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