Magnetic Stereoscopy of the Coronal Loops
L.Feng, T.Wiegelmann, B.Inhester, S.Solanki, P.Ruan Max-Planck Institute for Solar System Research
Feng et al. 206/03/2007
Task: 3D loop geometry from the two-viewpoint 2D images
Problems in the classical stereoscopy An application of the magnetic stereoscopy
3D reconstruction from two TRACE images
with the help of the magnetic field lines
A preparation tool for the EUVI image pair
Feng et al. 306/03/2007
Two-view TRACE images mimicking the EUVI image pair
Classical stereoscopy: Correspondence problem: Which two loops in the two images are the projections of the same loop in the real 3D case? (difficult)
Reconstruction problem: how to determine the 3D coordinates
solar rotation:
two viewpoints
Feng et al. 406/03/2007
Solution to the reconstruction problem of curve-like features
Intersection of two back-projection surfaces generated from two view directions. (Inhester, 2007, submitted)
Feng et al. 506/03/2007
Reconstruction ambiguity
Reconstruction of east-west orientation loops has two solutions, which one is correct?
Two-viewpoint images are not sufficient
Feng et al. 606/03/2007
An application of the magnetic stereoscopy
3D geometry of the coronal loops in AR 8891
Two unsolved problems in Part I1. The correspondence problem2. The ambiguity problem
3D magnetic field lines in the corona are important
Feng et al. 706/03/2007
Description of AR 8891
long-lived active region (12 days)
Stereoscopy:
1-Mar-2000, 2-Mar-2000
quite, no flare happening
The global magnetic field evolves very slowly
quasi-stationary loop structures
MDI/SOHO 1-Mar-2000 15 ： 39
Feng et al. 806/03/2007
Loop identification The loops are traced by eye (subjective)The loop segmentation tool for EUVI (talk of Inhester)
1-Mar-2000, 14:22 2-Mar-2000, 17:44
Feng et al. 906/03/2007
3D Magnetic field line in the corona
0
B
BB Linear force-free field model: αis constant over the AR Input data: line-of-sight MDI magnetogram
45 α values 4183 field lines are stored
an example of
α =0, potential field
Feng et al. 1006/03/2007
footpoints: randomly selected
Field line projection onto two TRACE images
Feng et al. 1106/03/2007
Magnetic Stereoscopy
Step 1:
Loop pair identification - correspondence problem Step 2:
Geometrical stereoscopy – reconstruction problem
Reconstruction materials:For viewpoint A, we have 4183 field lines and 5 loops
For viewpoint B, we have 4183 field lines and 6 loops
Feng et al. 1206/03/2007
For every loop combination: LA (Image A)- LB (ImageB)
CLALB (bi) =( CLA (bi) + CLB (bi) ) / 2,
CL (bi): averaged distance between L and bi
a field line b (LA, LB) best fitted with (LA, LB) is found by
CLALB = min { CLALB (bi) } ,
goodness of the correspondence
the smaller, the better .
Sorting CLALB
Lbi
Looking for loop pairs
Feng et al. 1306/03/2007
random starting points in the MDI map a new refined group of field lines
Loop pair (1, 1), C=3.71 Loop pair (0, 0), C=1.54
loop correspondence measure
Feng et al. 1406/03/2007
Identified loop pairs - correspondence problem
loop pair 0-0 1-1 1-2 2-3 4-4
α*L -1.2 -1.5 -1.5 -0.2 0.8
Possible loop pairs: the evolution of the coronal loops during a day
Feng et al. 1506/03/2007
Complete loop feature identification
Best fitting field line helps find loop footpoints and trace a complete loop
Feng et al. 1606/03/2007
Geometrical stereoscopy
solutions: real 3D loop & ghost features
Method testing ： 3D reconstruction from 2 projected field lines of b(0,0)
ghost features
Magnetic stereoscopy
The extent of the two surfaces is limited.
Z
Step2: Geometrical stereoscopy
Reconstruction ambiguity
Feng et al. 1706/03/2007
Magnetic stereoscopy of the loop pair 0-0
The loop top will be the most uncertain part for any stereoscopic reconstruction of loops in the east-west orientation.
Feng et al. 1806/03/2007
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