Abstract
We evaluate the validity of Nonlinear Force Free Field (NLFFF) reconstruction performed with Optimization class (OPTI) codes. We present a postprocessing method that removes the inevitable non-solenoidality of the magnetic field calculated by OPTI codes, which is caused by the noticeable role played by the gradient of the gas pressure in the force balance at photospheric heights, and by some of the mathematical properties of the optimization procedure and the associated boundary value problem (BVP). In essence, postprocessing converts the entire non-solenoidal part of the magnetic field into a solenoidal field, which possibly represents an actual deviation of the magnetic field from its force-free approximation in the photosphere and the corona. Two forms of postprocessing are analyzed in this paper. Postprocessing I eliminates the non-solenoidal component without changing the transverse field at the measurement level, and Postprocessing II leaves the normal field component unchanged. Magnetic field reconstruction, postprocessing, and the comparison of certain values and energy characteristics are performed for active region AR 11158 over a short part of its temporal evolution including the X-class flare in 2011 February. Our version of the OPTI code showed that the free energy decreased by \(\sim10^{32}\) erg within 1 hour, which corresponds to theoretical estimations of the flare-caused magnetic energy loss. This result differs significantly from the one in Sun et al. (Astrophys. J. 748, 15, 2012). Therefore, we also comment on some features of our OPTI code, which may cause significant differences between our results and those obtained using the Wiegelmann (Solar Phys. 219, 87, 2004) version of OPTI code in the study by Sun et al. (Astrophys. J. 748, 15, 2012).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
For this value we use the terminology introduced in Sun et al. (2012). We note that the term ‘mean free energy density’ is somewhat misleading. Formally the free energy is not an additive quantity in the sense that every integral of the free energy density over a subvolume of the calculational domain could be regarded as the free energy of that subvolume. The reason for this is that the potential reference field does not satisfy the correct boundary conditions on the boundaries of the subvolume. Hence, the ‘mean free energy’, as defined by Sun et al. (2012) does not have the same physical properties as the free energy. In particular, it does not have to be always positive.
References
Alissandrakis, C.E.: 1981, On the computation of constant alpha force-free magnetic field. Astron. Astrophys.100, 197. ADS.
Barnes, G., Leka, K.D., Schrijver, C.J., Colak, T., Qahwaji, R., Ashamari, O.W., Yuan, Y., Zhang, J., McAteer, R.T.J., Bloomfield, D.S., Higgins, P.A., Gallagher, P.T., Falconer, D.A., Georgoulis, M.K., Wheatland, M.S., Balch, C., Dunn, T., Wagner, E.L.: 2016, A Comparison of flare forecasting methods. I. Results from the “ALL-CLEAR” workshop. Astrophys. J.829(2), 89. DOI.
Bleybel, A., Amary, T., van Driel-Gesztelyi, L., Leka, K.D.: 2002, Global budget for an eruptive active region. I. Equilibrium reconstruction approach. Astron. Astrophys.395, 685. DOI. ADS.
Brackbill, J.U., Barnes, D.C.: 1980, The Effect of Nonzero \(\nabla\cdot B\) on the numerical solution of the magnetohydrodynamic equations. J. Chem. Phys.35(3), 426. DOI. ADS.
Calabretta, M.R., Greisen, E.W.: 2002, Representations of celestial coordinates in FITS. Astron. Astrophys.395, 1077. DOI. ADS.
Forbes, T.G.: 2000, A review on the genesis of coronal mass ejections. J. Geophys. Res.105, 23153. DOI. ADS.
Hudson, H.S.: 1991, Solar flares, microflares, nanoflares, and coronal heating. Solar Phys.133, 357. DOI. ADS.
Lawrence, C.E.: 1998, Partial Differential Equations, Graduate Studies in Mathematics. AMS, Providence. ISBN 9780821807729. https://books.google.ru/books?id=5Pv4LVB_m8AC.
Livshits, M.A., Rudenko, G.V., Katsova, M.M., Myshyakov, I.I.: 2015, The magnetic virial theorem and the nature of flares on the Sun and other G stars. Adv. Space Res.55, 920. DOI. ADS.
Low, B.C., Lou, Y.Q.: 1990, Modeling solar force-free magnetic fields. Astrophys. J.352, 343. DOI. ADS.
Mastrano, A., Wheatland, M.S., Gilchrist, S.A.: 2018, A check on the validity of magnetic field reconstructions. Solar Phys.293, 130. DOI. ADS.
Metcalf, T.R., DeRosa, M.L., Schrijver, C.J., Barnes, G., van Ballegooijen, A.A., Wiegelmann, T., Wheatland, M.S., Valori, G., McTtiernan, J.M.: 2008, Nonlinear force-free modeling of coronal magnetic fields. II. Modeling a filament arcade and simulated chromospheric and photospheric vector fields. Solar Phys.247, 269. DOI.
Rudenko, G.V., Anfinogentov, S.A.: 2017, Algorithms of the potential field calculation in a three-dimensional box. Solar Phys.292, 103. DOI. ADS.
Schrijver, C.J., DeRosa, M.L., Metcalf, T.R., Liu, Y., McTiernan, J., Régnier, S., Valori, G., Wheatland, M.S., Wiegelmann, T.: 2006, Nonlinear force-free modeling of coronal magnetic fields part I: a quantitative comparison of methods. Solar Phys.235, 161. DOI. ADS.
Sun, X., Hoeksema, J.T., Liu, Y., Wiegelmann, T., Hayashi, K., Chen, Q., Thalmann, J.: 2012, Evolution of magnetic field and energy in a major eruptive active region based on SDO/HMI observation. Astrophys. J.748, 15. DOI. ADS.
Thompson, W.T.: 2006, Coordinate systems for solar image data. Astron. Astrophys.449, 791. DOI. ADS.
Valori, G., Démoulin, P., Pariat, E., Masson, S.: 2013, Accuracy of magnetic energy computations. Astron. Astrophys.553, A38. DOI. ADS.
Wheatland, M.S., Régnier, S.: 2009, A self-consistent nonlinear force-free solution for a solar active region magnetic field. Astrophys. J.700(2), L88. DOI. ADS.
Wheatland, M.S., Sturrock, P.A., Roumeliotis, G.: 2000, An optimization approach to reconstructing force-free fields. Astrophys. J.540, 1150. DOI. ADS.
Wiegelmann, T.: 2004, Optimization code with weighting function for the reconstruction of coronal magnetic fields. Solar Phys.219, 87. DOI. ADS.
Wiegelmann, T., Inhester, B., Sakurai, T.: 2006, Preprocessing of vector magnetograph data for a nonlinear force-free magnetic field reconstruction. Solar Phys.233, 215. DOI. ADS.
Acknowledgements
This study was supported by the Program of Basic Research No. II.16 and the Russian Foundation of Basic Research under grant 20-02-00150. The authors thank Irkutsk Supercomputer Center of SB RAS for providing the access to HPC-cluster Akademik V.M. Matrosov (Irkutsk Supercomputer Center of SB RAS, Irkutsk: ISDCT SB RAS; http://hpc.icc.ru, accessed 16.05.2019).
Author information
Authors and Affiliations
Corresponding authors
Ethics declarations
Disclosure of Potential Conflicts of Interest
The authors declare that they have no conflicts of interest.
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Rudenko, G.V., Dmitrienko, I.S. Validity of Nonlinear Force-Free Field Optimization Reconstruction. Sol Phys 295, 85 (2020). https://doi.org/10.1007/s11207-020-01647-7
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11207-020-01647-7