1. Non-ideal MHD and the Formation of Disks Shantanu Basu Western University, London, Ontario, Canada Wolf Dapp ( Juelich Supercomputing Centre, Germany ), Matt Kunz ( Princeton Univ., USA ) Magnetic Fields Workshop, Heidelberg Thursday, May 23, 2013

3. resolve ‘Second Core’ disks can form, albeit initially small Usual approach Non-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 >~10 20 cm -3 (for realistic magnetic field strength, e.g., Mellon & Li, Hennebelle & Ciardi) slide courtesy Wolf Dapp

4. 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 ~ R sun 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

5. - 40 -20 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

6. Mass-to-flux ratio

7. 1.Prestellar core collapse profile 2.Magnetic diffusion shock 3.Expansion wave outside first core 4.First core at ~ 1 AU 5.Collapse profile within first core 6.Second expansion wave outside second core 7.Second stellar core, size ~ R sun Column Density Profile

8. Disk formation gravitational instability introduction of sink cell after 2 nd core formation (few R sun ) centrifugal balance is achieved, and disk fragments into ring magnetic braking catastrophe centrifugal balance N column density / cm -2

9. 1. UV ionization 2. cosmic ray ionization 3. ionization due to radiation liberated in radioactive decay 4. thermal ionization through collisions Chemistry  Ionization balance Detailed 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

10. Effective (total) diffusion coefficient Fixed grain size a gr or MRN distribution charge adsorption onto grains thermal ionization followed by destruction of grains

11. 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.

12. 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

13. Class 0  Class II disks 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 (M disk, init ~ 0.1 M star ) disk will expand in size as it becomes a lower mass disk. For R disk, initial ~ 3 AU, end up with R disk,final ~ 300 AU for final ratio M disk,final /M star ~ 0.01

14. 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