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arxiv: 2606.19546 · v1 · pith:FIX2HAWXnew · submitted 2026-06-17 · 🌌 astro-ph.SR

Effects of the Background Magnetic Field on Flux Rope Eruptions

Xianyu Liu , Spiro K. Antiochos , Igor V. Sokolov , Tamas I. Gombosi , Bart van der Holst , G\'abor T\'oth , Nishtha Sachdeva , Lulu Zhao This is my paper

Pith reviewed 2026-06-26 18:50 UTC · model grok-4.3

classification 🌌 astro-ph.SR
keywords solar eruptionsmagnetic flux ropescoronal mass ejectionsbackground magnetic fieldMHD simulationflare reconnectiontorus instability
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The pith

An antiparallel background magnetic field lowers the free-energy threshold for flux rope eruption but does not guarantee a successful coronal mass ejection.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper runs three MHD simulations of an identical bipolar active region containing a pre-existing magnetic flux rope, varying only the orientation of the surrounding background field. In the antiparallel case the rope reaches eruption conditions at lower stored energy and experiences faster but briefer flare reconnection. Two runs produce full eruptions while one produces only a confined flare, showing that the background field modulates both the initiation threshold and the outcome.

Core claim

Simulations demonstrate that an antiparallel background field reduces the magnetic free-energy threshold required for eruption relative to parallel configurations, enables earlier breakout reconnection that drives a rapid exponential rise phase, and shortens the duration of flare reconnection, yet still permits a failed eruption in one instance.

What carries the argument

Three MHD simulations that hold the active-region flux rope fixed while changing only the background magnetic field orientation, then track free energy, acceleration profile, torus-instability criterion, and the timing of breakout versus flare reconnection.

If this is right

  • Breakout reconnection, not the torus instability, initiates the rapid-rise phase in the successful cases.
  • Antiparallel background fields produce faster flare reconnection of shorter total duration.
  • Eruption outcome (CME versus confined flare) cannot be predicted from free energy alone when background orientation varies.
  • The background field must be included when classifying whether a given active-region flux rope will erupt.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Real-time vector magnetograms of the quiet-Sun field surrounding active regions could improve forecasts of whether an observed flux rope will produce a geoeffective CME.
  • The same background-orientation dependence may explain why some flux ropes in decaying active regions erupt while others remain confined even at comparable free energies.
  • Extending the simulations to include a wider range of background tilt angles would map the full boundary between successful and failed eruptions.

Load-bearing premise

The chosen initial magnetic configurations and the MHD equations capture the dominant reconnection and instability processes without numerical effects that would change whether an eruption succeeds or fails.

What would settle it

A solar active region whose measured background field is antiparallel yet requires higher free energy to erupt than the parallel case, or whose parallel background allows eruption at lower energy than predicted.

Figures

Figures reproduced from arXiv: 2606.19546 by Bart van der Holst, G\'abor T\'oth, Igor V. Sokolov, Lulu Zhao, Nishtha Sachdeva, Spiro K. Antiochos, Tamas I. Gombosi, Xianyu Liu.

