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

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.

The magnetic field in the solar atmosphere

“…Photospheric vector field measurements with different instrumentation can differ from each other and influence the corresponding coronal field models. Tadesse et al (2013) performed a comparison of global NLFF models based on full-disk vector magnetograms from SOLIS/VSM and SDO/HMI. In this work, some of the TELs clearly observed in coronal images were reproduced with the help of NLFF modeling based on SOLIS/VSM data, but not from the modeling based on SDO/HMI data.…”

A Comparison Between Nonlinear Force-Free Field and Potential Field Models Using Full-Disk SDO/HMI Magnetogram

“…We used a standard preprocessing parameter set µ 1 = µ 2 = 1, µ 3 = 0.001 and µ 4 = 0.05, which are similar to the values calculated from vector data used in previous studies (Wiegelmann, T. and Thalmann, J. K. and Inhester, B. and Tadesse, T. et al, 2012;Tadesse et al, 2012c) for HMI data. The preprocessing influences the structure of the magnetic vector data.…”

“…), so that the model field can be iterated closer to a force-free solution even if the observations are inconsistent. In order to control the speed with which the lower boundary is injected during the NLFFF extrapolation, we have used the Langrangian multiplier of ν = 0.001 as suggested by Tadesse et al (2012c). For more details of the method used in this work we direct the readers to the study by Tadesse et al (2011).…”

“…The term (n = 3) controls the difference between measured and preprocessed vector fields. After preprocessing the HMI data, we solve the force-free equations (1) and (2) using optimization principle (Wheatland, Sturrock, and Roumeliotis, 2000;Wiegelmann, 2004) in spherical geometry (Wiegelmann, 2007;Tadesse, Wiegelmann, and Inhester, 2009;Tadesse et al, 2012c).…”

“…DeRosa, M. L. and Schrijver, C. J. and has studied that different NLFFF models have markedly different field line configurations and provided widely varying estimates of the magnetic free energy in the coronal volume. The main reasons for that problem are (1) the forces acting on the field within the photosphere, (2) the uncertainties on vectorfield measurements, particularly on the transverse component, and (3) the large domain that needs to be modeled to capture the connections of an active region to its surroundings (Wiegelmann, 2007;Tadesse et al, 2011;Tadesse et al, 2012b;Tadesse et al, 2012c). In this study, we have considered those three points explicitly into account for modeling coronal magnetic field in a full-disk.…”