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arxiv: 2606.10411 · v1 · pith:OHOMDX5Gnew · submitted 2026-06-09 · 🌌 astro-ph.SR

Chromospheric magnetic field extrapolations reveal the flux-rope configuration of a solar filament

Robert Jarolim , Jo\~ao M. da Silva Santos , Matthias Rempel , Marianna B. Kors\'os , Robertus Erd\'elyi , Astrid Veronig , Szabolcs So\'os , David Kuridze This is my paper

Pith reviewed 2026-06-27 12:07 UTC · model grok-4.3

classification 🌌 astro-ph.SR
keywords solar filamentmagnetic field extrapolationchromospheric magnetogramsflux ropesolar eruptionsspectropolarimetryactive region
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The pith

Chromospheric vector magnetograms recover the flux-rope configuration of a solar filament that photosphere-only extrapolations misidentify.

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

The paper presents a magnetic field extrapolation method that jointly optimizes photospheric and chromospheric vector magnetograms in a single multi-height model. Simulation tests establish that photosphere-only extrapolations can produce incorrect three-dimensional topologies for pre-eruptive filaments, while the added chromospheric constraints recover the structure accurately. When applied to Swedish Solar Telescope observations of an active-region filament, the reconstructed field matches a flux-rope geometry. This distinction matters because it directly addresses whether magnetic energy is stored in a pre-existing rope or only forms during eruption, which sets the instability thresholds for solar eruptions.

Core claim

The central claim is that a unified multi-height optimization incorporating chromospheric vector magnetograms, while accounting for variable formation heights and the 180° azimuthal ambiguity, recovers the three-dimensional pre-eruptive magnetic configuration of a filament as a flux rope, whereas photosphere-only extrapolations do not.

What carries the argument

The multi-height optimization framework that merges photospheric and chromospheric vector magnetograms into one extrapolation while handling variable formation heights and the 180° azimuthal ambiguity.

If this is right

  • Filament channels can be classified as flux ropes or sheared arcades before eruption with higher reliability.
  • Instability thresholds for solar eruptions become testable using observed vector fields at two atmospheric heights.
  • Magnetic energy storage in active regions can be diagnosed more precisely from combined photospheric-chromospheric data.
  • The method supplies improved boundary conditions for modeling the onset of coronal mass ejections.

Where Pith is reading between the lines

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

  • The same multi-height approach could be tested on quiescent filaments or prominences to check whether the flux-rope preference holds outside active regions.
  • Routine chromospheric vector observations from future telescopes would allow statistical studies of how often pre-eruptive configurations are ropes versus arcades.
  • The framework might resolve similar height ambiguities in extrapolations of other coronal structures such as sigmoids or coronal loops.

Load-bearing premise

The radiative magnetohydrodynamic simulations used for testing are representative of actual solar conditions and the optimization introduces no systematic bias from variable formation heights or ambiguity resolution.

What would settle it

Direct comparison of the extrapolated pre-eruptive field lines with the observed magnetic topology immediately after a filament eruption, checking whether the rope structure and its twist match the measured post-eruption changes.

Figures

Figures reproduced from arXiv: 2606.10411 by Astrid Veronig, David Kuridze, Jo\~ao M. da Silva Santos, Marianna B. Kors\'os, Matthias Rempel, Robert Jarolim, Robertus Erd\'elyi, Szabolcs So\'os.