Figure 1
Figure 1. Figure 1: The magnetic field in the y = 0 plane in the three cases. The strength of the background dipole is characterized by B BG,N r . The null points in Cases 2 and 3 are labeled with blue asterisks. and background pairs of magnetic charges have the same orientation and are both antisymmetric about the z = 0 plane, the primary photospheric PIL lies at the equator. Bex in Cases 2 and 3 exhibits a multipolar topolo… view at source ↗
Figure 2
Figure 2. Figure 2: Simulation setup. (a): The simulation grid in the y = 0 plane. (b): The simulated magnetic field in Case 3 before the insertion of the MFR. (c): The AR and the MFR (green field lines) in Case 3. rather than solving the 3-D MHD equations. Hereafter, the two regions are referred to as the 3D MHD region and the TFLM region, respectively. The TFLM region contains a set of 1D magnetic threads that connect the 3… view at source ↗
Figure 3
Figure 3. Figure 3: The MFR viewed from +z-axis during the relaxation from t = 0s to t = 2400 s in Case 1. [180◦ − ∆ϕ, 180◦ + ∆ϕ] × [−∆λ, ∆λ], where ∆ϕ = 10◦ and ∆λ = 15◦ . As in B. van der Holst et al. (2025), the modulation of ζ within this region is given by ζ (ϕ, λ) = ζ0 cos  π 2 ϕ − 180◦ ∆ϕ  cos  π 2 λ ∆λ  (3) By applying Equation 2 in the simulation, the initially stable MFR is driven to deviate from the equilibrium… view at source ↗
Figure 4
Figure 4. Figure 4: The simulation results for the three cases. Each row shows the magnetic field of one case at three different moments: (1) at the onset of driving, (2) near the end of driving, and (3) after the eruption. The red field lines are anchored to the footpoints of the MFR. The white rods indicate the field lines surrounding the configuration. The blue contours indicate J B = 2 µAm−2G−1 ≈ 17.5 µ0Rs , which show th… view at source ↗
Figure 5
Figure 5. Figure 5: The simulation results of Case 3 at t = 5400 s. (a): The field lines anchored to the footpoints of the initial MFR (red) and surrounding field lines (white). (b): The projected magnetic field vectors in the y = 0 plane. 3. RESULTS 3.1. Magnetic Field Evolution For each simulation, we saved the 3D distribution of the variables with a cadence of 120 s [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The evolution of ∆EB (upper panel) and ∆Ekin (lower panel) in each case. The vertical dashed-dotted lines indicate the end time of STITCH in each simulation. CS and breakout CS. However, we note that at t = 5160 s ( [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: (a)-(c): The kinetic energy on a logarithmic scale. The vertical dashed line labels the onset of flare reconnection. (d)-(f): The blue points represent the MFR apex height (H) as a function of time. The orange curve represent Hfit(t) derived using polynomial fit.(g)-(i): The RMS of |Hfit − H| using different values of D. (j)-(l): The acceleration on a logarithmic scale analytically derived from Hfit(t) usi… view at source ↗
Figure 8
Figure 8. Figure 8: (a): A two-dimensional sketch of the flare reconnection and breakout reconnection. (b)-(d): The time-latitude diagram of the field line length derived by tracing along the field line from a series of points lying on the intersection between the y = 0 plane and the 1.0Rs sphere. (e)-(g): The time-latitude diagram of the end point latitude of the field line tracing. The three columns represent Cases 1 to 3, … view at source ↗
Figure 9
Figure 9. Figure 9: Upper row: The MFR apex height (H) as a function of time. Middle row: The decay index as a function of height. Lower row: The decay index at the MFR apex. The three columns correspond to Cases 1 to 3, respectively. The red vertical lines in Cases 2 and 3 indicate the transition to the rapid exponential rise phase. A key point is the relation between the torus instability and the rapid exponential rise phas… view at source ↗
Figure 10
Figure 10. Figure 10: The timing of processes of interest and the energy curves for three cases. In each panel, the black solid curve and the black dashed curve indicate EB(t) and Ekin, respectively. The scales for EB(t) and Ekin are given by the left and right vertical axes, respectively. The red vertical lines label the onset and end of the flare reconnection. For each of Cases 2 and 3, the blue vertical lines label the onse… view at source ↗
read the original abstract

