1. Modeling Magnetic Reconnection in a Complex Solar Corona Dana Longcope Montana State University & Institute for Theoretical Physics

2. The Changing Magnetic Field TRACE 171: 1,000,000 K 8/10/01 12:51 UT 8/11/01 17:39 UT 8/11/01 9:25 UT (movie)(movie) THE CORONA PHOTOSPHERE

3. Is this Reconnection? TRACE 171: 1,000,000 K 8/10/01 12:51 UT 8/11/01 17:39 UT 8/11/01 9:25 UT (movie)(movie) THE CORONA PHOTOSPHERE

4. Outline 1.Developing a model magnetic field 2.A simple example of 3d reconnection 3.The general (complex) case --- approached via variational calculus. 4.A complex example

5. The Sun and its field Focus on the p-phere And the corona just above

6. Modeling the coronal field

7. Example: X-ray bright points EIT 195A image of “quiet” solar corona (1,500,000 K)

8. Example: X-ray bright points Small specks occur above pair of magnetic poles (Golub et al. 1977)

9. Example: X-ray bright points

10. When 2 Poles Collide All field lines from positive source P1 All field lines to negative source N1

11. Regions overlap when poles approach When 2 Poles Collide

12. Stress applied at boundary Concentrated at X-point to form current sheet Reconnection releases energy How it’s done in 2 dimensions

13. A Case Study TRACE & SOI/MDI observations 6/17/98 (Kankelborg & Longcope 1999)

14. The Magnetic Model  Poles  Converging: v = 218 m/sec  Potential field: - bipole - changing  1.6 MegaVolts (on separator)

15. Reconnection Energetics  Flux transferred intermittently:  Current builds between transfers  Minimum energy drops @ transfer:

16. Post-reconnection Flux Tube Flux Accumulated over Releases stored Energy Into flux tube just inside bipole (under separator) Projected to bipole location

17. Post-reconnection Flux Tube Flux Accumulated over Releases stored Energy Into flux tube just inside bipole (under separator)

18. A view of the model

19. More complexity From p-spheric field (obs). Find coronal coronal field Defines connectivity

20. Minimum Energy: Equilibrium Magnetic energy Variation: Fixed at photosphere:  Potential field

21. Minimization with constraints Ideal variations only  force-free field Constrain helicity ( w/ undet’d multiplier   constant-  fff

22. A new type of constraint… Photospheric field: f(x,y) -- the sources …flux in each domain

23. Domain fluxes Domain D ij connects sources P i & N j Flux in source i: Flux in Domain D ij Q: how are fluxes related: A: through the graph’s incidence matrix

24. The incidence matrix N s Rows: sources N d Columns: domains  Nc = Nd – Ns + 1 circuits

25. The incidence matrix

26. Reconnection possible allocation of flux…

27. Reconnection … another possibility

28. Reconnection Related to circuit in the domain graph Must apply 1 constraint to every circuit in graph

29. Separators: where domains meet 4 distinct flux domains

30. Separators: where domains meet 4 distinct flux domains Separator at interface

31. Separators: where domains meet 4 distinct flux domains Separator at interface Closed loop encloses all flux linking P2  N1

32. Minimum W subj. to constraint Constraint on P2  N1 flux Current-free within each domain  current sheet at separator

33. Minimum W subj. to constraint 2d version: X-point @ boundary of 4 domains becomes current sheet

34. A complex example Ns = 20

35. A complex example Ns = 20  Nc = 33

36. The original case study Approximate p-spheric field using discrete sources

37. The domain of new flux Emerging bipole P01-N03 New flux connects P01-N07

38. Summary 3d reconnection occurs at separators Currents accumulate at separators  store magnetic energy Reconnection there releases energy Complex field has numerous separators