Reconstruction of the solar coronal magnetic field in spherical geometry

Abstract

Context. High-resolution vector magnetographs either onboard spacecrafts or satellites (HMI/SDO, etc.) or ground based (SOLIS, etc.) now gives access to vector synoptic maps, composite magnetograms made of multiple interactive active regions, and full disk magnetograms. It thus become possible to reconstruct the coronal magnetic field on the full Sun scale. Aims. We present a method for reconstructing the global solar coronal magnetic field as a nonlinear force-free field. It is based on a well-posed Grad-Rubin iterative scheme adapted to spherical coordinates Methods. This method is a natural extension to spherical geometry of the one we previously developed in Cartesian geometry. It is implemented in the code XTRAPOLS, which is a massively parallel code. It allows dealing with the strong constraints put on the computational methods by having to handle the very large amounts of data contained in high-resolution large-scale magnetograms. The method exploits the mixed elliptic-hyperbolic nature of the Grad-Rubin boundary value problem. It uses a finite-difference method for the elliptic part and a method of characteristics for the hyperbolic part. The computed field guarantees to be divergence free up to round-off errors, by introducing a representation in terms of a vector potential satisfying specific gauge conditions. The construction of the latter -called here the restricted DeVore gauge -is described in detail in an appendix. Results. We show that XTRAPOLS performs well by applying it to the reconstruction of a particular semi-analytic force-free field that has already been considered by various authors.

Storing free magnetic energy in the solar corona

“…In a real three-dimensional (3-D) solar corona their structure could be quite complicated (Amari et al 1997). Therefore, here we explore a simplified model, where the magnetic field possesses all three spatial components but is invariant with respect to one coordinate (say, y).…”

First use of synoptic vector magnetograms for global nonlinear, force-free coronal magnetic field models

“…Even before SDO, it was known that large-scale connectivity is important for solar eruptive and noneruptive activity (e.g., studies of sympathetic flares, transequatorial loops (Pevtsov 2000), effects of distant active regions on large-scale coronal brightness (Pevtsov & Acton 2001), eruption of filaments triggered by remote flux emergence, and evolution (e.g., . Therefore, these needs motivate us to implement a NLFFF procedure in spherical geometry (Wiegelmann 2007;Tadesse et al 2009Tadesse et al , 2011Tadesse et al , 2012aTadesse et al ,b, 2013bTadesse et al , 2014Guo et al 2012;Amari et al 2013) Nonlinear force-free reconstruction of the global solar magnetic field from line-of-sight component of synoptic magnetograms has been developed by Contopoulos et al (2011). In this study, we estimate the free magnetic energy for global corona using the synoptic vector magnetograms from SOLIS/VSM.…”

Global Solar Free Magnetic Energy and Electric Current Density Distribution of Carrington Rotation 2124

“…Using Equations (1) and (2) as constraints equations, one can calculate the magnetic field density in a corona volume for photospheric measurements. Nonlinear force-free magnetic field (NLFFF) extrapolation techniques are the best mathemathical modeling tools currently being used to estimate the magnetic field in the higher solar atmosphere (Amari and Aly, 2010;Aschwanden and Malanushenko, 2012;Contopoulos, 2013;He and Wang, 2008;Malanushenko et al, 2012;Jiang and Feng, 2012;Song et al, 2007;Tadesse, Wiegelmann, and Inhester, 2009;Tadesse et al, 2013a;Wheatland, Sturrock, and Roumeliotis, 2000;Wiegelmann, 2004;Wiegelmann, 2007). For more detailed explanations of NLFFF methods, we direct the reader to the recent review by Wiegelmann and Sakurai (2012).…”

“…On the largest scales, the corona of a whole hemisphere was found to be magnetically coupled (Schrijver, 2009;h=80Mm and Acton, 2001). Therefore, it appears prudent to implement a NLFFF procedure in spherical geometry (Amari et al, 2013;Tadesse et al, 2013b) for use when global scale boundary data are available (see Figure 1), such as synoptic maps of photospheric vector magnetic field synthesized from Vector Spectromagnetograph (VSM) on Synoptic Optical Long-term Investigations of the Sun (SOLIS) (Gosain et al, 2013). In this work, we apply spherical NLFFF procedure to synoptic vector map of Carrington rotation 2124 to reconstruct 3D magnetic field solutions (potential and NLFFF) from which we infer the distributions of free magnetic energy and electric current density in corona volume globally.…”