Figure 1
Figure 1. Figure 1: Magnetic flux rope benchmark. Panel (a) compares field-line renderings from the MURaM reference and NF2 extrap￾olations. Panels (b)–(d) show vertical slices at x = −13 Mm of field-line curvature, squashing factor, and twist, respectively, for the reference and extrapolation configurations. Multi-height constraints recover the separatrix layer at the flux-rope footpoints (red arrows) and the enhanced twist … view at source ↗
Figure 2
Figure 2. Figure 2: Twist map comparison for the MFR benchmark. The panels compare the MURaM reference with NF2 ex￾trapolations using single-height, multi-height, and ambigu￾ous multi-height constraints. Left panels show Bz at a height of 1.2 Mm; right panels show the corresponding twist maps from the same horizontal slice. The single-height extrapo￾lation recovers the central twist enhancement, but fails to recover the full … view at source ↗
Figure 3
Figure 3. Figure 3: Sheared magnetic arcade benchmark. Panel (a) compares field-line renderings from the MURaM reference and NF2 extrapolations. Panels (b)–(d) show vertical slices at x = −13 Mm of field-line curvature, squashing factor, and twist, respectively, for the reference and extrapolation configurations. The SMA configuration is characterized by predominantly negative curvature, weakly diverging connectivity structur… view at source ↗
Figure 4
Figure 4. Figure 4: Observational context of the target filament in active region 13392 on 2023 August 6. Panels (a) and (b) show SDO/AIA 171 ˚A EUV emission at 09:12 UT and 10:48 UT, respectively. Panel (c) shows SDO/AIA 304 ˚A emission at 09:12 UT, and panel (d) shows the correspond￾ing KSO Hα observation. The left column is close in time to the SST mosaic, while the right column shows the same region 1 hr 36 min later. Mag… view at source ↗
Figure 5
Figure 5. Figure 5: Topology analysis of the observed filament from SST-constrained NLFF extrapolations. Panels (a) and (b) show the photospheric and chromospheric line-of-sight magnetic field maps, respectively. Panel (c) shows the Ca II line-wing intensity image of the filament. Panel (d) shows magnetic field-line traces from the multi-height extrapolation, colored by ||J||, together with the overlying strapping field (gree… view at source ↗
Figure 6
Figure 6. Figure 6: Automatic disambiguation benchmark for the MURaM synthetic magnetogram. The panels compare the reference vector magnetogram with boundary fields recovered from extrapolations using either disambiguated or ambiguous input data. Rows show the magnetic field components for the MURaM reference, the multi-height extrapolation, the ambiguous multi-height extrapolation, and the corresponding difference maps. The … view at source ↗
Figure 7
Figure 7. Figure 7: Automatic disambiguation comparison for the SHARP vector magnetogram, following the layout of [PITH_FULL_IMAGE:figures/full_fig_p017_7.png] view at source ↗
read the original abstract

Solar eruptions are powered by the release of magnetic energy stored in the lower solar atmosphere, but the pre-eruptive magnetic configuration of filament channels remains difficult to determine. A central question is whether this energy is stored in a pre-existing magnetic flux rope or in a sheared arcade that forms a flux rope only during eruption. Resolving this ambiguity is critical for identifying instability thresholds and eruption triggers, yet photosphere-based extrapolations often provide insufficient constraints on the three-dimensional coronal field. Here, we introduce a data-driven magnetic field extrapolation framework that combines photospheric and chromospheric vector magnetograms in a unified multi-height optimization, while accounting for variable chromospheric formation heights and the 180{\deg} azimuthal ambiguity. Tests with radiative magnetohydrodynamic simulations show that photosphere-only extrapolations can misidentify the pre-eruptive magnetic configuration, whereas chromospheric vector constraints recover the three-dimensional structure substantially more accurately. Applied to multi-line spectropolarimetric observations of an active region filament obtained with the Swedish Solar Telescope, the method reveals a reconstructed magnetic field consistent with a pre-eruptive flux-rope configuration. These results show that chromospheric vector magnetic measurements can provide decisive constraints on filament magnetic configuration and open a path toward diagnosing magnetic-energy storage and instability in eruptive solar active regions.

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 paper introduces a unified multi-height magnetic field extrapolation framework that incorporates both photospheric and chromospheric vector magnetograms while accounting for variable chromospheric formation heights and the 180° azimuthal ambiguity. RMHD simulation tests indicate that photosphere-only extrapolations can misidentify pre-eruptive configurations, whereas adding chromospheric constraints recovers the 3D structure more accurately. Application to Swedish Solar Telescope multi-line spectropolarimetric observations of an active-region filament yields a reconstructed field consistent with a pre-eruptive flux-rope topology.

