1. Newark, 31.03.2008Wiegelmann et al.: Coronal magnetic fields1 Solar coronal magnetic fields: Source of Space weather Thomas Wiegelmann, Julia Thalmann, Bernd Inhester, Li Feng, Peng Ruan

2. Newark, 31.03.2008Wiegelmann et al.: Coronal magnetic fields2 Usually we see the solar corona only during an eclipse 11. August 1999 total solar eclipse Solar corona is about 200 times hotter as photosphere. But only 10 -12 as dense. Corona is very faint and produces only about 10 -6 the visible brightness compared with photosphere. Observations from space allow us to observe the corona all the time in different wavelength.

3. Newark, 31.03.2008Wiegelmann et al.: Coronal magnetic fields3 Observation from Space with SOHO/EIT Coronal activity is driven by magnetic fields!

4. Newark, 31.03.2008Wiegelmann et al.: Coronal magnetic fields4

5. Newark, 31.03.2008Wiegelmann et al.: Coronal magnetic fields5

6. Newark, 31.03.2008Wiegelmann et al.: Coronal magnetic fields6 Space weather -Solar Storms -Charged particles impact Earth -Aurora Question: Origin of coronal eruptions

7. Newark, 31.03.2008Wiegelmann et al.: Coronal magnetic fields7

8. Newark, 31.03.2008Wiegelmann et al.: Coronal magnetic fields8 Coronal mass ejections and flares are assumed to occur due to instabilities in the coronal magnetic field configuration. It is important to investigate the coronal magnetic field

9. Newark, 31.03.2008Wiegelmann et al.: Coronal magnetic fields9

10. Newark, 31.03.2008Wiegelmann et al.: Coronal magnetic fields10 Solar magnetic field measured routinely only in photosphere

11. Newark, 31.03.2008Wiegelmann et al.: Coronal magnetic fields11

12. Newark, 31.03.2008Wiegelmann et al.: Coronal magnetic fields12 Effect of magnetic field visible in corona We cannot measure the 3D-coronal magnetic field accurately direct. Measurements of photospheric B-field. (Line-of-sight and vector magnetograms). Extrapolate photospheric field into corona. Extrapolation method depends on assumptions about coronal plasma. Magnetic ‘field lines’ observed with TRACE => Coronal magnetic field models

13. Newark, 31.03.2008Wiegelmann et al.: Coronal magnetic fields13

14. Newark, 31.03.2008Wiegelmann et al.: Coronal magnetic fields14 ModelMathematics Observations needed Validity Potential Fields Line of sight magnetogram (Global) current free regions, quiet sun Linear Force-Free LOS mag. + observations of plasma structures Local in active regions, low-beta plasma Nonlinear Force-Free Vectormag. (Noise, ambiguity Preprocessing) Active regions, low beta plasma in low corona MHS Equilibrium Vectormag. + Tomography Helmet streamer, finite beta plasma, full solar corona Coronal magnetic field models Better Models More Challenging Computational + Observational

15. Newark, 31.03.2008Wiegelmann et al.: Coronal magnetic fields15

16. Newark, 31.03.2008Wiegelmann et al.: Coronal magnetic fields16 Mathematical simple and requires only Line-of-sight magnetograms

17. Newark, 31.03.2008Wiegelmann et al.: Coronal magnetic fields17 -Minimize L numerically. -Boundary condition: Photospheric B-field vector. -Noise and inconsistencies in vector magnetograms require preprocessing. NLFFF-consortium: Most accurate and fastest method.

18. Newark, 31.03.2008Wiegelmann et al.: Coronal magnetic fields18 Ground based Vector magnetograph Solar Flare Telescope, Tokyo, (Sakurai et al.1995)

19. Newark, 31.03.2008Wiegelmann et al.: Coronal magnetic fields19

20. Newark, 31.03.2008Wiegelmann et al.: Coronal magnetic fields20 Coronal Magnetic Field Nonlinear Force-free code Preprocessing tool Vector magnetogram H-Alpha Image Chromospheric Magnetic Field Optional

21. Newark, 31.03.2008Wiegelmann et al.: Coronal magnetic fields21 Flare seen in Trace and H-Alpha, Jan. 20. 2004, (from Goff, van Driel-Gesztelyi, Demoulin, Sol. Phys. 2007) Evolution of Flaring Active Region NOAA 10540 (Thalmann and Wiegelmann, A&A 2008, in press)

22. Newark, 31.03.2008Wiegelmann et al.: Coronal magnetic fields22 SOHO/MDI NAO/SFT, Time cadence about 1 day

23. Newark, 31.03.2008Wiegelmann et al.: Coronal magnetic fields23 Evolution of AR10540 For movie the spatial resolution was reduced (factor 2) and from 4 magnetograms with a time cadence of (28h, 22h, 21h) we interpolated to 15 min [movie is only illustrative and not for data analysis].

