1. 3D Stereoscopic Reconstruction of CMEs by Forward Modeling 5th Consortium STEREO-SECCHI Meeting Orsay, March 2007 Y.BOURSIER – P.LAMY – F.GOUDAIL - A.LLEBARIA

2. Outline I – Introduction II – CME models and their parameters III – Method and algorithm IV – Results V – Conclusion

3. Classical stereoscopic techniques of computer vision cannot achieve a reliable reconstruction of CMEs: Problem 1: Morphology of CMEs too complicated. A solution : strong assumption on the shape : forward modeling. Problem 2: Optically thin medium. A solution : compare images with simulated well known images. Problem 3: High frequency noise and largescale stable structures superimposed on CMEs. A solution : find global characteristic quantities not sensitive to photometric changes and not sensitive to geometric details. STEREO – B COR2STEREO – A COR2 Top 3D view 3D view

4. Purpose : - Estimate the position and the direction of propagation of CMEs in space. - Characterize the global morphology of CMEs. - Reconstruct CMEs in Space. Method : - Build a library of simulated CMEs (forward modeling) sampling a large parameter space (position angles, shape, etc..) - Compute global parameters and invariants. - Compare these quantities with those calculated on the observed images. - Identify by minimization the CME in the library that best fits the observation. - The selected CME model is supposed to best describe the real CME.

5. CME Models I – Spherical cap - Very basic model. - Leading part of ice cream model of Schwenn et al. (2005). - Assume an hemispheric shape. - Four parameters : 3 for position, and the cone angle. - Thickness dr is fixed to 0.1 Rsun. y α x C Sun O dr r Lateral view Front view 3D view

6. CME Models II – Fluxrope model - More elaborated model (well suited to filament eruptions). - Model already introduced by Thernisien et al. (2006). - Six parameters : 3 for position, 1 for orientation and 2 for shape. - Shape parameters : the cone angle and the radius r max. Top view Lateral view 3D view y α x C Sun O r max r

7. CME Models III – Cloud-like model - Extension of the fluxrope model. - Well suited to filaments eruptions with magnetic reconnections. - Six parameters : 3 for position, 1 for orientation and 2 for shape. - Shape parameters : the cone angle and the radius r max. y α x C Sun O r max r Top view Lateral view 3D view

8. CMEs parameters x y z Sun O C r x y z O C r Spherical cap : 4 parameters 3 for position : Longitude Phi Latitude Theta Radial distance r 1 for shape : Angle of the cone Alpha Fluxrope and cloud-like : 6 parameters 3 for position : Longitude Phi Latitude Theta Radial distance r 2 for shape : Angle between feet Alpha Coefficient k linked to r max with the assumption r max =k*r 1 for orientation : Angle Psi System coordinates are compatible with the WCS. (see Thompson et al. 2006)

9. Library of images Three-dimensionnal electron density of the CME computed from its analytic expression. Then compressed by octree to significantly reduce the computation time (see Saez et al. 2005) Images generated by a raytracing algorithm incorporating Thomson scattering. STEREO – B COR2STEREO – A COR2

10. Library of images Space of parameters sampled for each model and domain reduced for symmetry reasons : Latitude : from 0° to 80° with a step of 10°. Spherical cap : 6300 images. Longitude : from 0° to 90° with a step of 10°. Radial distance r : from 2 Rsun to 8 Rsun with a step of 1 Rsun. Cone angle alpha : from 10° to 100° with a step of 10°. Fluxrope and Cloud-like : 27000 images for each model Longitude : from 40° to 90° with a step of 10°. Radial distance : from 2 Rsun to 8 Rsun with a step of 2 Rsun. Angle Alpha : from 10° to 90° with a step of 20°. Coefficient k : from 0.2 to 1.0 with a step of 0.2. Orientation Psi : from 0° to 80° with a step of 20°. Couples of stereoscopic images can be simulated with a separation angle between satellites ranging from 10° to 50° with a step of 10°.

