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Studying Magnetic Field Variations Accompanying the 2011 June 7 Eruptive Event, by Using Nonlinear Force-Free Field Modeling

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Abstract

We study the features of the magnetic field variations within the 2011 June 7 eruptive event that includes a large filament eruption, a flare, and a CME formation. The magnetic field characteristics were obtained by using vector measurements of the magnetic field with the SDO/HMI and 3D magnetic field calculations based on nonlinear force-free field (NLFFF) modeling. Strong and relatively fast variations in the photospheric field characteristics after the flare onset are shown to be observed only within a small site (\(20''\times 20''\)) of the eruption region in the neighborhood of the polarity inversion line (PIL).

We found that the magnetic field strength, the electric current density, current helicity density and free magnetic energy density above this region are growing with height reaching their maximums at the level of ∼15 Mm. After 2011 July 7 00:00 UT, this height started gradually reducing.

The NLFFF extrapolation revealed the presence of a magnetic flux rope elongated approximately along the main PIL and an arcade of magnetic field lines over it. The flux-rope axis is located at height of ∼15 Mm. The flux-rope footpoints approximately coincide with the eruptive filament footpoints. Thus, we concluded that the detected flux rope is associated with the magnetic structure of the observed filament. The detected strong variation of the magnetic field within the eruption region are most probably associated with the magnetic field reconfiguration after the filament eruption. The \(T_{n}\) parameter, which is the average magnetic field twist within the flux rope, was found to increase up to 2.5 rotations before the flare onset, and to dramatically decrease afterward. This may reflect the developing of kink instability that presumably triggered this eruption.

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Notes

  1. The evident conditional character of this notation should be noted, which is related to its value being non-additive. Equation 13 contains the value of the integral over subvolume, which, strictly speaking, is not free energy. For an arbitrary subvolume, the potential field used, does not, in the general case, satisfy the condition (necessary in the definition of “free energy”) that the normal components \(B_{P}\) and \(B_{N}\) be equal at the subvolume boundaries. As a result, the physical meaning of \(e_{f}^{m}(h,t)\) can substantially differ from the physical value of the “free energy” concept. For example, this value, unlike free energy, does not have to be always positive. On the contrary, its negative values in the lower layers (Figure 12(a, c)) reflect, in terms of physics, the force-free character of the \(B_{N}\) we obtain, following from the virial theorem for force-free fields (Livshits et al., 2015; Rudenko and Dmitrienko, 2020).

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Acknowledgements

The authors thank the SDO/AIA, SDO/HMI, and GOES teams for a possibility to freely use the data from these instruments. G.V. Rudenko would like to 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). The study was carried out within the basic funding from Basic Research Program II.16. Ya.I. Egorov, S.A. Anfinogentov and I.I. Myshyakov acknowledge partial support from the Russian Foundation for Basic Research Grants No. 18-32-20165. I.I. Myshyakov acknowledges partial support from the RFBR grant 18-32-00540. Ya.I. Egorov, V.G. Fainshtein and G.V. Rudenko acknowledge partial support from the Russian Foundation for Basic Research Grants No. 20-02-00150.

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  1. Institute of Solar-Terrestrial Physics SB RAS, PO Box 291, Irkutsk, Russia

    Y. I. Egorov, V. G. Fainshtein, I. I. Myshyakov, S. A. Anfinogentov & G. V. Rudenko

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Egorov, Y.I., Fainshtein, V.G., Myshyakov, I.I. et al. Studying Magnetic Field Variations Accompanying the 2011 June 7 Eruptive Event, by Using Nonlinear Force-Free Field Modeling. Sol Phys 295, 52 (2020). https://doi.org/10.1007/s11207-020-01613-3

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