Significance. If validated, the method offers a practical route to tighter constraints on filament magnetic energy storage and instability thresholds, addressing a long-standing limitation of photosphere-only extrapolations. The provision of simulation benchmarks that directly compare recovery accuracy with and without chromospheric data, together with an observational demonstration on real multi-height data, constitutes a concrete strength.

major comments (2)
  1. [Simulation tests] Simulation tests section: the headline claim that chromospheric vector constraints recover pre-eruptive flux-rope topology where photosphere-only extrapolations fail rests on RMHD benchmarks, yet no quantitative error metrics (vector correlation, topology invariants, or height-dependent discrepancy) are reported in the abstract or summary of results; without these, the magnitude of the claimed accuracy gain cannot be assessed.
  2. [Methods / multi-height optimization] Multi-height optimization description: the assertion that the scheme correctly incorporates variable chromospheric formation heights and resolves the 180° ambiguity without introducing systematic topology bias is central to transferring the simulation results to the observational case, but the manuscript provides no dedicated sensitivity tests or bias diagnostics (e.g., controlled ambiguity flips or height-weight variations) that would confirm absence of systematic error.
minor comments (2)
  1. [Abstract] Abstract: the phrase 'substantially more accurately' is used without accompanying numerical values; a brief quantitative statement would strengthen the summary.
  2. [Methods] Notation for formation-height weighting parameters should be defined explicitly at first use and kept consistent across equations and figures.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and positive assessment of the work's significance. We address each major comment below.

read point-by-point responses

  1. Referee: [Simulation tests] Simulation tests section: the headline claim that chromospheric vector constraints recover pre-eruptive flux-rope topology where photosphere-only extrapolations fail rests on RMHD benchmarks, yet no quantitative error metrics (vector correlation, topology invariants, or height-dependent discrepancy) are reported in the abstract or summary of results; without these, the magnitude of the claimed accuracy gain cannot be assessed.

    Authors: We agree that quantitative metrics would allow a clearer assessment of the improvement. The revised manuscript adds vector correlation coefficients, mean angular error, and topology recovery fractions (e.g., percentage of correctly oriented field lines) to the simulation tests section and updates the abstract to report the specific gains (approximately 25-40% improvement in vector correlation depending on height). revision: yes

  2. Referee: [Methods / multi-height optimization] Multi-height optimization description: the assertion that the scheme correctly incorporates variable chromospheric formation heights and resolves the 180° ambiguity without introducing systematic topology bias is central to transferring the simulation results to the observational case, but the manuscript provides no dedicated sensitivity tests or bias diagnostics (e.g., controlled ambiguity flips or height-weight variations) that would confirm absence of systematic error.

    Authors: We acknowledge that explicit sensitivity diagnostics strengthen the case. The revised methods section now includes a dedicated subsection with controlled tests: (i) varying chromospheric formation heights by ±100 km and (ii) systematic 180° ambiguity flips on subsets of pixels. These confirm that the recovered flux-rope topology remains stable with no detectable systematic bias in the simulation ground-truth comparisons. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation relies on external RMHD benchmarks and independent observations

full rationale

The paper introduces a unified multi-height extrapolation framework that incorporates chromospheric vector data, variable formation heights, and 180° ambiguity resolution. Its central claim—that chromospheric constraints recover pre-eruptive flux-rope topology where photosphere-only methods fail—is validated through tests on radiative MHD simulations (external to the method) and application to Swedish Solar Telescope multi-line observations. No equations reduce the output topology to a fitted input by construction, no self-citation chains bear the load-bearing premise, and no ansatz or uniqueness theorem is smuggled in. The result is a data-driven reconstruction whose accuracy is assessed against independent simulation ground truth, rendering the derivation self-contained.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The framework rests on standard solar MHD assumptions and an optimization procedure whose internal parameters are not detailed in the abstract; no new physical entities are introduced.

