1. Magnetic Activity and the Separation of Dust from Gas
Padgett et al. 1999
Neal Turner (Jet Propulsion Lab., Cal. Tech.)
with Takayoshi Sano, Augusto Carballido,
and Geoff Bryden, Jim Drake, Natalia Dziourkevitch, Hubert Klahr, Katherine Kretke, Doug Lin
Copyright 2009, California Institute of Technology. Government sponsorship acknowledged.

2. Three topics: Settling and Stirring Radial Transport
Infrared Variability
All 3 topics are related to the movements of dust grains in magnetized protostellar disks. All 3 draw on a single set of MHD calculations.
First, some motivation and an outline of the methods.

3. Cotera et al. 2001
Guilloteau et al. 2008
Hubble Heritage
Scattered and reprocessed starlight indicate micron-sized dust remains suspended in protostellar disk atmospheres for several Myr. At the same time, mm measurements show that some particles in the disk interior have grown to sand or pebble size.
Burrows et al. 1996

4. Turbulence is Needed to Keep Dust Suspended
Dullemond & Dominik 2004
Models of coagulation in laminar gas indicate the dust quickly grows and settles out, leaving the atmosphere optically thin, in conflict with what’s seen.

5. Turbulence Halts Particle Growth
Brauer et al. 2008
Yet with turbulence at levels suggested by disk evolution timescales, disruptive collisions halt growth of larger bodies. These difficulties can be resolved by a midplane dead zone with weaker turbulence.
Note that even if alpha-->0, growth can be prevented by fragmentation due to differential radial drift. A weakening of the turbulence is necessary but not sufficient for growth past cm!

6. Ionization and the Dead Zone
At 1 AU in the minimum mass Solar nebula
Stellar X-Rays
Interstellar Cosmic Rays
Short-Lived Radionuclides
Ionized mostly by CRs to 100 g/cm^2 with low fluxes, and X-rays to 10 g/cm^2 at higher rates. X-rays from Monte Carlo transfer calculation including scattering, by Igea & Glassgold At the high densities, recombination occurs mostly on grain surfaces.
Midplane ionisation is weak!
Long-Lived Radionuclides

7. Ionization—Recombination Reaction Network
Involves 12 species: H2, H2+, Mg, Mg+, e-, grains charged by up to +/-2 electrons, and grain-adsorbed H2 and Mg
X-Ray Ionization
Dissociative Recomb.
X-rays + CRs + RNs ionize H2. The ions recombine in usual way, or exchange charge with a metal atom. Radiative recomb. of metals slow so Mg+ long-lived. Grains mediate recombination when dust abundance within few decades of ISM.
Ilgner & Nelson found this simple model gives results similar to a detailed network of 2000 reactions.
Radiative Recomb.
Charge Exchange
Ilgner & Nelson 2006a

8. 1% of 1mm dust
Dead zone in MMSN computed using IN06a recombination network with the simple gas-phase chemistry. DZ extends up to 10 g/cm^2 and out to Saturn’s orbit.

9. Calculation Ingredients
Azimuth y
Calculation Ingredients
Magnetic forces drive turbulence through the magneto-rotational instability.
The Ohmic resistivity varies inversely with the ionization fraction and can shut off MRI.
Stellar X-ray ionization having an absorbing column 8 g cm-2 competes with recombination on grains.
Grains 1 mm in radius are initially well-mixed and settle at terminal speed.
The domain is a patch of the minimum mass solar nebula lying at 5 AU.
Height z
To Star
1 AU zones 16
1 AU 64 zones
We examine settling & turbulent stirring with 3-D MHD calculations of a small disk patch, treating (1) turbulent stresses from magneto-rotational instability; (2) Ohmic resistivity, which can shut down turbulence; (3) ionization & recombination reactions, incl. stellar X-ray ionization & recombination on grains (the most important processes controlling the resistivity); and (4) settling of grains through gas.
r / g cm-3
0.25 AU zones
Radius x 8
Boundaries Radial: shearing-periodic Azimuthal: periodic Vertical: outflow, no inflow

10. Terminal speed
Dust in MHD runs settles at terminal speed, found by balancing gas drag with gravity. Settling time = height / terminal speed is inversely proportional to the stopping time.
Use rhod=5 to see settling in half as many orbits. Notice stopping time < 1 orbit below 4H, so quickly reach vT. Even 1-um grains settle ~0.3H per orbit at z=4H.
100 mm
10 mm
1 mm

11. Settling and Stirring

12. 100 mm
10 mm
1 mm
Magnetic support allows the density to fall off slower with height than in the initial condition, reducing settling speeds in the atmosphere. Reduction is a factor of 5 to 8 at z=4H.
Grey bars show time-averaged dead zones.

