Testing magnetofrictional extrapolation with the Titov-Démoulin model of solar active regions

Abstract

We examine the nonlinear magnetofrictional extrapolation scheme using the solar active region model by Titov and Démoulin as test field. This model consists of an arched, line-tied current channel held in force-free equilibrium by the potential field of a bipolar flux distribution in the bottom boundary. A modified version, having a parabolic current density profile, is employed here. We find that the equilibrium is reconstructed with very high accuracy in a representative range of parameter space, using only the vector field in the bottom boundary as input. Structural features formed in the interface between the flux rope and the surrounding arcade-"hyperbolic flux tube" and "bald patch separatrix surface"-are reliably reproduced, as are the flux rope twist and the energy and helicity of the configuration. This demonstrates that force-free fields containing these basic structural elements of solar active regions can be obtained by extrapolation. The influence of the chosen initial condition on the accuracy of reconstruction is also addressed, confirming that the initial field that best matches the external potential field of the model quite naturally leads to the best reconstruction. Extrapolating the magnetogram of a Titov-Démoulin equilibrium in the unstable range of parameter space yields a sequence of two opposing evolutionary phases which clearly indicate the unstable nature of the configuration: a partial buildup of the flux rope with rising free energy is followed by destruction of the rope, losing most of the free energy.

14 pages, 10 figures

References in corpus (10)

• Torus instability
• Ideal kink instability of a magnetic loop equilibrium
• Preprocessing of vector magnetograph data for a non-linear force-free magnetic field reconstruction
• Non-linear force-free field modeling of a solar active region around the time of a major flare and coronal mass ejection
• Formation of current sheets and sigmoidal structure by the kink instability of a magnetic loop
• Numerical simulations of fast and slow coronal mass ejections
• Observations and modeling of the early acceleration phase of erupting filaments involved in coronal mass ejections
• Flux Rope Formation Preceding Coronal Mass Ejection Onset
• Can We Improve the Preprocessing of Photospheric Vector Magnetograms by the Inclusion of Chromospheric Observations?
• Testing non-linear force-free coronal magnetic field extrapolations with the Titov-Demoulin equilibrium

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