1. Magnetic activity in protoplanetary discs Mark Wardle Macquarie University Sydney, Australia Catherine Braiding (Macquarie) Arieh Königl (Chicago) BP Pandey (Macquarie) Raquel Salmeron (ANU)

2. Magnetic fields Role of magnetic field is unclear –MHD turbulence (magnetorotational instability)? –disc-driven MHD winds? –disc corona? –dynamo activity? –magnetic field strength?

3. Magnetic field strength Expect B > 10 mG given the measured strength in cloud cores –Compression during formation of disk and star –Shear in disc may wind up field and/or drive MRI Equipartition field in the minimum mass solar nebula Evidence for 0.1 – 1 G fields in the solar nebula at 1AU

4. B ~1G is required for angular momentum transport:

5. Protostellar disks are poorly conducting high density implies low conductivity –recombinations relatively rapid –drag on charged particles deeper layers shielded from ionising radiation for r < 5 AU –x-ray attenuation column ~10 g/cm 2 –cosmic ray attenuation column ~100 g/cm 2 –“dead zone” near midplane (Gammie 1996)

6. Magnetic diffusion Essential ingredient in any theory –large for YSO discs, so determines field evolution –permits accretion of matter, not magnetic field –energy dissipation –turbulent scales –boundary conditions for jet models –determined by abundances of charged particles and their collision cross sections with neutrals

7. Magnetic diffusion regimes fully ionizedpartially ionized Ideal MHD ions and electrons tied to field ions, electrons and neutrals tied to field Ambipolar –neutrals decoupled Hall ions decoupledions and neutrals decoupled Ohmic ions and electrons decoupled ions, electrons and neutrals decoupled

9. If the only charged species are ions and electrons, Three distinct diffusion regimes: –see Pandey & Wardle (2008) for generalisation to all levels of ionisation – Ohmic (resistive) – Hall – Ambipolar log n log B ohmic hall ambipolar A

10. Wardle 2007

11. Mellon & Li 2009 Initial conditions: large scale poloidal field

12. Shu et al 2007

13. B drift due to ambipolar diffusion

14. Hall diffusion

15. Braiding - thesis

18. Magnetorotational instability Wardle & Salmeron in prep Pandey & Wardle in prep

19. Ambipolar or ohmic diffusion (B z > 0)

20. Ambipolar or ohmic diffusion (B z < 0)

21. Hall diffusion (B z < 0)

22. Hall diffusion (B z > 0)

23. Wardle & Salmeron in prep

24. Maximum growth rate and corresponding wavenumber Wardle & Salmeron in prep

25. log n / n H log  (s -1 ) M+M+ C+C+ m+m+ e He + H+H+ H3H3 + Abundances: 1AU, no grains z / h Wardle 2007

27. MRI growth rate (Ω)

28. ohmic+ambipolar diffusion MRI growth rate (Ω)

29. Full diffusion (B z > 0)

30. no Hall diffusion MRI growth rate (Ω) Full diffusion (B z < 0)

31. Salmeron & Konigl 2009 Disc-wind launching at 1 AU

32. z / h log n / n H -14 0 1 2 3 -13 -11 -12 M+M+ -4 -3 -2 C+C+ m+m+ e He + H+H+ H3H3 + Abundances: 1AU, 0.1  m grains log  (s -1 ) Wardle 2007

33. MRI growth rate (Ω)

35. Summary Magnetically-driven accretion requires B ~ 1 gauss at 1 AU Molecular cloud core collapse calculations give B of this order –magnetic braking too severe? –magnetic flux problem? –relevance of zero net flux MRI calculations? Magnetic diffusion varies quantitatively and qualitatively within the disk –MRI-driven turbulence with strong hall diffusion relatively unexplored –is wind launching possible across a range of radii? –dead zones: B z 0 Even a small residual population of grains increase magnetic diffusion –in absence of grains, X-rays   active ≈ 150 g cm –2 at 1AU –1 AU: 0.1 µm  active ≈ 2 g cm –2 3 µm  active ≈ 80 g cm –2 –require ~1000-fold reduction in grain charge carrying capacity relative to 0.1µm grains (dust:gas mass = 0.01)