Solar eruptive events are generally believed to involve magnetic flux ropes (MFR), formed either in the pre-eruptive phase of the event or during the eruption itself. These MFR eruptions exhibit significant complexity and variations due to the interplay of the physical mechanisms involved, in particular magnetic reconnection and ideal instabilities. This work considers the effect of the background magnetic field on the nature of eruptions with pre-existing MFRs. We used a new MHD model to simulate the whole MFR eruption process, including the pre-eruptive stage and the initiation. Three simulations were performed, all of which used an identical bipolar active region, but with different background magnetic fields in the three cases. The simulations resulted in two successful eruptions (CMEs) and one failed eruption (a confined flare). We analyzed the energetics and the acceleration of the MFR in detail, and found a transition to a rapid exponential rise phase in two of the simulations. We also calculated the criterion for the torus instability and the timing of the breakout and flare reconnections. Our results show that the rapid exponential rise phase is likely due to breakout reconnection. We conclude that a background field antiparallel to the active-region field lowers the magnetic free-energy threshold for eruption; but, does not guarantee a successful eruption. We also found that an antiparallel background field leads to faster flare reconnection, but of shorter duration. Our findings underscore the importance of the background magnetic field in understanding CMEs.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript reports results from three MHD simulations of pre-existing magnetic flux ropes embedded in a bipolar active region, each with a different background magnetic field. Two cases produce successful eruptions (CMEs) while one produces a confined flare. The authors conclude that an antiparallel background field lowers the free-energy threshold for eruption (but does not guarantee success) and produces faster yet shorter-duration flare reconnection, with the rapid exponential rise phase attributed to breakout reconnection.

Significance. If the results hold after addressing numerical concerns, the work demonstrates the role of background field orientation in modulating eruption thresholds and reconnection dynamics via forward simulations, which could inform observational interpretations of CME initiation and the interplay between ideal instabilities and reconnection.

major comments (2)
  1. [Abstract and simulation description paragraph] Abstract and simulation description paragraph: the central claims on lowered eruption threshold and altered reconnection timing rest on differences across three runs, but no grid resolution, explicit resistivity, or convergence tests are reported. In ideal MHD the only reconnection is numerical; without these checks the attribution of outcomes to background-field orientation rather than discretization effects cannot be verified.
  2. [Results section on flare reconnection and torus instability criterion] Results section on flare reconnection and torus instability criterion: the reported differences in reconnection speed/duration and the success/failure classification are load-bearing for the conclusions, yet the manuscript provides no quantitative error analysis or resolution study to confirm that the measured reconnection rates and eruption outcomes are insensitive to numerical diffusivity.
minor comments (2)
  1. Specify the precise orientations and strengths of the three background fields relative to the active-region field, including any vector components or decay profiles used.
  2. Clarify whether the new MHD code employs any explicit resistivity or relies solely on numerical diffusion, and state the grid resolution employed in each run.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive report and the opportunity to address the numerical concerns. We agree that additional details on resolution and convergence are needed to strengthen the attribution of results to the background field. We respond point-by-point below and will revise accordingly.

read point-by-point responses

  1. Referee: [Abstract and simulation description paragraph] Abstract and simulation description paragraph: the central claims on lowered eruption threshold and altered reconnection timing rest on differences across three runs, but no grid resolution, explicit resistivity, or convergence tests are reported. In ideal MHD the only reconnection is numerical; without these checks the attribution of outcomes to background-field orientation rather than discretization effects cannot be verified.

    Authors: We agree that the original manuscript does not report grid resolution, explicit resistivity (none is used), or convergence tests. All runs employ the same ideal MHD setup on identical grids, so numerical diffusivity is the same across cases; the observed differences in eruption success and reconnection timing therefore cannot be numerical artifacts of differing discretizations. In the revised manuscript we will add an explicit numerical methods subsection stating the grid resolution, domain size, and code scheme, together with a limited resolution-doubling test on one case to confirm that the qualitative classification (eruptive vs. confined) and the relative timing of breakout versus flare reconnection remain unchanged. revision: yes

  2. Referee: [Results section on flare reconnection and torus instability criterion] Results section on flare reconnection and torus instability criterion: the reported differences in reconnection speed/duration and the success/failure classification are load-bearing for the conclusions, yet the manuscript provides no quantitative error analysis or resolution study to confirm that the measured reconnection rates and eruption outcomes are insensitive to numerical diffusivity.

