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

¹ LESIA, Observatoire de Paris, CNRS, UPMC, Université Paris Diderot, 5 place Jules Janssen, 92190 Meudon, France e-mail: gherardo.valori@obspm.fr
² Universität Potsdam, Institut für Physik und Astronomie, 14482 Potsdam, Germany
³ University College London, Mullard Space Science Laboratory, Holmbury St. Mary, Dorking, Surrey, RH5 6NT, UK
⁴ Naval Research Laboratory, Space Science Division, Washington, DC 20375, USA
⁵ Predictive Science, Inc., 9990 Mesa Rim Road, Suite 170, San Diego, CA 92121-2910, USA

Received: 12 March 2010
Accepted: 28 April 2010

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 with 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.