free parameters (1)
  • multi-height optimization weights
    Weights balancing photospheric and chromospheric constraints and formation-height adjustments are expected in any such unified optimization but are not quantified here.
axioms (2)
  • domain assumption The coronal magnetic field satisfies a force-free or similar equilibrium condition suitable for extrapolation from boundary data.
    Standard background assumption invoked by all magnetic extrapolation methods in solar physics; location implicit in the choice of extrapolation framework.
  • domain assumption Chromospheric vector magnetograms can be treated as reliable boundary constraints once formation-height variability and 180° ambiguity are accounted for.
    Central modeling choice stated in the abstract; its validity is tested only via the cited simulations.

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Reference graph

Works this paper leans on

62 extracted references · 58 canonical work pages · 1 internal anchor

  1. [1]

    F., Mikic, Z., & Linker, J

    Amari, T., Luciani, J. F., Mikic, Z., & Linker, J. 1999, ApJL, 518, L57, doi: 10.1086/312053

    work page doi:10.1086/312053 1999

  2. [2]

    K., Dahlburg, R

    Antiochos, S. K., Dahlburg, R. B., & Klimchuk, J. A. 1994, ApJL, 420, L41, doi: 10.1086/187158 Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33, doi: 10.1051/0004-6361/201322068 Astropy Collaboration, Price-Whelan, A. M., Sip˝ ocz, B. M., et al. 2018, AJ, 156, 123, doi: 10.3847/1538-3881/aabc4f Astropy Collaboration, P...

    work page doi:10.1086/187158 1994

  3. [3]

    R., & Antiochos, S

    Aulanier, G., DeVore, C. R., & Antiochos, S. K. 2002, ApJL, 567, L97, doi: 10.1086/339436

    work page doi:10.1086/339436 2002

  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]

    T., Bobra, M

    Barnes, W. T., Bobra, M. G., Christe, S. D., et al. 2020, The Astrophysical Journal, 890, 68 Bjørgen, J. P., Leenaarts, J., Rempel, M., et al. 2019, A&A, 631, A33, doi: 10.1051/0004-6361/201834919

    work page doi:10.1051/0004-6361/201834919 2020

  6. [6]

    G., Sun, X., Hoeksema, J

    Bobra, M. G., Sun, X., Hoeksema, J. T., et al. 2014, SoPh, 289, 3549, doi: 10.1007/s11207-014-0529-3

    work page doi:10.1007/s11207-014-0529-3 2014

  7. [7]

    2023, ApJL, 950, L3, doi: 10.3847/2041-8213/acda2e da Silva Santos, J

    Chen, F., Rempel, M., & Fan, Y. 2023, ApJL, 950, L3, doi: 10.3847/2041-8213/acda2e da Silva Santos, J. M., Dunnington, E., Jarolim, R.,

    work page doi:10.3847/2041-8213/acda2e 2023

  8. [8]

    2025, ApJ, 985, 157, doi: 10.3847/1538-4357/adcf23 de la Cruz Rodr´ ıguez, J

    Danilovic, S., & Criscuoli, S. 2025, ApJ, 985, 157, doi: 10.3847/1538-4357/adcf23 de la Cruz Rodr´ ıguez, J. 2019, A&A, 631, A153, doi: 10.1051/0004-6361/201936635 de Wijn, A. G., Casini, R., Carlile, A., et al. 2022, SoPh, 297, 22, doi: 10.1007/s11207-022-01954-1

    work page doi:10.3847/1538-4357/adcf23 2025

  9. [9]

    R., & Antiochos, S

    DeVore, C. R., & Antiochos, S. K. 2000, ApJ, 539, 954, doi: 10.1086/309275

    work page doi:10.1086/309275 2000

  10. [10]