    Authors: We acknowledge the absence of quantitative error bars or a dedicated resolution study for the reconnection-rate time series. Because the three simulations share identical numerical parameters, any systematic bias from numerical diffusivity affects all runs equally and cannot explain the systematic dependence on background-field orientation. In revision we will (i) report the grid resolution and numerical diffusivity estimate, (ii) add a short resolution-convergence subsection showing that the exponential-rise phase and the relative durations of flare reconnection are preserved at higher resolution, and (iii) include a simple energy-conservation diagnostic as a quantitative check on numerical dissipation. Full quantitative convergence of every metric would require additional runs that exceed our current resources, but the evidence we can provide will be sufficient to support the main conclusions. revision: partial

Circularity Check

0 steps flagged

No significant circularity; results from independent forward simulations

full rationale

The paper reports outcomes from three new MHD simulations that vary only the background field orientation while holding the active-region flux rope fixed. Conclusions on free-energy thresholds, eruption success/failure, and reconnection timing/duration are extracted directly from the simulated time series (energetics, acceleration profiles, reconnection timing). No equations, fitted parameters, or self-citations are shown that reduce any reported 'prediction' or criterion to the input data by construction. The derivation chain consists of forward integration under stated initial conditions; it does not contain self-definitional loops, fitted-input renamings, or load-bearing self-citation chains. This is the normal non-circular case for simulation-based studies.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review based solely on abstract; no explicit free parameters, invented entities, or ad-hoc axioms are stated. Relies on standard MHD domain assumptions for solar corona plasma.

axioms (1)
  • domain assumption Magnetohydrodynamic equations govern the evolution of plasma and magnetic fields in the solar corona
    Implicit in all described simulations; standard in the field.

pith-pipeline@v0.9.1-grok · 5829 in / 1207 out tokens · 20730 ms · 2026-06-26T18:50:34.716014+00:00 · methodology

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Reference graph

Works this paper leans on

51 extracted references · 48 canonical work pages

  1. [1]

    Antiochos, S. K. 2013, ApJ, 772, 72, doi: 10.1088/0004-637X/772/1/72

    work page doi:10.1088/0004-637x/772/1/72 2013

  2. [2]

    K., Dahlburg, R

    Antiochos, S. K., Dahlburg, R. B., & Klimchuk, J. A. 1994, ApJL, 420, L41, doi: 10.1086/187158

    work page doi:10.1086/187158 1994

  3. [3]

    K., DeVore, C

    Antiochos, S. K., DeVore, C. R., & Klimchuk, J. A. 1999, ApJ, 510, 485, doi: 10.1086/306563

    work page doi:10.1086/306563 1999

  4. [4]

    Aulanier, G., T¨ or¨ ok, T., D´ emoulin, P., & DeLuca, E. E. 2010, ApJ, 708, 314, doi: 10.1088/0004-637X/708/1/314

    work page doi:10.1088/0004-637x/708/1/314 2010

  5. [5]

    1978, MHD instabilities

    Bateman, G. 1978, MHD instabilities

    1978

  6. [6]

    2023, ApJL, 951, L35, doi: 10.3847/2041-8213/acdef5 23

    Chen, J., Cheng, X., Kliem, B., & Ding, M. 2023, ApJL, 951, L35, doi: 10.3847/2041-8213/acdef5 23

    work page doi:10.3847/2041-8213/acdef5 2023

  7. [7]

    Chen, P. F. 2011, Living Reviews in Solar Physics, 8, 1, doi: 10.12942/lrsp-2011-1

    work page doi:10.12942/lrsp-2011-1 2011

  8. [8]

    2023, ApJ, 959, 67, doi: 10.3847/1538-4357/ad09d8

    Chen, Y., Cheng, X., Chen, J., Dai, Y., & Ding, M. 2023, ApJ, 959, 67, doi: 10.3847/1538-4357/ad09d8

    work page doi:10.3847/1538-4357/ad09d8 2023

  9. [9]

    1928, Mathematische Annalen, 100, 32, doi: 10.1007/BF01448839

    Courant, R., Friedrichs, K., & Lewy, H. 1928, Mathematische Annalen, 100, 32, doi: 10.1007/BF01448839

    work page doi:10.1007/bf01448839 1928

  10. [10]

