1. Some Key Issues in Solar Plasmas (Leiden, March 21, 2005) Eric Priest

2. “I have my calculations, teaching & students - and I love it” “My ‘retirement’ approaches this summer - but is not to be taken too literally as far as I am concerned”

3. “Principles of MHD” - already a hit with new generation of researchers

4. “Milo shows signs of interest in geometry - and playing with grandpa Hans - What could be nicer ? ”

5. “Some Key Issues in Solar Plasmas” CONTENT: 1. Introduction 2. Structure of the Sun 3. Sunspots 4. Corona 5. MHD - Reconnection 6. Key advances - SOHO satellite * Interior * Solar Flares and CME's * Heating Atmosphere Conclusions

6. 1. INTRODUCTION Our Sun 1. Of great scientific interest in own right 2. Influence on Earth 3. Important for Astronomy -- fundamental cosmic processes 4. Many basic properties of Sun a mystery B generated ? Solar wind accel d ? Corona heated ? Nature sunspots ? Eruptions occur ? Flare particles accel d ? Today some of progress

7. James Gregory 1st regius prof maths at St Andrews (1668) age 30 Co-founder of Calculus Invented Reflecting Telescope Traditionally close link St Andrews - Holland St Andrews founded 1411 Many students came from Low Countries (16/17 C) Dutch stone masons.

8.  In his lab -- see meridian line -- clock designed by C Huygens (stud. at Leiden) James Gregory

9. D iscovered: -- General binomial theorem -- Taylor expansions -- Ratio test for convergence of a series -- Series for sin x and tan x -- Integral of log x and sec x -- Differentiation is inverse of integration -- How to use change of variable in integration James Gregory - died 1675 (37)

10. Interior: Core (< 0.25 R 0 ), [R 0 = 700 Mm] Radiative zone, Convection zone (> 0.7 R 0 ) Atmosphere: Photosphere (6000K), Chromosphere (10 4 K), Corona (10 6 K) 2. Overall Structure of Sun

11. Classical Picture: So need analytical / comput l MHD (e.g., Keppens) - idealised 1D models + physical insight - sophisticated 2D & 3D - both -> understanding static plane-parallel atmosphere - rise in T But - highly nonuniform - multi-T - strongly t-dept - plasma heating/cooling dynamically

12. Even 1D model of Chromosphere (B=0) tough Start with 1D atmosphere T(h) Impose small osc n at photo (Carlsson & Stein) Similar process in flux tubes -> spicules (De Pontieu, Erdelyi) Need high-resolution adaptive grid to resolve shocks

13. Covered with turbulent convection cells: “Granulation” (1 Mm) “Supergranulation” (15 Mm) Photosphere

14. 2. Tiny intense magnetic fields over whole Sun Map of Photospheric Magnetic Field B carried to edges of supergran. cells White -- towards Black -- away from 1. around spots -- bipolar "Active Regions" 3. Diff l. rotation

15. Model of Flux Emergence from Interior to Corona V Archontis, F Moreno-Insertis, K Galsgaard, A Hood 3D compressible MHD, through 10 8 in density

16. Model of Flux Emergence from Interior to Corona V Archontis, F Moreno-Insertis, K Galsgaard, A Hood 3D compressible MHD, through 10 8 in density

17. Magnetic field lines expanding into corona Similar to TRACE images

18. Current sheet formsHigh-velocity jets ReconnectionHigh temperatures

19. Amazing images at 0.1” from Swedish telescope,La Palma (G Scharmer)

20. In close- up: effects of B around each granule points, flowers, ribbons - half flux in supergran.

21. Vertical Magnetic Field Temperature Produce many observed features of granulation Magnetoconvection models (e.g. Bushby) [256 x 256 x 120 points]

22. Results depend on B through Chandra. no Q=10 -> points Q=100 -> ribbons

23. Photosphere --> Sunspots Dark because cool 3. SUNSPOTS - magnetic field (B) stops granulation Vertical magnetic flux tubes “Not so simple !” Vary with 11-year cycle

24. Stunning Image (Swedish telescope) [Scharmer & van der Voort] Close-up of penumbral structure (created by B) -> new surprises:

25. Points moving along lanes; Bright flows in/out; Strange dark cores

26. New Model (Weiss, Thomas et al) Dark filaments- (low) held down by granule flux pumping Bright filaments- (high) Penumbra - a mixture of interlocked field lines

27. See below sunspot by t- distance seismology (eg Bogdan) Wave speed slower - cooler Wave speed higher - B

28. -- See at ECLIPSE of Sun Temperature is million degrees 4. CORONA Iran (1999) - Koutchmy Magnetic field dominates plasma -> magnetic world -- heats corona But how ??

