1. Sept. 13, 2007 CORONAL HEATING (Space Climate School, Saariselka, March, 2009) Eric Priest (St Andrews)

2. Sept. 13, 2007 1. Introduction - The Corona (Eclipse)

3. Sept. 13, 2007 Coronal holes -- loops -- X-ray bright points Skylab -- X-ray telescope

4. Sept. 13, 2007 A dynamic magnetic world - subtle interactions B & plasma Yohkoh (5 arcsec)

5. Sept. 13, 2007 Hinode (1 arcsec) Stunning detail on structure & dynamics (see Tsuneta) How is corona heated?

6. Sept. 13, 2007 Waves or reconnection? - Space Obs ns :  Low-freq. waves in loops [TRACE]-too weak to heat  High-freq. waves [UVCS] -- ?? heat outer corona  Hinode -- Chromospheric Spicules swaying (straw, prairy) Hansteen, Suematsu --?? Solar wind/ coronal heating

7. Sept. 13, 2007 2. Reconnection - most likely in low corona Many brightenings X-ray bright points - above emerging and/or cancelling fields in photosphere [30-sec cadence, 12-hour duration] Quiet Sun: [XRT on Hinode, Tsuneta, golub]

8. Sept. 13, 2007 Hinode XRT - active region (Schmeltz et al, 2009) Observations inside white region Differential emission measure Normal active region emission at 3 MK Plus peak at 20 MK (?nanoflares)

9. Sept. 13, 2007 Parker’s classical Nanoflare Model by braiding (1972) Initial B uniform / motions braiding

10. Sept. 13, 2007 Numerical Experiment (Galsgaard) Braiding --> Current sheets grow --> turb. recon.

11. Sept. 13, 2007 Magnetic sources in surface are concentrated 3. Coronal Tectonics Model (development of Parker’s model) 3.1 Effect “Magnetic Carpet”

12. Sept. 13, 2007 Flux Sources Highly Dynamic Magnetogram movie (white +ve, black -ve)  Flux emerges... cancels  Reprocessed very quickly (14 hrs !!!)

13. Many Sources--> Corona has Complex Topology In 2D -- Separatrix curves In 3D -- Separatrix surfaces

14. In 3D, reconnection at separator In 2D, reconnection at X In complex fields we form the SKELETON-- set separatrices

15. 3.3 “Simple” binary interaction of 2 photospheric sources (Haynes et al) Separator - and + sources in overlying B.  Separatrix surfaces. Move sources & watch Interaction  flux tube joining sources

16. Cross-sections of Separatrix Surfaces 2 separators 5 separators Separatrix surfaces (positive, negative) & Separators ( ) Number of separators: X

17. Sept. 13, 2007 Life of Magnetic Flux in Surface  (a) 50%? flux in Quiet Sun emerges as ephemeral regions [1 per 8 hrs per supergran, 3 x 10 19 Mx]  (b) Each pole migrates to boundary (4 hours), fragments --> 10 "network elements" (3x10 18 Mx)  (c) -- move along boundary (0.1 km/s) -- cancel

18. Sept. 13, 2007 From observed magnetograms - construct coronal field lines Time for all field lines to reconnect only 1.5 hours (Close et al)  much more tectonics heating low down where field is more complex than higher up - each source connects to 8 others

19. Sept. 13, 2007 Coronal Tectonics Model ( Priest, Heyvaerts & Title )  Each "Loop" --> surface in many sources  Flux from each source separated by separatrix surfaces  As sources move --> J sheets on separatrices & separators --> Reconnect --> Heat  Corona filled w. myriads of J sheets, heating impulsively (updated version of Parker nanoflare/topological dissipation)

20. Sept. 13, 2007 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 -- 800 sep rs, 1600 sep ces 80 sep rs, 160 sep ces

21. Sept. 13, 2007 TRACE Loop Reaches to surface in many footpoints. Separatrices form web in corona

22. Sept. 13, 2007 Corona - Myriads Different Loops Each flux element --> many neighbours But in practice each source has 8 connections

23. Sept. 13, 2007 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

24. Sept. 13, 2007 4. If reconnection heats corona at many sheets, 1. How does energy spread out ? -- conduction along B -- reconnection jets -- waves across B 2. If reconnection time-dependent, how much energy liberated locally/globally? Simple model problem [Longcope & Priest]

25. Sept. 13, 2007 Magnetic field of Current Sheet in X At large r, B = B 0 + B 1 (line current), Lots of energy far from CS

26. Sept. 13, 2007 Suppose sheet reconnects Local process but has global consequences: Decrease I --> B must change at large distances How ?? Current (I) dissipates

27. Sept. 13, 2007 Model for effect of reconnection Linearize about X-point B 0 :  is “turned on” current diffuses i.e. reconnection Assume B 1 @ t=0 is due to current sheet

28. Sept. 13, 2007 Combine equations: Put = twice current enclosed in r r I r (r)  I 0 Expect: wave diffusion

29. Sept. 13, 2007 (i) Large r (wave) limit: when >> I(R,t)=I 0 -F(t-R) R I0I0 (ii) Small r (diffusive) limit: r I0I0 NB --> 0 at origin as t increases wave diffusion

30. Sept. 13, 2007 Numerical Solution Diffusive solution I(r) R t Wave solution Transition: diffusive to wave solution

31. Sept. 13, 2007 EVEV But flow near X does not disappear -- it slowly increases ! Sheath of Current propagates out In wake of sheath a flow, assoc d with increasing t

32. Sept. 13, 2007 Resolving the Paradox - 3rd regime At large t Advectiondiffusion = Peak in j remains at X and produces a steady E (indep of )

33. Sept. 13, 2007 5. Summary Response to enhanced  in current sheet (CS) during coronal tectonics: (i) Diffusion spreads CS out (ii) Wave carries current out at v A - as sheath Most magnetic energy is converted into kinetic energy in wave -- may later dissipate. (iii) Peak in j at X remains --> steady E independent of i.e. fast Coronal heating -- reconnection + wave Coronal tectonics -- updated version of Parker braiding

34. Sept. 13, 2007