1. Problems in MHD Reconnection ?? (Cambridge, Aug 3, 2004) Eric Priest St Andrews

2. CONTENTS 1. Introduction 2. 2D Reconnection 3. 3D Reconnection 4. [Solar Flares] 5. Coronal Heating

3. 1. INTRODUCTION  Reconnection is a fundamental process in a plasma:  Changes the topology  Converts magnetic energy to heat/K.E  Accelerates fast particles  In solar system --> dynamic processes:

4. Magnetosphere Reconnection -- at magnetopause (FTE’s) & in tail (substorms) [Birn]

5. Solar Corona Reconnection key role in Solar flares, CME’s [Forbes] + Coronal heating

6. Induction Equation  B changes due to transport + diffusion [Drake, Hesse, Pritchett]  R m >>1 in most of Universe --> B frozen to plasma -- keeps its energy Except SINGULARITIES -- & j & E large Heat, particle acceler n

7. Current Sheets - how form ?  Driven by motions  At null points  Occur spontaneously  By resistive instability in sheared field  Along separatrices  By eruptive instability or nonequilibrium  In many cases shown in 2D but ?? in 3D

8. 2. 2D RECONNECTION  In 2D theory well developed : * (i) Slow Sweet-Parker Reconnection (1958) * (ii) Fast Petschek Reconnection (1964) * (iii) Many other fast regimes -- depend on b.c.'s  Almost-Uniform (1986)  Nonuniform (1992)  In 2D takes place only at an X-Point -- Current very large -- Strong dissipation allows field-lines to break / change connectivity

9. Sweet- Parker (1958) Simple current sheet - uniform inflow

10. Petschek (1964)  SP sheet small - bifurcates Slow shocks - most of energy  Reconnection speed v e -- any rate up to maximum

11. ?? Effect of Boundary Conditions on Steady Reconnection NB - lessons: 3. Global ideal environment depends on bc’s 5. Maximum rate depends on bc’s 1.Bc’s are crucial 2. Local behaviour is universal - Sweet-Parker layer 4. Reconnection rate - the rate at which you drive it

12. Newer Generation of Fast Regimes  Depend on b.c.’s Almost uniformNonuniform  Petschek is one particular case - can occur if enhanced in diff. region  Theory agrees w numerical expts if bc’s same

13. Nature of inflow affects regime Converging Diverging -> Flux Pileup regime Same scale as SP, but different f, different inflow  Coll less models w. Hall effect (GEM, Birn, Drake) -> fast reconnection - rate = 0.1 v A

14. 2D - Questions ?  2D mostly understood  But -- ? effect of outflow bc’s - -- fast-mode MHD characteristic -- effect of environment  Is nonlinear development of tmi understood ??  Linking variety of external regions to collisionless diffusion region ?? [Drake, Hesse, Pritchett, Bhatt ee ]

15. 3. 3D RECONNECTION Simplest B = (x, y, -2z) Spine Field Line Fan Surface (i) Structure of Null Point Many New Features 2 families of field lines through null point:

16. Most generally, near a Null (Neukirch…) B x = x + (q-J) y/2, B y = (q+J) x/2 + p y, B z = j y - (p+1) z, in terms of parameters p, q, J (spine), j (fan) J --> twist in fan, j --> angle spine/fan

17. (ii) Topology of Fields - Complex In 2D -- Separatrix curves In 3D -- Separatrix surfaces -- intersect in Separator

18. transfers flux from one 2D region to another. In 3D, reconnection at separator transfers flux from one 3D region to another. In 2D, reconnection at X

19. ? Reveal structure of complex field ? plot a few arbitrary B lines E.g. 2 unbalanced sources SKELETON -- set of nulls, separatrices -- from fans

20. 2 Unbalanced Sources Skeleton: null + spine + fan (separatrix dome)

21. Three-Source Topologies

22. Simplest configuration w. separator: Sources, nulls, fans -> separator

23. Looking Down on Structure Bifurcations from one state to another

24. Movie of Bifurcations Separate -- Touching -- Enclosed

25. Higher-Order Behaviour Multiple separators Coronal null points [ ? more realistic models corona: Longcope, Maclean]

26. (iii) 3D Reconnection At Null -- 3 Types of Reconnection: Can occur at a null point (antiparallel merging ??) or in absence of null (component merging ??) Spine reconnection Fan reconnection [Pontin, Hornig] Separator reconnection [Longcope, Galsgaard]