    T., Antiochos, S

    Dahlin, J. T., Antiochos, S. K., Qiu, J., & DeVore, C. R. 2022a, ApJ, 932, 94, doi: 10.3847/1538-4357/ac6e3d

    work page doi:10.3847/1538-4357/ac6e3d

  11. [11]

    T., Antiochos, S

    Dahlin, J. T., Antiochos, S. K., Wyper, P. F., Qiu, J., & DeVore, C. R. 2025, ApJ, 993, 31, doi: 10.3847/1538-4357/ae03c5

    work page doi:10.3847/1538-4357/ae03c5 2025

  12. [12]

    T., DeVore, C

    Dahlin, J. T., DeVore, C. R., & Antiochos, S. K. 2022b, ApJ, 941, 79, doi: 10.3847/1538-4357/ac9e5a D´ emoulin, P., & Aulanier, G. 2010, ApJ, 718, 1388, doi: 10.1088/0004-637X/718/2/1388

    work page doi:10.3847/1538-4357/ac9e5a 2010

  13. [13]

    R., & Antiochos, S

    DeVore, C. R., & Antiochos, S. K. 2008, ApJ, 680, 740, doi: 10.1086/588011

    work page doi:10.1086/588011 2008

  14. [14]

    M., et al

    Downs, C., Warmuth, A., Long, D. M., et al. 2021, ApJ, 911, 118, doi: 10.3847/1538-4357/abea78

    work page doi:10.3847/1538-4357/abea78 2021

  15. [15]

    2010, ApJ, 719, 728, doi: 10.1088/0004-637X/719/1/728

    Fan, Y. 2010, ApJ, 719, 728, doi: 10.1088/0004-637X/719/1/728

    work page doi:10.1088/0004-637x/719/1/728 2010

  16. [16]

    2016, ApJ, 824, 93, doi: 10.3847/0004-637X/824/2/93

    Fan, Y. 2016, ApJ, 824, 93, doi: 10.3847/0004-637X/824/2/93

    work page doi:10.3847/0004-637x/824/2/93 2016

  17. [17]

    2017, ApJ, 844, 26, doi: 10.3847/1538-4357/aa7a56

    Fan, Y. 2017, ApJ, 844, 26, doi: 10.3847/1538-4357/aa7a56

    work page doi:10.3847/1538-4357/aa7a56 2017

  18. [18]

    Fan, Y., & Gibson, S. E. 2007, ApJ, 668, 1232, doi: 10.1086/521335

    work page doi:10.1086/521335 2007

  19. [19]

    Fisher, G. H. 2024, ApJ, 975, 206, doi: 10.3847/1538-4357/ad7f53

    work page doi:10.3847/1538-4357/ad7f53 2024

  20. [20]

    Forbes, T. G. 2000, J. Geophys. Res., 105, 23153, doi: 10.1029/2000JA000005

    work page doi:10.1029/2000ja000005 2000

  21. [21]

    G., & Isenberg, P

    Forbes, T. G., & Isenberg, P. A. 1991, ApJ, 373, 294, doi: 10.1086/170051

    work page doi:10.1086/170051 1991

  22. [22]

    E., Foster, D., Burkepile, J., de Toma, G., & Stanger, A

    Gibson, S. E., Foster, D., Burkepile, J., de Toma, G., & Stanger, A. 2006, ApJ, 641, 590, doi: 10.1086/500446

    work page doi:10.1086/500446 2006

  23. [23]

    E., & Low, B

    Gibson, S. E., & Low, B. C. 1998, ApJ, 493, 460, doi: 10.1086/305107

    work page doi:10.1086/305107 1998

  24. [24]

    I., De Zeeuw, D

    Gombosi, T. I., De Zeeuw, D. L., Powell, K. G., et al. 2003, Space Plasma Simulation, 247, doi: 10.1007/3-540-36530-3 12

    work page doi:10.1007/3-540-36530-3 2003

  25. [25]

