Reconstruction of magnetic fields in the solar corona

The quiescent solar corona is regularly modified by very fast ejections of coronal material and magnetic field (CME) that occur preferably above active regions. Most CME models require the formation of twisted magnetic field structures (flux ropes) before or during such events. Unfortunately, the coronal magnetic field is not directly measurable at present, and therefore it is difficult to verify the validity of different CME models. In order to remove this obstacle, the extrapolation of photospheric magnetic field measurements can be used to reconstruct the missing coronal information. In such applications it is necessary to estimate how well an extrapolation code can reproduce all aspects of highly nonlinear structures such as flux ropes. This is of course possible only using test fields.
In this talk I will present a series of applications of the magneto-frictional extrapolation code to both test fields and measured data. One of the considered test field is the Titov and Démoulin force-free equilibrium (Titov and Démoulin, Astr. and Astrophys. 351, 707, (1999), hereafter TD). The TD equilibrium models a semi-circular, 3D current-carrying flux rope by means of a current ring embedded in a potential field. The parameters of the TD model can be adjusted to create both stable and kink- and torus-unstable configurations. Employing the TD equilibrium as a test field, I will show that our magnetofrictional extrapolation code can reproduce the energy and the twist of the magnetic field within a percent accuracy. This information is essential for the reconstruction of coronal fields involved in eruptions because the twist is, together with the height profile of the overlying potential field, the most important stability parameter - at least as long as the TD equilibrium is a good model of an active region. In the talk I will also show extrapolations of measured magnetograms. In this case, the assumption made in the derivation of the extrapolation methods are not entirely fulfilled, leading to a lower self-consistency of the reconstructed field. The conflict between measurements’ properties and model’s assumption can be partially reconciled employing a data-preprocessing method. However, a significant dependence of the extrapolation results on the details of the employed methods and on their numerical implementation is found. Therefore, in applications to measured magnetograms, an extensive comparison of the extrapolated field with subsidiary observations is essential to assess the reliability of the reconstructed coronal field.