27. Spine Reconnection Assume kinematic, steady, ideal. Impose B = (x, y, -2z) Solve E + v x B = 0 and curl E = 0 for v and E. --> E = grad F B.grad F = 0, v = ExB/B 2 -> Singularity at Spine Impose continuous flow on lateral boundary across fan

28. Fan Reconnection (kinematic) Impose continuous flow on top/bottom boundary across spine [? Resolve singularities, ? Properties: Pontin, Hornig, Galsgaard]

29. Separator Reconnection (Longcope) Numerical: Galsgaard & Parnell

30. In Absence of Null Qualitative model - generalise Sweet Parker. 2 Tubes inclined at : Reconnection Rate (local): Varies with - max when antipar l Numerical expts: (i) Sheet can fragment (ii) Role of magnetic helicity

31. Numerical Exp t (Linton & Priest) 3D pseudo- spectral code, 256 3 modes. Impose initial stag n -pt flow v = v A /30 R m = 5600 Isosurfaces of B 2 :

32. B-Lines for 1 Tube Colour shows locations of strong E p stronger E p Final twist

33. Features  Reconnection fragments (cf Parnell & Galsgaard)  Complex twisting/ braiding created Initial mutual helicity = final self helicity  Higher R m -> more reconnection locations & braiding  Approx conservation of magnetic helicity: ? keep as tubes / add twist: Linton

34. (iv) Nature of B-line velocities (w) In 2D  Inside D, w exists everywhere except at X- point.  Flux tubes rejoin perfectly  B-lines change connections at X  Outside diffusion region (D), v = w [Hornig, Pontin]

35. In 3D : w does not exist for an isolated diffusion region (D)  i.e., no solution for w to  fieldlines continually change their connections in D (1,2,3 different B-lines)  flux tubes split, flip and in general do not rejoin perfectly !

36. Locally 3D Example Tubes split & flip

37. Fully 3D Example Tubes split & flip - - but don’t rejoin perfectly

38. 3D - Questions ?  Topology - nature of complex coronal fields ? [Longcope, Maclean]  Spine, fan, separator reconnection - models ?? [Galsgaard, Hornig, Pontin]  Non-null reconnection - details ?? [Linton]  Basic features 3D reconnection such as nature w ? [Hornig, Pontin]

39. 4. FLARE - OVERALL PICTURE Magnetic tube twisted - erupts - magnetic catastrophe/instability drives reconnection

40. Reconnection heats loops/ribbons [Forbes] - rise / separate

41. 5. HOW is CORONA HEATED ? Bright Pts, Loops, Holes Recon- nection likely

42. Reconnection can Heat Corona: (i) Drive Simple Recon. at Null by phot c. motions --> X-ray bright point (Parnell) (ii) Binary Reconnection -- motion of 2 sources (iii) Separator Reconnection -- complex B (iv) Braiding (v) Coronal Tectonics

43. (ii) Binary Reconnection (P and Longcope) Many magnetic sources in solar surface  Relative motion of 2 sources -- "binary" interaction  Suppose unbalanced and connected --> Skeleton  Move sources --> "Binary" Reconnection  Flux constant - - but individual B-lines reconnect

44. Cartoon Movie (Binary Recon.) Potential B Rotate one source about another

45. (iii) Separator Reconnection [Longcope, Galsgaard]  Relative motion of 2 sources in solar surface  Initially unconnected Initial state of numerical expt. (Galsgaard & Parnell)

46. Comput. Expt. (Parnell / Galsgaard Magnetic field lines -- red and yellow Strong current Velocity isosurface

47. (iv) Braiding Parker’s Model Initial B uniform / motions braiding

48. Numerical Experiment (Galsgaard) Current sheets grow --> turb. recon.

49. Current Fluctuations Heating localised in space -- Impulsive in time

50. (v) CORONAL TECTONICS ? Effect on Coronal Heating of “Magnetic Carpet”  * (I) Magnetic sources in surface are concentrated

