1. The Solar Corona B. C. Low High Altitude Observatory National Center for Atmospheric Research The National Center for Atmospheric Research is operated by the University Corporation for Atmospheric Research under sponsorship of the National Science Foundation. An Equal Opportunity/Affirmative Action Employer.

2. The White-Light Corona

3. Mark IV Coronameter Mauna Loa Solar Observatory

4. The Magnetic Sun

5. The Magnetic Corona Activity Maximum 1980 Activity Minimum 1994

6. A CME out to 32 R_ Sun

7. A Shower of MeV Protons

9. The 2-3 Million-Degree Corona

10. Solar EUV Output

11. Orbit Height of the SMM Satellite

12. Coronal Drivers of Space Weather Variable heating of the Earth’s Upper Atmosphere Episodes of CME-Magnetospheric Interaction High-energy particles Evolution of the corona-heliosphere over the 11-year solar cycle

13. The Solar Corona as a Hydromagnetic Atmosphere Maintained at million-degree temperatures – cooling time ~ 1 day – dissipative heating A nearly perfect conductor of heat: – solar-wind expansion A nearly perfect conductor of electricity: – low-beta plasma atmosphere dominated by a ~10G global magnetic field reversing in cycles of 11 years

14. Time-Dependent Ideal MHD

15. Magnetic Helicity The magnetic vector potential: Magnetic helicity: Helicity transport:

16. Magnetic Helicity & Linkage Numbers

17. The Hydromagnetic Induction Equation “The magnetic field is frozen into the embedding plasma with perfect electrical conductivity. The perfect conductor is a singular limit of the weakly resistive conductor; being nearly perfect is not the same as just being perfect. ”

18. The Surprisingly Dissipative Corona Quiescent heating & flares – heating by a turbulent dissipation of spontaneous current sheets (Parker 1994)

19. Petschek Reconnection

20. A Good Question If magnetic reconnection under conditions of high electrical conductivity makes a plasma readily dissipative, what are we to say about its canonical properties of being an excellent electrical conductor? Can magnetic reconnection short away all the electric currents in a magnetized plasma under conditions of ?

21. Limits on Magnetic Reconnection under Longevity of astronomical-scale magnetic flux, e.g., potential fields as minimum- energy ground states: “very hard to get rid of magnetic flux”. Conservation of (relative) magnetic helicity within “sufficiently large” magnetic structures (Taylor 1974, Berger 1984): “very hard to get rid of magnetic twist”.

22. Petschek Reconnection

23. Coalescence of Two Ropes of Twisted Fields

24. The Ideal and Dissipative Nature of High-Temperature Plasmas Magnetic reconnection under does not destroy but transfer magnetic flux and helicity among subsystems of flux. Despite its dissipative nature, there is a limit to how much magnetic energy magnetic reconnection can liberate. The approximate conservation of magnetic helicity stores magnetic energy against flaring – origin of long-lived coronal structures.

25. Emergence of a Twisted Magnetic Field (The Magnetic End-Product of a Confined Flare) Manchester et al. 2004

26. Magnetic Flux Ropes in the Solar Atmosphere Potential State with Zero Helicity Minimum-Energy State with a conserved Net Helicity

27. Sigmoidal Plasma Structures and Magnetic Flux Ropes The sigmoid separatrix flux surface ( Parker 1994,Titov & Demoulin 1999, Low & Berger 2003 ) Fan & Gibson (2003)

28. Preferred Sigmoidal X-ray Plasma Structures in the two Hemispheres Left- and right- handed twisted flux ropes are preferred in the northern and southern hemispheres respectively (Canfield, Petstov, Rust, …..). Helicity Rule holds for all solar cycles. North South

33. A Role of CMEs in Coronal Evolution Large-scale expulsion of coronal mass clear out into interplanetary space: Is there a collective effect of the CMEs on the solar corona over an 11-year solar cycle? Is energy release the only consequence of the CMEs for the corona?

34. Magnetic-flux Emergence and the Complementary Roles of Flares and CMEs Magnetic reconnection as flares serves to shed excess energy and simplify field topologies but cannot destroy the large-scale magnetic flux threading across the solar photosphere. Under its approximate conservation law, the magnetic-helicity emerging into the corona can be removed either by the mutual cancellation of opposite helicities or by an outward transport into interplanetary space, in order to avoid an unbounded accumulation in the corona – the global helicity rule identifies the latter mechanism with the CMEs.

35. Creation & Removal of Magnetic Flux Across a Geometric Surface

36. CMEs and Coronal Magnetic-Field Reversals CMEs are episodes of hydromagnetic expulsions of the magnetic flux and helicity of the old cycle out into the interplanetary solar wind, to make room for the new-cycle flux of the opposite polarity ( Low & Zhang 2004 ). SMM & LASCO observations suggest a direct association between the progress of a field reversal at a solar pole and the rates of CMEs taking off near that ( Gopalswamy et al. 2003 ).

37. Gopalswamy et al. 2003

38. The Solar-Heliospheric Outflow of Magnetic Flux and Helicity There is a global transport of magnetic flux system from the solar interior out into the solar wind, obeying the Helicity Rule. Complementary roles for flares & prominence and CME eruptions. Sub-photospheric origin of atmospheric magnetic helicity–are we seeing clear through into the interior dynamo? The hydromagnetic interplay between dissipative (flares) and ideal (CMEs) processes is the basic drama of solar activity that is the origin of space weather (Zhang & Low 2005, Ann. Rev. Astron Astrophys.).

39. References Hundhausen, A. J. 1997, in Cosmic Winds and the Heliosphere, ed. J. R.Jokipii, C. P. Sonnett, \& M. S. Giampapa, U. of Arizona Press, p. 259 Low, B. C. 2001, JGR 106, 25141 & references therein Zhang, M., \& B. C. Low 2005, ARAA vol. 43, in press, download: /toshi/ftp/pub/zhm/ZhangLow.pdf & references therein.