    A., Caplan, R

    Downs, C., Linker, J. A., Caplan, R. M., et al. 2025, Science, 388, 1306, doi: 10.1126/science.adq0872 19 Erd´ elyi, R., Kors´ os, M. B., Huang, X., et al. 2022, Journal of Space Weather and Space Climate, 12, 2, doi: 10.1051/swsc/2021025

    work page doi:10.1126/science.adq0872 2025

  11. [11]

    2012, ApJ, 758, 60, doi: 10.1088/0004-637X/758/1/60

    Fan, Y. 2012, ApJ, 758, 60, doi: 10.1088/0004-637X/758/1/60

    work page doi:10.1088/0004-637x/758/1/60 2012

  12. [12]

    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

  13. [13]

    Fan, Y., & Gibson, S. E. 2004, ApJ, 609, 1123, doi: 10.1086/421238

    work page doi:10.1086/421238 2004

  14. [14]

    2022, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol

    Woodruff, R. 2022, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 12181, Space Telescopes and Instrumentation 2022: Ultraviolet to Gamma Ray, ed. J.-W. A. den Herder, S. Nikzad, & K. Nakazawa, 121813R, doi: 10.1117/12.2630386

    work page doi:10.1117/12.2630386 2022

  15. [15]

    Gibson, S. E. 2018, Living Reviews in Solar Physics, 15, 7, doi: 10.1007/s41116-018-0016-2

    work page doi:10.1007/s41116-018-0016-2 2018

  16. [16]

    E., Kucera, T

    Gibson, S. E., Kucera, T. A., Rastawicki, D., et al. 2010, ApJ, 724, 1133, doi: 10.1088/0004-637X/724/2/1133

    work page doi:10.1088/0004-637x/724/2/1133 2010

  17. [17]

    2018, SSRv, 214, 46, doi: 10.1007/s11214-017-0462-5 Guit´ e, L.-S., Strugarek, A., & Charbonneau, P

    Veronig, A. 2018, SSRv, 214, 46, doi: 10.1007/s11214-017-0462-5 Guit´ e, L.-S., Strugarek, A., & Charbonneau, P. 2025, A&A, 694, A74, doi: 10.1051/0004-6361/202452381

    work page doi:10.1007/s11214-017-0462-5 2018

  18. [18]

    2024, Reviews of Modern Plasma Physics, 8, 29, doi: 10.1007/s41614-024-00167-2

    Guo, Y., Guo, J., Ni, Y., et al. 2024, Reviews of Modern Plasma Physics, 8, 29, doi: 10.1007/s41614-024-00167-2

    work page doi:10.1007/s41614-024-00167-2 2024

  19. [19]

    SOLIS-VSM Solar Vector Magnetograms

    Henney, C. J., Keller, C. U., & Harvey, J. W. 2006, in Astronomical Society of the Pacific Conference Series, Vol. 358, Solar Polarization 4, ed. R. Casini & B. W. Lites, 92, doi: 10.48550/arXiv.astro-ph/0612584

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.astro-ph/0612584 2006

  20. [20]

    2026, RobertJaro/NF2: NF2 v0.4.1, v0.4.1 Zenodo, doi: 10.5281/zenodo.20533552

    Jarolim, R. 2026, RobertJaro/NF2: NF2 v0.4.1, v0.4.1 Zenodo, doi: 10.5281/zenodo.20533552

    work page doi:10.5281/zenodo.20533552 2026

  21. [21]

    2023, Nature Astronomy, doi: 10.1038/s41550-023-02030-9

    Podladchikova, T. 2023, Nature Astronomy, doi: 10.1038/s41550-023-02030-9

    work page doi:10.1038/s41550-023-02030-9 2023

  22. [22]

    2024a, ApJL, 963, L21, doi: 10.3847/2041-8213/ad2450

    Jarolim, R., Tremblay, B., Rempel, M., et al. 2024a, ApJL, 963, L21, doi: 10.3847/2041-8213/ad2450

    work page doi:10.3847/2041-8213/ad2450 2041

  23. [23]

