Full-disk nonlinear force-free field extrapolation of SDO/HMI and SOLIS/VSM magnetograms

¹ Department of PhysicsDrexel University, Philadelphia, PA, 19104-2875 USA
e-mail: tasfaw@einstein.physics.drexel.edu
² Addis Ababa University, Institute of Geophysics, Space Science, and Astronomy, PO Box 1176 Addis Ababa, Ethiopia
e-mail: tilaye.tadesse@gmail.com
³ Max-Planck-Institut für Sonnensystemforschung, Max-Planck-Strasse 2, 37191 Katlenburg-Lindau, Germany
⁴ NASA/GSFC, Greenbelt, MD, USA
⁵ National Solar Observatory, Sunspot, NM 88349, USA
⁶ W.W. Hansen Experimental Physics Laboratory, Stanford University, Stanford, CA 94305, USA

Received: 17 July 2012
Accepted: 1 November 2012

Abstract

Context. The magnetic field configuration is essential for understanding solar explosive phenomena, such as flares and coronal mass ejections. To overcome the unavailability of coronal magnetic field measurements, photospheric magnetic field vector data can be used to reconstruct the coronal field. Two complications of this approach are that the measured photospheric magnetic field is not force-free and that one has to apply a preprocessing routine to achieve boundary conditions suitable for the force-free modeling. Furthermore the nonlinear force-free extrapolation code should take uncertainties into account in the photospheric field data. They occur due to noise, incomplete inversions, or azimuth ambiguity-removing techniques.

Aims. Extrapolation codes in Cartesian geometry for modeling the magnetic field in the corona do not take the curvature of the Sun’s surface into account and can only be applied to relatively small areas, e.g., a single active region. Here we apply a method for nonlinear force-free coronal magnetic field modeling and preprocessing of photospheric vector magnetograms in spherical geometry using the optimization procedure to full disk vector magnetograms. We compare the analysis of the photospheric magnetic field and subsequent force-free modeling based on full-disk vector maps from Helioseismic and Magnetic Imager (HMI) onboard the solar dynamics observatory (SDO) and Vector Spectromagnetograph (VSM) of the Synoptic Optical Long-term Investigations of the Sun (SOLIS).

Methods. We used HMI and VSM photospheric magnetic field measurements to model the force-free coronal field above multiple solar active regions, assuming magnetic forces to dominate. We solved the nonlinear force-free field equations by minimizing a functional in spherical coordinates over a full disk and excluding the poles. After searching for the optimum modeling parameters for the particular data sets, we compared the resulting nonlinear force-free model fields. We compared quantities, such as the total magnetic energy content, free magnetic energy, the longitudinal distribution of the magnetic pressure, and surface electric current density, using our spherical geometry extrapolation code.

Results. The magnetic field lines obtained from nonlinear force-free extrapolation based on HMI and VSM data show good agreement. However, the nonlinear force-free extrapolation based on HMI data contain more total magnetic energy, free magnetic energy, the longitudinal distribution of the magnetic pressure, and surface electric current density than do the VSM data.