    W., & Priest, E

    Hood, A. W., & Priest, E. R. 1981, Geophysical and Astrophysical Fluid Dynamics, 17, 297, doi: 10.1080/03091928108243687

    work page doi:10.1080/03091928108243687 1981

  26. [26]

    A., Forbes, T

    Isenberg, P. A., Forbes, T. G., & Demoulin, P. 1993, ApJ, 417, 368, doi: 10.1086/173319

    work page doi:10.1086/173319 1993

  27. [27]

    2021, Nature Astronomy, 5, 1126, doi: 10.1038/s41550-021-01414-z

    Jiang, C., Feng, X., Liu, R., et al. 2021, Nature Astronomy, 5, 1126, doi: 10.1038/s41550-021-01414-z

    work page doi:10.1038/s41550-021-01414-z 2021

  28. [28]

    J., Cheung, M

    Jin, M., Schrijver, C. J., Cheung, M. C. M., et al. 2016, ApJ, 820, 16, doi: 10.3847/0004-637X/820/1/16

    work page doi:10.3847/0004-637x/820/1/16 2016

  29. [29]

    T., Antiochos, S

    Karpen, J. T., Antiochos, S. K., & DeVore, C. R. 2012, ApJ, 760, 81, doi: 10.1088/0004-637X/760/1/81

    work page doi:10.1088/0004-637x/760/1/81 2012

  30. [30]

    G., Priest, E

    Kliem, B., Lin, J., Forbes, T. G., Priest, E. R., & T¨ or¨ ok, T. 2014, ApJ, 789, 46, doi: 10.1088/0004-637X/789/1/46

    work page doi:10.1088/0004-637x/789/1/46 2014

  31. [31]

    2006, PhRvL, 96, 255002, doi: 10.1103/PhysRevLett.96.255002

    Kliem, B., & T¨ or¨ ok, T. 2006, PhRvL, 96, 255002, doi: 10.1103/PhysRevLett.96.255002

    work page doi:10.1103/physrevlett.96.255002 2006

  32. [32]

    2004, SoPh, 219, 169, doi: 10.1023/B:SOLA.0000021798.46677.16

    Lin, J. 2004, SoPh, 219, 169, doi: 10.1023/B:SOLA.0000021798.46677.16

    work page doi:10.1023/b:sola.0000021798.46677.16 2004

  33. [33]

    Lin, J., & Forbes, T. G. 2000, J. Geophys. Res., 105, 2375, doi: 10.1029/1999JA900477

    work page doi:10.1029/1999ja900477 2000

  34. [34]

    A., Miki´ c, Z., Lionello, R., et al

    Linker, J. A., Miki´ c, Z., Lionello, R., et al. 2003, Physics of Plasmas, 10, 1971, doi: 10.1063/1.1563668

    work page doi:10.1063/1.1563668 2003

  35. [35]

    V., Zhao, L., et al

    Liu, W., Sokolov, I. V., Zhao, L., et al. 2025, ApJ, 985, 82, doi: 10.3847/1538-4357/adc4e3

    work page doi:10.3847/1538-4357/adc4e3 2025

  36. [36]

    G., & Zurbuchen, T

    Luhmann, J. G., & Zurbuchen, T. H. 2008, ApJ, 683, 1192, doi: 10.1086/589738

    work page doi:10.1086/589738 2008

  37. [37]

    H., DeVore, C

    Mackay, D. H., DeVore, C. R., & Antiochos, S. K. 2014, ApJ, 784, 164, doi: 10.1088/0004-637X/784/2/164

    work page doi:10.1088/0004-637x/784/2/164 2014

  38. [38]

    Manchester, W., Kilpua, E. K. J., Liu, Y. D., et al. 2017, SSRv, 212, 1159, doi: 10.1007/s11214-017-0394-0

    work page doi:10.1007/s11214-017-0394-0 2017

  39. [39]