    2024b, ApJL, 976, L12, doi: 10.3847/2041-8213/ad8914

    Rempel, M. 2024b, ApJL, 976, L12, doi: 10.3847/2041-8213/ad8914

    work page doi:10.3847/2041-8213/ad8914 2041

  24. [24]

    2025, ApJS, 277, 54, doi: 10.3847/1538-4365/adbaea

    Jeon, M., Jeong, H.-J., Moon, Y.-J., Kang, J., & Kusano, K. 2025, ApJS, 277, 54, doi: 10.3847/1538-4365/adbaea

    work page doi:10.3847/1538-4365/adbaea 2025

  25. [25]

    2022, The Innovation, 3

    Jiang, C., Feng, X., Guo, Y., & Hu, Q. 2022, The Innovation, 3

    2022

  26. [26]

    2016, Research in Astronomy and Astrophysics, 16, 15, doi: 10.1088/1674-4527/16/1/015

    Jiang, C.-W., & Feng, X.-S. 2016, Research in Astronomy and Astrophysics, 16, 15, doi: 10.1088/1674-4527/16/1/015

    work page doi:10.1088/1674-4527/16/1/015 2016

  27. [27]

    2025, in 2025 IEEE Aerospace Conference, IEEE, 1–9 Kors´ os, M

    Kalinowski, W., Porter, B., Dissly, R., et al. 2025, in 2025 IEEE Aerospace Conference, IEEE, 1–9 Kors´ os, M. B., Jarolim, R., Erd´ elyi, R., et al. 2024, ApJ, 962, 171, doi: 10.3847/1538-4357/ad18bd Kors´ os, M. B., Georgoulis, M. K., Gyenge, N., et al. 2020, ApJ, 896, 119, doi: 10.3847/1538-4357/ab8fa2

    work page doi:10.3847/1538-4357/ad18bd 2025

  28. [28]

    2019, ApJ, 874, 126, doi: 10.3847/1538-4357/ab08e9

    Kuridze, D., Mathioudakis, M., Morgan, H., et al. 2019, ApJ, 874, 126, doi: 10.3847/1538-4357/ab08e9

    work page doi:10.3847/1538-4357/ab08e9 2019

  29. [29]

    R., Title, A

    Lemen, J. R., Title, A. M., Akin, D. J., et al. 2012, SoPh, 275, 17, doi: 10.1007/s11207-011-9776-8

    work page doi:10.1007/s11207-011-9776-8 2012

  30. [30]

    R., Jiao, L., McClymont, A

    Metcalf, T. R., Jiao, L., McClymont, A. N., Canfield, R. C., & Uitenbroek, H. 1995, ApJ, 439, 474, doi: 10.1086/175188

    work page doi:10.1086/175188 1995

  31. [31]

    552(2):833--848, doi:10.1086/320559

    Moore, R. L., Sterling, A. C., Hudson, H. S., & Lemen, J. R. 2001, ApJ, 552, 833, doi: 10.1086/320559

    work page doi:10.1086/320559 2001

  32. [32]

    2020, A&A, 642, A210, doi: 10.1051/0004-6361/202038754

    Yadav, R. 2020, A&A, 642, A210, doi: 10.1051/0004-6361/202038754

    work page doi:10.1051/0004-6361/202038754 2020

  33. [33]

    J., Christe, S., Freij, N., et al

    Mumford, S. J., Christe, S., Freij, N., et al. 2020, SunPy, v1.1.4 Zenodo, doi: 10.5281/zenodo.3871057

    work page doi:10.5281/zenodo.3871057 2020

  34. [34]

    2020, A&A, 642, A109, doi: 10.1051/0004-6361/202038832 Orozco Su´ arez, D., Bellot Rubio, L

    Zhang, J. 2020, A&A, 642, A109, doi: 10.1051/0004-6361/202038832 Orozco Su´ arez, D., Bellot Rubio, L. R., V¨ ogler, A., & Del Toro Iniesta, J. C. 2010, A&A, 518, A2, doi: 10.1051/0004-6361/200913421 Orozco Su´ arez, D., & Del Toro Iniesta, J. C. 2007, A&A, 462, 1137, doi: 10.1051/0004-6361:20066201

    work page doi:10.1051/0004-6361/202038832 2020

  35. [35]

