Non-ideal MHD and the Formation of Disks

Shantanu BasuWestern University, London, Ontario, Canada

Wolf Dapp (Juelich Supercomputing Centre, Germany), Matt Kunz (Princeton Univ., USA)

Magnetic Fields Workshop, HeidelbergThursday, May 23, 2013

• resolve ‘Second Core’

• disks can form, albeit initially small

Usual approachNon-ideal MHD down to stellar core

• several AU-sized sink cells

• no disk formation found

AU-sized ‘sink cell’

resolution down to

stellar size

proto-star; hydrostatic object of stellar

dimensions;density >~1020 cm-3

(for realistic magnetic field strength, e.g., Mellon & Li, Hennebelle & Ciardi)

slide courtesy Wolf Dapp

Methodology• model core collapse to onset of disk formation• axisymmetric ‘thin-disk’ model, aligned rotator• adapting logarithmic grid ensures high resolution

down to stellar core, size ~ Rsun

• chemical multi-fluid model (up to 19 species), grain physics, inelastic collisions to determine partial ionization

• ambipolar diffusion (AD) + Ohmic dissipation (OD)

• barotropic pressure-density relation• magnetic braking in steady-state approximation

- 40

-2

0

0

20

40

AU

0 20 40 60 80 • Dashed lines are for flux-freezing model (no magnetic diffusion)

extreme flaring of field lines long lever arm magnetic braking catastrophe• Solid lines are for model with magnetic diffusion - field lines more relaxed (straight)

Second core located at origin

- 4

-2

0

2

4

AU

0 2 4 6 8 10 AU

Magnetic Field Lines

Mass-to-flux ratio

1. Prestellar core collapse profile2. Magnetic diffusion shock3. Expansion wave outside first

core4. First core at ~ 1 AU5. Collapse profile within first

core6. Second expansion wave

outside second core7. Second stellar core, size ~ Rsun

Column Density Profile

Disk formation

gravitational instability

• introduction of sink cell after 2nd core formation (few Rsun)

• centrifugal balance is achieved, and disk fragments into ring

magnetic braking

catastrophe

centrifugal balance

Nco

lum

n de

nsity

/ c

m-2

1. UV ionization2. cosmic ray ionization3. ionization due to radiation liberated in radioactive decay4. thermal ionization through collisions

Chemistry Ionization balanceDetailed chemical network with at least nine charged species including grains and the effects of radiative and dissociative recombination of ions and electrons, charge exchange b/w atomic and molecular ions, absorption of charge onto grains, and charge exchange b/w grains. Ionization sources are:

charge adsorption onto grains

electron-ion recombination

cosmic ray shielding

radioactive decay

thermal ionization

Effective (total) diffusion coefficient

2

4eff AD OD

cD

Fixed grain size agr or MRN distribution

charge adsorption onto grains

thermal ionization followed by

destruction of grains

Ohmic dissipation vs Ambipolar Diffusion

OD dominates within AU scale and shuts off magnetic braking in this region. Without OD, catastrophic magnetic braking occurs within 1 AU and all the way to stellar surface.

Key Conclusions

• Disk forms at earliest times even for aligned rotator, the most difficult geometry for disk formation according to Hennebelle & Ciardi (2009) and Li, Krasnopolsky, & Shang (2013)

• Expect small “initial” disk of several AU size, within Ohmic dissipation zone

• More exotic explanations: turbulent resistivity, extremely disorganized field lines in inner collapse zone (again due to strong turbulence), reconnection, may not be required for (small) disk formation

• Small class 0 disk may be consistent with observations of larger Class II disks

Class 0 Class II disks

2

,, ,

,

disk initdisk final disk initial

disk final

MR R

M

Angular momentum conservation, see e.g., Basu (1998)

• Earliest phase of disk evolution: rapid flushing of disk through episodic bursts of accretion (Vorobyov & Basu 2005, 2006, 2010)

• At end of burst phase, have “initial” disk with mass 10%-40% of central mass, which then evolves more smoothly and without significant mass loading from envelope

• “Initial” massive (Mdisk, init ~ 0.1 Mstar) disk will expand in size as it becomes a lower mass disk.

• For Rdisk, initial ~ 3 AU, end up with Rdisk,final ~ 300 AU for final ratio Mdisk,final/Mstar ~ 0.01

Broad Conclusions

• Inclusion of detailed microphysics resolves catastrophic magnetic braking on smallest scales and at earliest times after protostar formation

• Rather than being a problem for disk formation, magnetic fields (including magnetic diffusion) may actually be necessary to explain the observed sizes of Class II disks

• ALMA can test hypothesis of small but massive early disks that later expand to become low mass ~100 AU size Class II disks

• If small class 0 disks B + diffusion provide good explanation. If large class 0 disks need to explore more robust/exotic reasons for breakdown of magnetic braking