## 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

*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.

Key words: magnetic fields / Sun: corona / Sun: atmosphere / methods: numerical

*© ESO, 2013*