Nonlinear force-free coronal magnetic stereoscopy

Abstract: Getting insights into the 3D structure of the solar coronal magnetic field have been done in the past by two completely different approaches: (1.) Nonlinear force-free field (NLFFF) extrapolations, which use photospheric vector magnetograms as boundary condition. (2.) Stereoscopy of coronal magnetic loops observed in EUV coronal images from different vantage points. Both approaches have their strength and weaknesses. Extrapolation methods are sensitive to noise and inconsistencies in the boundary data and the accuracy of stereoscopy is affected by the ability of identifying the same structure in different images and by the separation angle between the view directions. As a consequence, for the same observational data, the computed 3D coronal magnetic field with the two methods do not necessarily coincide. In an earlier work (Paper I) we extended our NLFFF optimization code by the inclusion of stereoscopic constrains. The method was successfully tested with synthetic data and within this work we apply the newly developed code to a combined data-set from SDO/HMI, SDO/AIA and the two STEREO spacecraft. The extended method (called S-NLFFF) contains an additional term that monitors and minimizes the angle between the local magnetic field direction and the orientation of the 3D coronal loops reconstructed by stereoscopy. We find that prescribing the shape of the 3D stereoscopically reconstructed loops the S-NLFFF method leads to a much better agreement between the modeled field and the stereoscopically reconstructed loops. We also find an appreciable decrease by a factor of two in the angle between the current and the magnetic field which indicates the improved quality of the force-free solution obtained by S-NLFFF.