1. 1 Solar stereoscopy - where we are and which developments do we require to progress? Thomas Wiegelmann, Bernd Inhester, Li Feng, Judith de Patoul

2. 2 EUV-images from 2 viewpoints 3D geometry/physics of e.g. coronal loops and polar plumes What do we have and what we want? How? 1. Extract curve-like objects 2. Associate objects in both images 3. Geometric Stereoscopy 4. Estimate reconstruction error in 3D 5. Derive physical quantities

3. 3 1. Extract curve-like objects Processed image: A 7x7 boxcar smoothed image was subtracted from original Original Trace-image (from Aschwanden, Sol. Phys. 2008)

4. 4 1.Extract curve-like objects a) Manual loop tracing 210 manually traced loops.Trace-image, central part (Aschwanden, 2008) Can we teach the computer to trace loops automatically?

5. 5 Ridge detection Definition of a ridge Image intensity I (x, y) satisfies: Inhester et al, Sol. Phys. 2008 1. Extract curve-like objects b) Automatic loop tracing

6. 6

7. 7 Ridge location and orientation

8. 8 Interpolation of ridge positions (ridgel)

9. 9 Ridgel connection to chains

10. 10 Polynomial fits

11. 11 Merging and cleaning Done by hand until now

12. 12 Correspondence problem: Which two loops in the two images are the projections of the same loop in the real 3D case? solar rotation: two viewpoints Two-view TRACE images mimicking the EUVI image pair (Feng et al., Sol. Phys. 2007) 2. Associate objects in both images

13. 13 Plasma outlines magnetic field lines Can we use coronal magnetic field models as a proxy for 3D plasma loops? Magnetic field and EUV-images

14. 14 Single viewpoint: SOHO/EIT, TRACE Use B-Field for feature-recognition (Wiegelmann et al., Sol. Phys. 2005) Extrapolate coronal magnetic field from photosphere. Project 3D field lines onto an EUV-image. Emissivity and gradient along projected field lines. Alternative-1: Compare field lines and plasma. How well are they aligned? Alternative-2: Extract 1-D loops out of the EUV-images and compare with projections of magnetic field lines thereafter.

15. 15 Linear force-free field with α=-0.01 [Mm -1 ] 3D-magnetic field lines, linear force-free α=-0.01 [Mm -1 ]. Used in Marsch et. al. 2005 to study plasma flows with Sumer. Alternative-1: Compare projected field lines direct with EUV-image

16. 16 Alternative-2: Compare projected field lines with extracted EUV-loops Dotted lines: Projection of best-fit linear force-free field lines. Loops extracted from EUVI-image with automatic feature recognition tool.

17. 17 Can we extend this method to solve the correspondence problem of STEREO-images? A 3D magnetic field lines is unique. Project field lines onto EUVI-images [or loops extracted from EUVI]. Measure distance of loops and projected magnetic field lines in both images. Loops close to the same field line in both images are very likely associated.

18. 18 Epipolar geometry reduces 3D-reconstruction problem to several 2D problems. Coordinate system is defined by spacecraft locations and rotation axis of the Sun. 3. Geometric Stereoscopy From Inhester, ISSI 2006

19. 19 From Inhester, ISSI 2006 Epipolar geometry provides necessary criterium for loop association: Related loops in both images must intersect with same epipolar lines. Epipolar range often not easy to specify, because ends of loops can be very faint => Parts of loops not visible in one or both images.

20. 20 Reconstruction ambiguity Reconstruction of east-west orientation loops has two solutions, which one is correct? Two-viewpoint images are not sufficient 3. Geometric Stereoscopy

21. 21 4. Estimate reconstruction error in 3D Features tangential to epipolar lines have highest reconstruction error. For east-west coronal loops this means that largest reconstruction errors occur at the loop top. From Inhester, ISSI 2006 curve segment in- clined to epipolar line curve segment par- rallel to epipolar line

22. 22 3D reconstruction error depends on the resolution w of EUVI-images and on the angle between projection planes. Projection angle is smaller or equal as angle between STEREO-A or B. For loop segments in the epipolar plane the projection angle is zero and the error infinite. 4. Estimate reconstruction error in 3D From Inhester, ISSI 2006

23. 23 4. Estimate reconstruction error in 3D Small separation angle between spacecraft: Association problem easy to solve, Large 3D reconstruction error. Large separation angle: Association problem difficult to solve, Small 3D reconstruction error. 2. Associate objects in both images

24. 24 Artificial STEREO-images from a model Active Region. (Wiegelmann & Inhester, Solar Phys. 2006) Magnetic stereoscopy

25. 25 a)Original exact solution b)Pure geometric stereoscopic 3D-reconstruction. The reconstructed 3D loops have ambiguities.