24. Newark, 31.03.2008Wiegelmann et al.: Coronal magnetic fields24 Flaring Active Region Quiet Active Region Solar X-ray flux. Vertical blue lines: vector magnetograms available Magnetic field extrapolations from Solar Flare telescope Extrapolated from SOLIS vector magnetograph M6.1 Flare Magnetic energy builds up and is releases during flare Future plans: Study flaring ARs with higher time cadence with Solar Dynamics Observatory. M6.1 Flare

25. Newark, 31.03.2008Wiegelmann et al.: Coronal magnetic fields25 Future: Combine magnetic field extrapolation with vector tomographic methods based on coronal Faraday and Hanle measurements. (feasibility study by Kramar and Inhester 2006)

26. Newark, 31.03.2008Wiegelmann et al.: Coronal magnetic fields26 Coronal plasma and magnetic field Lorentz force pressure gradient gravity B for vertical scales < 0.1 R S (gravitational scale height) => Pressure constant on field lines Plasma outlines magnetic field lines

27. Newark, 31.03.2008Wiegelmann et al.: Coronal magnetic fields27 Force-free equilibria and coronal plasma small

28. Newark, 31.03.2008Wiegelmann et al.: Coronal magnetic fields28 Coronal magnetic fieldPlasma in EUV SOHO/EIT, Trace etc. show 2D projections of coronal plasma 3D Structure?

29. Newark, 31.03.2008Wiegelmann et al.: Coronal magnetic fields29 The STEREO-mission within the NASA/STP program Two almost identical spacecrafts observe the Sun and heliosphere Launched October 2006 Aim: 3D view of Solar corona. Spacecraft have different orbits due to swing-by at moon. The two STEREO spacecraft seperate about 44 o every year.

30. Newark, 31.03.2008Wiegelmann et al.: Coronal magnetic fields30 Stereoscopic Reconstruction of 3D coronal loop structures ( Li Feng et al. 2007) EUVI_BEUVI_A June 8, 2007 Angle 11.8 o

31. Newark, 31.03.2008Wiegelmann et al.: Coronal magnetic fields31 Coronal loops in NOAA 10960 EUVI_AEUVI_B Loops identified from unsharp mask filtered images.

32. Newark, 31.03.2008Wiegelmann et al.: Coronal magnetic fields32 2007-06-08T03:12:00 UT MDI : 2007-06-08T03:12:00 UT Linear force-free extrapolation  3D magnetic field lines : a guide to the loop correspondence Loop correspondence

33. Newark, 31.03.2008Wiegelmann et al.: Coronal magnetic fields33 correspondence in the northern active region Loop correspondence

34. Newark, 31.03.2008Wiegelmann et al.: Coronal magnetic fields34 Loop reconstruction 3D loop is the intersection of two back-projection surfaces generated from two view directions.

35. Newark, 31.03.2008Wiegelmann et al.: Coronal magnetic fields35 3D Loop reconstruction Yellow: reconstructed 3D loops Red: best fit magnetic field lines view from STEREO_ANortheast of AR

36. Newark, 31.03.2008Wiegelmann et al.: Coronal magnetic fields36 Loop parameters 1. The linear force-free assumption is often not adequate. 2. Most of the loops cannot be approximated by planar curve segments. 3. Most of the loops are not circular. Still to do: Reconstruct density, temperature, plasma flow along loops

37. Newark, 31.03.2008Wiegelmann et al.: Coronal magnetic fields37 Outlook: Self-consistent B-Field and Plasma model Force-free code Vector magnetogram MHS code Force-free magnetic field -Length+shape of loops -Magnetic field strength -Electric current density compare STEREO images Plasma along magnetic loops Scaling laws Artificial images LOS-integration Tomography Self-consistent equilibrium

38. Newark, 31.03.2008Wiegelmann et al.: Coronal magnetic fields38