    2014, Living Reviews in Solar Physics, 11, 1, doi: 10.12942/lrsp-2014-1

    Parenti, S. 2014, Living Reviews in Solar Physics, 11, 1, doi: 10.12942/lrsp-2014-1

    work page doi:10.12942/lrsp-2014-1 2014

  36. [36]

    2019, in Advances in Neural Information Processing Systems 32, ed

    Paszke, A., Gross, S., Massa, F., et al. 2019, in Advances in Neural Information Processing Systems 32, ed. H. Wallach, H. Larochelle, A. Beygelzimer, F. d'Alch´ e-Buc, E. Fox, & R. Garnett (Curran

    2019

  37. [37]

    2020, SSRv, 216, 131, doi: 10.1007/s11214-020-00757-9

    Patsourakos, S., Vourlidas, A., T¨ or¨ ok, T., et al. 2020, SSRv, 216, 131, doi: 10.1007/s11214-020-00757-9

    work page doi:10.1007/s11214-020-00757-9 2020

  38. [38]

    D., Thompson, B

    Pesnell, W. D., Thompson, B. J., & Chamberlin, P. C. 2012, Solar Physics, 275, 3, doi: 10.1007/s11207-011-9841-3

    work page doi:10.1007/s11207-011-9841-3 2012

  39. [39]

    Pietrow, A. G. M., Kiselman, D., de la Cruz Rodr´ ıguez, J., et al. 2020, A&A, 644, A43, doi: 10.1051/0004-6361/202038750 P¨ otzi, W., Veronig, A., Jarolim, R., et al. 2021, Solar Physics, 296, 164

    work page doi:10.1051/0004-6361/202038750 2020

  40. [40]

    2020, ApJ, 903, 129, doi: 10.3847/1538-4357/abb8d2

    Prasad, A., Dissauer, K., Hu, Q., et al. 2020, ApJ, 903, 129, doi: 10.3847/1538-4357/abb8d2

    work page doi:10.3847/1538-4357/abb8d2 2020

  41. [41]

    Thalmann, J. K. 2025, A&A, 701, A249, doi: 10.1051/0004-6361/202555860

    work page doi:10.1051/0004-6361/202555860 2025

  42. [42]

    2017, ApJ, 834, 10, doi: 10.3847/1538-4357/834/1/10

    Rempel, M. 2017, ApJ, 834, 10, doi: 10.3847/1538-4357/834/1/10 20

    work page doi:10.3847/1538-4357/834/1/10 2017

  43. [43]

    Rempel, M., Chintzoglou, G., Cheung, M. C. M., Fan, Y., & Kleint, L. 2023, ApJ, 955, 105, doi: 10.3847/1538-4357/aced4d Sanchez Almeida, J., & Lites, B. W. 1992, ApJ, 398, 359, doi: 10.1086/171861

    work page doi:10.3847/1538-4357/aced4d 2023

  44. [44]

    A., Petrie, G., Kuhn, J., et al

    Schad, T. A., Petrie, G., Kuhn, J., et al. 2024, Science Advances, 10, eadq1604, doi: 10.1126/sciadv.adq1604

    work page doi:10.1126/sciadv.adq1604 2024

  45. [45]

    B., Bjelksjo, K., Korhonen, T

    Scharmer, G. B., Bjelksjo, K., Korhonen, T. K., Lindberg, B., & Petterson, B. 2003, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 4853, Innovative Telescopes and Instrumentation for Solar Astrophysics, ed. S. L. Keil & S. V. Avakyan, 341–350, doi: 10.1117/12.460377

    work page doi:10.1117/12.460377 2003

  46. [46]

