Nonlinear force-free coronal magnetic field modelling and preprocessing of vector magnetograms in spherical geometry

¹ Max-Planck-Institut für Sonnensystemforschung, Max-Planck-Strasse 2, 37191 Katlenburg-Lindau, Germany e-mail: [tadesse;wiegelmann;inhester]@mps.mpg.de
² Addis Ababa University, College of Education, Department of Physics education, PO Box 1176, Addis Ababa, Ethiopia

Received: 19 May 2009
Accepted: 16 September 2009

Abstract

Context. Knowledge about the coronal magnetic field is important to the understanding of many phenomena, such as flares and coronal mass ejections. Routine measurements of the solar magnetic field vector are traditionally carried out in the photosphere. We compute the field in the higher layers of the solar atmosphere from the measured photospheric field under the assumption that the corona is force-free. However, those measured data are inconsistent with the above force-free assumption. Therefore, one has to apply some transformations to these data before nonlinear force-free extrapolation codes can be applied.

Aims. Extrapolation codes of cartesian geometry for medelling the magnetic field in the corona do not take the curvature of the Sun's surface into account. Here we develop a method for nonlinear force-free coronal magnetic field medelling and preprocessing of photospheric vector magnetograms in spherical geometry using the optimization procedure.

Methods. We describe a newly developed code for the extrapolation of nonlinear force-free coronal magnetic fields in spherical coordinates over a restricted area of the Sun. The program uses measured vector magnetograms on the solar photosphere as input and solves the force-free equations in the solar corona. We develop a preprocessing procedure in spherical geometry to drive the observed non-force-free data towards suitable boundary conditions for a force-free extrapolation.

Results. We test the code with the help of a semi-analytic solution and assess the quality of our reconstruction qualitatively by magnetic field line plots and quantitatively with a number of comparison metrics for different boundary conditions. The reconstructed fields from the lower boundary data with the weighting function are in good agreement with the original reference fields. We added artificial noise to the boundary conditions and tested the code with and without preprocessing. The preprocessing recovered all main structures of the magnetogram and removed small-scale noise. The main test was to extrapolate from the noisy photospheric vector magnetogram with and without preprocessing. The preprocessing was found to significantly improve the agreement between the extrapolated and the exact field.