26. 26 Magnetic modeling with different models (c) potential, d) linear force-free, e) nonlinear force-free). Yellow dotted lines show the original exact loops. We used (artificial) EUV-images from two different viewpoints to constrain the magnetic loops.

27. 27 Geometric stereoscopy. We removed ambiguities (multiple solutions) in the stereoscopic reconstruction by choosing the solution which is closest to a given magnetic field model. (Here we used the worst model, a potential field, which was, however, sufficient to remove the ambiguities.)

28. 28 Magnetic stereoscopy Wiegelmann&Inhester 2006

29. 29 Rigorous Test of B-field models. Obtain free model parameters. Test scaling laws. Get plasma parameters along loops - Temperature - Density - Pressure Compare real + artificial images, Loops + B-lines Modeling, Tomography 5. Derive physical quantities

30. 30 EUVI_AEUVI_B Example-1: Active Region loops, Feng et al., ApJL 2007 NOAA 10960

31. 31 EUVI_AEUVI_B Loops identified from unsharp mask filtered images. 1. Extract curve-like objects

32. 32 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 2. Associate objects in both images

33. 33 correspondence in the northern active region Loop correspondence 2. Associate objects in both images

34. 34 Loop reconstruction Yellow: reconstructed 3D loops Red: best fit magnetic field lines view from STEREO_A Northeast of AR 3. Geometric Stereoscopy

35. 35 4. Estimate reconstruction error in 3D Yellow: Reconstructed loop with error bars. Red: Best fit linear force-free field line.

36. 36 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. 5. Derive physical quantities

37. 37 01 23 4 0123 4 EUVI_A EUVI_B Example-2: Polar Plumes (Feng et al., ApJ, submitted) 1. Extract curve-like objects. Here: straight lines, intensity maximum. 2. Associate objects in both images. Easy for small separation angle.

38. 38 dotted lines: 3D reconstruction results solid lines: extrapolations back to the solar surface. solar limb as seen from STEREO A Side View 3. Geometric Stereoscopy 4. Estimate reconstruction error in 3D Small separation angle: Correspondence problem easy to solve, no reconstruction ambiguity. But: Large 3D reconstruction error.

39. 39 Project 3D plumes on SUMER observations (1)Doppler Shift map: No obvious outflows detected in plume regions. (2) N e measured from density sensitive Si VIII line ratio (3) T e measured from Mg IX temperature sensitive line pair. 5. Derive quantities Density, Temperature, Plasma flow

40. 40 Outflow velocity along plumes is to small to make it a dominant contributor to the fast solar wind. 3D plumes are more horizontal than a dipole field. Plumes are in hydrostatic equilibrium. Temperature derived from the density scale height is higher than electron temperature. 5. Derive quantities Density, Temperature, Plasma flow Polar Plumes, Feng et al. 2009

41. 41 Stereoscopy vs. coronal field extrapolation Hinode FOV From DeRosa et al. 2009: Blue lines are stereoscopic reconstructed loops (Aschwanden et al 2008), Red lines nonlinear force-free extrapolated field lines from Hinode/SOT.

42. 42 Stereoscopy vs. coronal field extrapolation Vector magnetogram data (Hinode/SOT) are essential for nonlinear force-free field modeling. Unfortunately Hinode-FOV covered only a small fraction (about 10%) of area spanned by loops reconstructed from STEREO-SECCHI images. Quantitative comparison was unsatisfactory. Plan: Compare magnetic field extrapolations from SDO/HMI and stereoscopy with STEREO/SECCHI and SDO/AIA. Can we combine extrapolations from photospheric measurements with stereoscopy?

43. 43 Self-consistent equilibrium Artificial images LOS-integration Where to go in stereoscopy? Where to go in corona modeling? Force-free code SDO/HMI magnetogram MHS code 3D Force-free magnetic field 3D field lines compare Plasma along magnetic loops Scaling laws Tomography Stereoscopy STEREO images 3D EUV loops consistent?