Testing magnetofrictional extrapolation with the Titov-D\'emoulin model of solar active regions

TL;DR

This study validates the magnetofrictional extrapolation method by accurately reconstructing a complex solar active region model, demonstrating its effectiveness in capturing key structural features and energy states from boundary data.

Contribution

The paper shows that force-free fields with realistic structural elements of solar active regions can be reliably reconstructed using magnetofrictional extrapolation from boundary vector fields.

Findings

High-accuracy reconstruction of the Titov-Demoulin model

Reliable reproduction of flux rope and separatrix surface features

Detection of unstable configurations through extrapolation

Abstract

We examine the nonlinear magnetofrictional extrapolation scheme using the solar active region model by Titov and D\'emoulin 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-D\'emoulin 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.