11. Geometric characterization A pixel of brigthness maxima on edge on one image = a line-of-sight (los) tangent to the surface. We define manually n pixels and we search the surface tangent to n los. Spherical cap : surface of order 2. - Exact reconstruction by minimization is possible (downhill simplex method). - Set of 4 parameters is estimated. Fluxrope and cloud-like : surface of order 4. - Two many parameters. - Need more information. - Local approximation by a spherical cap. - Use the distance “d” between Sun center and leading edge of the approximated spherical cap. leading edge of the approximated spherical cap. STEREO – B COR2 STEREO – A COR2 Top 3D view 3D view LOS

12. Characteristic quantities Maximum of geometric criteria and minimum of photometric criteria : - Angular witdh AW. - Gravity center G (geometric moments of order 1). - Area of ellipse of inertia E (geometric moments of order 2). - 3 geometric invariants by translation, rotation, homotethy computed from geometric moments of order 3. G AW E G E Fluxrope : Cloud :

13. Reconstruction of fluxrope and cloud-like 1 – Work on couple of images : Reconstruct G in space : Estimate of longitude and latitude. Local approximation of edge by a sphere and measure of : comparison with the library (Elimination of non relevant cases – tolerance 15%). 2 – Work independently on images : Compare the characteristic quantities and with those of the library (Elimination of non relevant cases – tolerance 15%). Correlate the vector of 3 invariants with those of the library (Elimination of correlations <0.95). 3 – Fusion of results of each image : Set of 4 remaining parameters present for both views are conserved.

14. Tests and results : spherical cap - Tests on 6100 couples of stereoscopic images with separation angle from 10° to 50°. - 6 ‘edge’ pixels were automatically selected on each image : 12 tangent lines-of-sight. - Longitude and latitude (then direction of propagation) are well recovered. - Estimate of distance r and cone angle alpha efficient but sensitive to occultations near Sun and next to 15 Rsun : Longitude Latitude

15. Tests and results : cloud-like with separation angle from 10° to 50°. Tests on 5062 couples of simulated COR2 images with separation angle from 10° to 50°. - Local approximation by a spherical cap constrained with 12 lines-of-sight. - Excellent estimate of longitude and latitude by reconstruction of G. Longitude Latitude

16. Tests and results : cloud-like The algorithm returns a list of possible set of parameters for the observed CME. When the correct set of parameters is proposed in the list, the test is considered as successful. When no set is proposed or when the correct set is not present in the final list, the algorithm fails. Probability of success : 96.2 % Probability of failure : 3.8 % No value returned : 3.7 % False values returned : 0.1% When success : Probability of 1 set : 46 % Probability of 1 or 2 sets : 66 % Probability of less than 5 sets : 91.5 % Histogram of number of set of 4 parameters returned when success

17. Conclusion - Tests on fluxrope in progress. - Refining the sampling of space of parameters in progress. - Quantitative and qualitative results have revealed that : - Position parameters and then direction of propagation are very well recovered. - Global morphology of CME is well characterized. - 3D velocity will be easily calculated from position and shape parameters. - Method purely geometric based on parametric models of CMEs. - Need minimum manual interaction (the user must locate the CME front with few points). - Algorithm can be turned into a fully automatic process if CME is properly isolated from other structures on images. - New models can be easily added. Suggestions ?? - Algorithm can use additional points of view (LASCO/C2-C3).

18. Reconstruction of fluxrope and cloud-like 1 - Local approximation of leading edge by a spherical cap : measure of distance between center of Sun and leading edge. Analytic expression of d=f(r,alpha,k) : comparison of all d in the library with and elimination of non relevant cases (tolerance of +/- 15 % on ). First estimate of longitude and latitude. 2 - Computation of G on STEREO-A and STEREO-B images, then reconstruction in Space. Second estimate of longitude and latitude. 3 - On each image : a - Measure of angular width and of the area of ellipse of inertia. Comparison with AW and E in library and elimination of non relevant set of parameters (tolerance of +/- 15 %). b - Correlation with a vector with 3 discriminant geometric invariants. Elimination of correlations <0.95. 4 - Fusion of results obtained on each image : set of parameters present for both views are conserved.