which fluid elements exchange heat with their surroundings as they oscillate radially, amplifying the oscillation through buoyancy.
- streaming instability
- An instability from two-way coupling between dust and gas, the leading theory for planetesimal formation.
- zonal flow
- Alternating super-Keplerian and sub-Keplerian angular velocity bands in the disk, corresponding to pressure variations, which can act as dust traps.
- Stokes number
- A dimensionless number describing how strongly dust grains couple to the gas, characterising grain size.
- resonant drag instability
- A modern framework explaining dust instabilities as a resonance between wave speeds and the dust drift velocity.
How to listen
Graduate students and postdocs doing numerical simulations of protoplanetary disks, planet formation or dust dynamics, and astrophysicists interested in how accretion flows and MHD affect planetesimal formation.
The conference introduction and planet formation review at the start, 0:18–6:21, can be skipped; go straight to the hydrodynamic instability part after 6:21.