13. Meanwhile, density fluctuations driven by the magnetic forces increase mean settling speeds. Net result is settling at 4H several times slower than in the Gaussian density profile.
10 mm
1 mm
100 mm

14. Settling in a Hydrostatic Disk
1 mm grains
With no turbulence, initially well-mixed dust settles fastest in the outer layers, where the gravity is strong and the low density means weak gas drag.
Settling is quick: the last snapshot is at just 60 orbits. Coagulation can make the settling faster still, but here we assumed the particles do not stick to one another.

15. Settling with Turbulence and a Dead Zone
With turbulence, the more-settled material is mixed down to denser layers, leading to faster concentration of the solids there.
This contradicts the usual wisdom that turbulence counteracts settling.

16. Dust-to-gas mass ratio vs. time at 3 heights: 2. 5, 1. 5 and 0 H
Dust-to-gas mass ratio vs. time at 3 heights: 2.5, 1.5 and 0 H. Blue lines: laminar, with outflow. Red lines: MHD results. Dust abundance at midplane follows laminar curve: settling of dust deep in DZ is unaffected by turbulent layers.

17. Particles near dead zone boundary can cross it both directions
1 mm grains
Particles near dead zone boundary can cross it both directions
We also tracked individual dust grains, finding that they are carried in and out of DZ when turbulent gas motions overshoot DZ boundary.
Notice grains near midplane oscillate vertically.

18. 1 mm grains
Compare results with different grain sizes, hence different dead zone depths. (1) 1-micron grains.

19. 10 mm grains
(2) 10-micron grains.

20. 100 mm grains
(3) 100-micron grains. Conclude that vertical transport by turbulence extends about 1H into dead zone.

21. 100 mm
10 mm
1 mm
Mean stress increases w. active layer thickness. Height-integrated accretion rates 2, 3, 7x10^-8 Solar masses/yr.
Dead zone gas oscillates in (1) MHD waves launched in turbulent layers, (2) vertically-symmetric density waves, (3) magnetic stresses associated with weak large-scale fields. The flows are not overturnings! Stress ~ independent of z in DZ.

22. 1 mm grains
Total x y z
RMS flow speed ~ 700 m/s at 4H and <20 m/s at midplane.

23. Radial Transport

24. Wild-2 samples include crystalline silicates, indicating temperatures ~1000 K found only very near the star. Yet the comets formed at 5-40 AU where temperatures were much lower. Outward transport required. Problem: midplane transport ineffective. I suggest transport occurs in the magnetically-active disk atmosphere.
Zolensky et al. 2006

25. 1 mm grains

26. after 2 orbits
Particles crossing top and bottom boundaries are placed at midplane. Periodic structure near top due to kz=0 density waves.

27. after 4 orbits
Grains spread radially in atmosphere, while oscillating in dead zone. Thickness of midplane dust layer set by waves launched from atmosphere.

28. Particles with 3<z/H<4
Grains in atmosphere sometimes move at sound speed, traveling distance to the star in few orbits.

29. Particles with 3<-z/H<4
Movements will probably be weaker in global calculations, but so far are not much weaker with domain 4x wider.

30. Infrared Variability

31. Luhman et al. 2008
About half of young stars with disks in Taurus that were observed more than once with Spitzer IRAC show variability.
Given limited sampling, probably a majority of accreting young stars vary in the near- to mid-IR.

32. Variability timescales are as short as a day, which is less than an orbit at the dust sublimation radius.
I would like to show how the variability can come from the stirring of dust by magnetic activity in the starlit disk atmosphere.
LRLL 31
Muzerolle et al. 2009

33. 1 mm grains
Shows how the dust abundance varies over time in the run with settling 1-um grains. Gas becomes more dusty at base of the layer with magnetic pressure high relative to gas pressure. Reason: MRI turbulence shuts down, density is low, grains settle.

34. Dust-to-Gas Mass Ratio
Movie of last 9 orbits. Toroidal fields grow strong through shear, forcing gas to expand. Dust builds up near stagnation point which now lies within the domain. Grains settle quickly, forming a thin dusty layer. Layer mixes with deeper material. Fields become buoyant and escape. Gas rising into the void carries the dust back up.

35. 1000 cm2 g-1 100 cm2 g-1 1 mm grains 10 cm2 g-1
Disk photosphere height varies over time by about a scale height, depending on opacity: 1000, 100 and 10 cm^2 per gram of dust.
Geometric cross-section 1500 cm^2/g for the 1-µm grains. 10-um opacity 982 cm^2/g for grains in dense molecular cloud cores.
10 cm2 g-1

36. gas dust at z = 3.75 H 1 mm grains
Shows extinction variations that in a global model could lead to changes in the size and shape of the shadows cast on the outer disk.
Radial column of gas (black) and dust (red) in the rotating frame, 3.75H above the origin. Dust column varies by factors of 2 on timescales down to 0.1 orbit.
1 mm grains

37. Conclusions
Active layers with a dead zone can explain several features of the dust in protostellar disks:
The turbulent layers keep some dust aloft while planet formation proceeds in the dead zone.
Magnetic stresses in the atmosphere transport particles over long distances.
Grains in the active layers move in and out of the starlight, contributing to the IR variability.