    B., Gombosi, T

    Manchester, W. B., Gombosi, T. I., Roussev, I., et al. 2004, Journal of Geophysical Research (Space Physics), 109, A01102, doi: 10.1029/2002JA009672

    work page doi:10.1029/2002ja009672 2004

  40. [40]

    Martin, S. F. 1998, SoPh, 182, 107, doi: 10.1023/A:1005026814076

    work page doi:10.1023/a:1005026814076 1998

  41. [41]

    McIntosh, P. S. 1972, Reviews of Geophysics and Space Physics, 10, 837, doi: 10.1029/RG010i003p00837 Miki´ c, Z., Downs, C., Linker, J. A., et al. 2018, Nature Astronomy, 2, 913, doi: 10.1038/s41550-018-0562-5

    work page doi:10.1029/rg010i003p00837 1972

  42. [42]

    M., & Filippov, B

    Molodenskii, M. M., & Filippov, B. P. 1987, Soviet Ast., 31, 564 24

    1987

  43. [43]

    L., & Roumeliotis, G

    Moore, R. L., & Roumeliotis, G. 1992, in IAU Colloquium 133: Eruptive Solar Flares, ed. Z. Svestka, B. V. Jackson, & M. E. Machado, Vol. 399, 69, doi: 10.1007/3-540-55246-4 79

    work page doi:10.1007/3-540-55246-4 1992

  44. [44]

    1995, ApJL, 451, L83, doi: 10.1086/309688

    Shibata, K., Masuda, S., Shimojo, M., et al. 1995, ApJL, 451, L83, doi: 10.1086/309688

    work page doi:10.1086/309688 1995

  45. [45]

    S., & Pogorelov, N

    Singh, T., Yalim, M. S., & Pogorelov, N. V. 2018, ApJ, 864, 18, doi: 10.3847/1538-4357/aad3b4

    work page doi:10.3847/1538-4357/aad3b4 2018

  46. [46]

    V., & Gombosi, T

    Sokolov, I. V., & Gombosi, T. I. 2023, ApJ, 955, 126, doi: 10.3847/1538-4357/aceef5

    work page doi:10.3847/1538-4357/aceef5 2023

  47. [47]

    V., Holst, B

    Sokolov, I. V., Holst, B. v. d., Manchester, W. B., et al. 2021, ApJ, 908, 172, doi: 10.3847/1538-4357/abc000

    work page doi:10.3847/1538-4357/abc000 2021

  48. [48]

    S., & D´ emoulin, P

    Titov, V. S., & D´ emoulin, P. 1999, A&A, 351, 707

    1999

  49. [49]

    S., T¨ or¨ ok, T., Mikic, Z., & Linker, J

    Titov, V. S., T¨ or¨ ok, T., Mikic, Z., & Linker, J. A. 2014, ApJ, 790, 163, doi: 10.1088/0004-637X/790/2/163 T¨ or¨ ok, T., & Kliem, B. 2007, Astronomische Nachrichten, 328, 743, doi: 10.1002/asna.200710795 T¨ or¨ ok, T., Downs, C., Linker, J. A., et al. 2018, ApJ, 856, 75, doi: 10.3847/1538-4357/aab36d T¨ or¨ ok, T., Lugaz, N., Lee, C. O., et al. 2023, ...

    work page doi:10.1088/0004-637x/790/2/163 2014

  50. [50]

    F., & Howard, T

    Webb, D. F., & Howard, T. A. 2012, Living Reviews in Solar Physics, 9, 3, doi: 10.12942/lrsp-2012-3

    work page doi:10.12942/lrsp-2012-3 2012

  51. [51]

    2004, Journal of Geophysical Research (Space Physics), 109, A07105, doi: 10.1029/2003JA010282

    Yashiro, S., Gopalswamy, N., Michalek, G., et al. 2004, Journal of Geophysical Research (Space Physics), 109, A07105, doi: 10.1029/2003JA010282

    work page doi:10.1029/2003ja010282 2004