Testing non-linear force-free coronal magnetic field extrapolations with the Titov-Demoulin equilibrium

Abstract

CONTEXT: As the coronal magnetic field can usually not be measured directly, it has to be extrapolated from photospheric measurements into the corona. AIMS: We test the quality of a non-linear force-free coronal magnetic field extrapolation code with the help of a known analytical solution. METHODS: The non-linear force-free equations are numerically solved with the help of an optimization principle. The method minimizes an integral over the force-free and solenoidal condition. As boundary condition we use either the magnetic field components on all six sides of the computational box in Case I or only on the bottom boundary in Case II. We check the quality of the reconstruction by computing how well force-freeness and divergence-freeness are fulfilled and by comparing the numerical solution with the analytical solution. The comparison is done with magnetic field line plots and several quantitative measures, like the vector correlation, Cauchy Schwarz, normalized vector error, mean vector error and magnetic energy. RESULTS: For Case I the reconstructed magnetic field shows good agreement with the original magnetic field topology, whereas in Case II there are considerable deviations from the exact solution. This is corroborated by the quantitative measures, which are significantly better for Case I. CONCLUSIONS: Despite the strong nonlinearity of the considered force-free equilibrium, the optimization method of extrapolation is able to reconstruct it; however, the quality of reconstruction depends significantly on the consistency of the input data, which is given only if the known solution is provided also at the lateral and top boundaries, and on the presence or absence of flux concentrations near the boundaries of the magnetogram.

6 pages, 2 figures, Research Note

References in corpus (10)

• Confined and ejective eruptions of kink-unstable flux ropes
• Ideal kink instability of a magnetic loop equilibrium
• Optimization code with weighting function for the reconstruction of coronal magnetic fields
• Preprocessing of vector magnetograph data for a non-linear force-free magnetic field reconstruction
• Eruption of a Kink-Unstable Filament in Active Region NOAA 10696
• Formation of current sheets and sigmoidal structure by the kink instability of a magnetic loop
• Comparing magnetic field extrapolations with measurements of magnetic loops
• Nonlinear force-free magnetic field extrapolations: comparison of the Grad-Rubin and Wheatland-Sturrock-Roumeliotis algorithm
• Magnetic modelling and tomography: First steps towards a consistent reconstruction of the solar corona
• Computing nonlinear force free coronal magnetic fields

Cited by in corpus (14)

• Structure, Stability, and Evolution of Magnetic Flux Ropes from the Perspective of Magnetic Twist
• Solar Force-free Magnetic Fields
• Testing magnetofrictional extrapolation with the Titov-Démoulin model of solar active regions
• Can We Improve the Preprocessing of Photospheric Vector Magnetograms by the Inclusion of Chromospheric Observations?
• Pre-Eruptive Magnetic Reconnection within a Multi-Flux-Rope System in the Solar Corona
• A comparison of preprocessing methods for solar force-free magnetic field extrapolation
• Nonlinear force-free modelling: influence of inaccuracies in the measured magnetic vector
• Astrophysics in 2006
• Testing a Solar Coronal Magnetic Field Extrapolation Code with the Titov-Demoulin Magnetic Flux Rope Model
• Vector Magnetic Fields and Electric Currents from the Imaging Vector Magnetograph
• On the Weakening of Chromospheric Magnetic Field in Active Regions
• Formation and Eruption of Hot Channels during an M6.5 Class Solar Flare
• Reconstruction of Coronal Magnetic Fields Using a Poloidal-Toroidal Representation
• Reconstructing Highly-twisted Magnetic Fields