51. * (II) Flux Sources Highly Dynamic Magnetogram movie (white +ve, black -ve)  Sequence is repeated 4 times  Flux emerges... cancels  Reprocessed very quickly (14 hrs !!!) ? Effect of structure/motion of carpet on Heating

52. Life of Magnetic Flux in Surface  (a) 90% flux in Quiet Sun emerges as ephemeral regions  (b) Each pole migrates to boundary, fragments --> 10 "network elements" (3x10 18 Mx)  (c) -- move along boundary -- cancel

53. From observed magnetograms - construct coronal field lines - statistical properties: most close low down Time for all field lines to reconnect only 1.5 hours (Close, Parnell, Priest): - each source connected to 8 others

54. Coronal Tectonics Model (Priest, Heyvaerts & Title)  Each "Loop" --> surface in many sources  Flux from each source topolog y distinct -- Separated by separatrix surfaces  Corona filled w. myriads of separatrix/ separator J sheets, heating impulsively  As sources move, coronal fields slip ("Tectonics") --> J sheets on separatrices & separators --> Reconnect --> Heat

55. Fundamental Flux Units  Intense tubes (B -- 1200 G, 100 km, 3 x 10 17 Mx) 100 sources 10 finer loops not Network Elements  Each network element -- 10 intense tubes  Single ephemeral region (XBP) --  Each TRACE Loop -- 80 sep rs, 160 sep ces 800 sep rs, 1600 sep ces

56. Theory  Parker -- uniform B -- 2 planes -- complex motions  Tectonics -- array tubes (sources) -- simple motions (a) 2.5 D Model  Calculate equilibria -- Move sources --> Find new f-f equilibria  --> Current sheets and heating

57. 3 D Model Demonstrate sheet formation Estimate heating Preliminary numerical expt. (Galsgaard, Mellor …)

58. Results  Heating uniform along separatrix  Elementary (sub-tel c ) tube heated uniformly  But 95% phot c. flux closes low down in carpet -- remaining 5% forms large-scale connections  --> Carpet heated more than large-scale corona  So unresolved observations of coronal loops --> Enhanced heat near feet in carpet --> Upper parts large-scale loops heated uniformly & less strongly

59. 6. CONCLUSIONS  2D recon - many fast regimes - depend on nature inflow  Reconnection on Sun crucial role - * Solar flares * Coronal heating  3D - can occur with or without nulls - several regimes (spine, fan, separator) - sheet can fragment - role of twist/braiding - concept of single field-line vel y replaced - field lines continually change connections in D - tubes split, flip, don’t rejoin perfectly

60. ?? Extra Questions ??  ? Threshold / conditions for onset of reconnection  ? Occur equally easily at nulls or without  ? Rate and partition of energy  ? How does reconnection accelerate particles - cf DC electric fields, stochastic acc n, shocks  ? Determines where non-null recon. occurs  ? Role of microscopic processes

61. PS-Example from SOHO (EIT - 1.5 MK)  Eruption  Inflow to reconnection site  Rising loops that have cooled (Yokoyama)

62. Example from TRACE  Eruption  Rising loops  Overlying current sheet (30 MK) with downflowing plasma

63. (Priest and Schrijver 1999) Reconnection proceeds New loops form Old loops cool

64. PS-B-Lines for 1 Tube

65. PS-Cause of Eruption ? Magnetic Catastrophe 2.5 D Model

66. Numeric al Model Suggestive of Catastrophe

67. PS- Recon n - Elegant Explanation for many Recent Space Observations Yohkoh  Hottest loops are cusps or interacting loops  X-ray jets - accelerated by reconnection SOHO  X-ray bright points (NIXT, EIT, TRACE)  Magnetic carpet (MDI)  Explosive events (SUMER)  Nanoflares (EIT, TRACE, CDS)

68. TRACE Loop Reaches to surface in many footpoints. Separatrices & Separators form web in corona

69. Corona - Myriads Different Loops Each flux element --> many neighbours But in practice each source has 8 connections