29. Can observe corona direct in x-rays/euv Early image from Skylab - bright pts, holes, loops, act. reg.

30. TRACE (Active region) - from above

31. TRACE - from side - intricate structure Not isolated coronal loops - plasma that is at one temp. [1.5 MK]

32. Key Discovery from SOHO/TRACE MHD WAVES in CORONA (eg Nakariakov) Periods 2-20 min, amplitudes 2-5% -> insuff. to heat corona But Coronal Seismology: B, structure, transp coeffs. 1D slabs/tubes - basis (Hans G) 2 & 3D modelling (Andries, Bogdan, Erdelyi, Goossens, Poedts, Young ….)

33. 5. Eqns of Magnetohydrodynamics But - in corona:? H - in photosphere: optically thick ? Correct forms for transport coeffs. need collisionless effects when l < 30 km

34. Induction Equation  [B changes due to transport + diffusion]  In most of Universe R m >>1, B frozen to plasma Except SINGULARITIES -- & large Reconnecting current sheets Resonant absorption layers Shock waves

35. In 2D, reconnecting sheets form at NULL POINTS, B = 0 (e.g., Baty)  In 3D reconnection can take place at nulls or at non-null points (eg Galsgaard)

36. 5.1 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:

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

38. Note Coronal magnetic field - highly complex - many sources. 1. When constructing coronal field/ numerical expts - useful to construct skeleton (web of separatrix surfaces). 2. Understand nature bifurcations [3. For continuous sources: quasi-separatrix surfaces,quasi-separator, - no discont., but steep change in mapping grad]

39. (iii)Numerical Experiment (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 :

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

41. 6. SOHO (Solar & Heliospheric Observatory) Observing Sun continuously for 1st time (ESA/NASA) Launched 1995. Orbiting Sun at point in phase with Earth MANY NEW ADVANCES - only 3 today --> 1st comprehensive view of Sun

42. QN. 1 -- ? Structure of Solar Interior Measures velocity of Sun's surface at million pts/min -> frequencies: -> T(r) [agrees with model to < 1%] SOHO (MDI) detected several million normal modes

43. Deduce Internal Rotation Observe: * Faster at equator -- Expect: * const. on cylinders * B generated throughout conv. zone Surprise: -- const on radial lines -- intense shear layer ? site dynamo Need build models for tacocline (see Rosner)

44. Photosphere QN. 2 -- ? How Do Flares & CME’s Occur Oct-Nov, 2003 - v. complex sunspot group -> largest flares + mass ejections

45. Outer Corona from SOHO CME 2000 km/s (5 times faster than normal) Snow -- rel c particles

46. Thurs Aurora in St Andrews

47. Overall Picture of Eruption twisted magnetic tube - erupts drives reconnection

48. (Priest and Schrijver 1999) Reconnection heats loops Continues: new loops Form Old loops cool & drain

49. Example from TRACE (171 A) 20 MK [Fe XVI] + 1 MK [Fe IX]

50. RHESSI Overlay of TRACE Red contours: 12 – 25 keV X-ray flux. Blue contours: 50 – 100 keV X-ray flux. Particle acceleration: DC acceleration in sheet + Fermi in collapsing trap

51. Cause of Eruption ? Magnetic Catastrophe 2.5 D Model

52. 3D Numerical Model (Amari, Mikic et al) Converging motions -> eruption

53. QN. 3 -- HOW is CORONA HEATED ? Bright Pts, Loops, Holes Recon- nection possible

54. Numerical 3D MHD Experiment 171 195 (Gudiksen and Nordlund) - start with “realistic” potential active region field - impose “realistic” photo c velocity - find Poynting flux maintains a corona at 1 MK - assume that somehow at realistic R m energy would cascade down - but ? details of energy dissipation - deduce TRACE images

55. Reconnection can heat low corona: (i) Drive Simple Recon. by phot c. motions --> X- ray bright point (Parnell) (ii) Separator Reconnection -- complex B (Galsgaard) (iii) Coronal Tectonics -- modern version of Parker braiding

56. ? Effect on Coronal Heating of “Magnetic Carpet” Magnetic sources in surface are concentrated

57. From observed magnetograms - construct coronal field lines - statistical properties: most close low down Time for all field lines to reconnect only 1.5 hours

58. Coronal Tectonics Model Each "Loop" --> surface in many sources  Flux from each source separated by (separatrix) surfaces  As sources move --> J sheets on surfaces --> Reconnect --> Heat  Corona filled w. myriads of J sheets, heating impulsively

59. 7. CONCLUSIONS  Solar Physics - golden age - observations  Sense of vitality will continue  Computational plasma expts. playing a key role - present missions (SOHO 1995 -, TRACE 1998 -, RHESSI 2002) --> Stereo 2006, Solar B 2006, SDO 2008, Orbiter 2013  Need - numerical expts in 1,2,3D + analytical theory - link macro / micro physics - link with astro- and lab plasma community

60. spirit & high quality example of Hans Goedbloed