A comparison of preprocessing methods for solar force-free magnetic field extrapolation

¹ Institut für Physik und Astronomie, Universität Potsdam, Karl-Liebknecht-Str. 24/25, 14476 Potsdam, Germany
e-mail: fuhrmann@agnld.uni-potsdam.de, seehafer@uni-potsdam.de
² LESIA, Observatoire de Paris, CNRS, UPCM, Université Paris Diderot, 5 place de Jules Janssen, 92190 Meudon, France
e-mail: gherardo.valori@obspm.fr
³ Max-Planck-Institut für Sonnensystemforschung, Max-Planck-Str. 2, 37191 Katlenburg-Lindau, Germany
e-mail: wiegelmann@mps.mpg.de

Received: 22 July 2010
Accepted: 12 October 2010

Abstract

Context. Extrapolations of solar photospheric vector magnetograms into three-dimensional magnetic fields in the chromosphere and corona are usually done under the assumption that the fields are force-free. This condition is violated in the photosphere itself and a thin layer in the lower atmosphere above. The field calculations can be improved by preprocessing the photospheric magnetograms. The intention here is to remove a non-force-free component from the data.

Aims. We compare two preprocessing methods presently in use, namely the methods of Wiegelmann et al. (2006, Sol. Phys., 233, 215) and Fuhrmann et al. (2007, A&A, 476, 349).

Methods. The two preprocessing methods were applied to a vector magnetogram of the recently observed active region NOAA AR 10 953. We examine the changes in the magnetogram effected by the two preprocessing algorithms. Furthermore, the original magnetogram and the two preprocessed magnetograms were each used as input data for nonlinear force-free field extrapolations by means of two different methods, and we analyze the resulting fields.

Results. Both preprocessing methods managed to significantly decrease the magnetic forces and magnetic torques that act through the magnetogram area and that can cause incompatibilities with the assumption of force-freeness in the solution domain. The force and torque decrease is stronger for the Fuhrmann et al. method. Both methods also reduced the amount of small-scale irregularities in the observed photospheric field, which can sharply worsen the quality of the solutions. For the chosen parameter set, the Wiegelmann et al. method led to greater changes in strong-field areas, leaving weak-field areas mostly unchanged, and thus providing an approximation of the magnetic field vector in the chromosphere, while the Fuhrmann et al. method weakly changed the whole magnetogram, thereby better preserving patterns present in the original magnetogram. Both preprocessing methods raised the magnetic energy content of the extrapolated fields to values above the minimum energy, corresponding to the potential field. Also, the fields calculated from the preprocessed magnetograms fulfill the solenoidal condition better than those calculated without preprocessing.