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. 2 06/03/2007 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. 3 06/03/2007 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. 4 06/03/2007 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. 5 06/03/2007 Reconstruction ambiguity Reconstruction of east-west orientation loops has two solutions, which one is correct? Two-viewpoint images are not sufficient

Feng et al. 6 06/03/2007 An application of the magnetic stereoscopy 3D geometry of the coronal loops in AR 8891 Two unsolved problems in Part I 1. The correspondence problem 2. The ambiguity problem 3D magnetic field lines in the corona are important

Feng et al. 7 06/03/2007 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 ： 39

Feng et al. 8 06/03/2007 Loop identification The loops are traced by eye (subjective) The loop segmentation tool for EUVI (talk of Inhester) 1-Mar-2000, 14:222-Mar-2000, 17:44

Feng et al. 9 06/03/2007 3D Magnetic field line in the corona 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 /03/2007 footpoints: randomly selected Field line projection onto two TRACE images

Feng et al /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 /03/2007  For every loop combination: L A (Image A)- L B (ImageB) C LALB (bi) =( C LA (bi) + C LB (bi) ) / 2, C L (bi): averaged distance between L and b i a field line b (L A, L B ) best fitted with (L A, L B ) is found by C LALB = min { C LALB (bi) }, goodness of the correspondence the smaller, the better.  Sorting C LALB L bibi Looking for loop pairs

Feng et al /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 /03/2007 Identified loop pairs - correspondence problem loop pair α*L Possible loop pairs: the evolution of the coronal loops during a day

Feng et al /03/2007 Complete loop feature identification Best fitting field line helps find loop footpoints and trace a complete loop

Feng et al /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 /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 /03/2007