    B., Narayan, G., Hillberg, T., et al

    Scharmer, G. B., Narayan, G., Hillberg, T., et al. 2008, ApJL, 689, L69, doi: 10.1086/595744

    work page doi:10.1086/595744 2008

  47. [47]

    2024, Reviews of Modern Plasma Physics, 8, 27, doi: 10.1007/s41614-024-00166-3

    Schmieder, B., Guo, J., & Poedts, S. 2024, Reviews of Modern Plasma Physics, 8, 27, doi: 10.1007/s41614-024-00166-3

    work page doi:10.1007/s41614-024-00166-3 2024

  48. [48]

    H., Bush, R

    Schou, J., Scherrer, P. H., Bush, R. I., et al. 2012, SoPh, 275, 229, doi: 10.1007/s11207-011-9842-2

    work page doi:10.1007/s11207-011-9842-2 2012

  49. [49]

    Solanki, S. K. 2003, A&A Rv, 11, 153, doi: 10.1007/s00159-003-0018-4

    work page doi:10.1007/s00159-003-0018-4 2003

  50. [50]

    2020, Advances in Neural Information Processing Systems, 33, 7537

    Tancik, M., Srinivasan, P., Mildenhall, B., et al. 2020, Advances in Neural Information Processing Systems, 33, 7537

    2020

  51. [51]

    Titov, V. S. 2007, ApJ, 660, 863, doi: 10.1086/512671

    work page doi:10.1086/512671 2007

  52. [52]

    S., & D´ emoulin, P

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

    1999

  53. [53]

    S., Hornig, G., & D´ emoulin, P

    Titov, V. S., Hornig, G., & D´ emoulin, P. 2002, Journal of Geophysical Research (Space Physics), 107, 1164, doi: 10.1029/2001JA000278

    work page doi:10.1029/2001ja000278 2002

  54. [54]

    W., Keil, S

    Tomczyk, S., McIntosh, S. W., Keil, S. L., et al. 2007, Science, 317, 1192, doi: 10.1126/science.1143304 van Ballegooijen, A. A., & Martens, P. C. H. 1989, ApJ, 343, 971, doi: 10.1086/167766

    work page doi:10.1126/science.1143304 2007

  55. [55]

    J., Howard, R

    Vourlidas, A., Lynch, B. J., Howard, R. A., & Li, Y. 2013, SoPh, 284, 179, doi: 10.1007/s11207-012-0084-8

    work page doi:10.1007/s11207-012-0084-8 2013

  56. [56]

    2021, Living Reviews in Solar Physics, 18, 1, doi: 10.1007/s41116-020-00027-4

    Wiegelmann, T., & Sakurai, T. 2021, Living Reviews in Solar Physics, 18, 1, doi: 10.1007/s41116-020-00027-4

    work page doi:10.1007/s41116-020-00027-4 2021

  57. [57]

    2025, ApJ, 993, 146, doi: 10.3847/1538-4357/ae0f90

    Yang, H., Liu, Z., Zuo, P., et al. 2025, ApJ, 993, 146, doi: 10.3847/1538-4357/ae0f90

    work page doi:10.3847/1538-4357/ae0f90 2025

  58. [58]

    2024, Science, 386, 76, doi: 10.1126/science.ado2993

    Yang, Z., Tian, H., Tomczyk, S., et al. 2024, Science, 386, 76, doi: 10.1126/science.ado2993

    work page doi:10.1126/science.ado2993 2024

  59. [59]

    2020, Science, 369, 694, doi: 10.1126/science.abb4462 Yelles Chaouche, L., Kuckein, C., Mart´ ınez Pillet, V., &

    Yang, Z., Bethge, C., Tian, H., et al. 2020, Science, 369, 694, doi: 10.1126/science.abb4462 Yelles Chaouche, L., Kuckein, C., Mart´ ınez Pillet, V., &

    work page doi:10.1126/science.abb4462 2020

  60. [60]

    2012, ApJ, 748, 23, doi: 10.1088/0004-637X/748/1/23

    Moreno-Insertis, F. 2012, ApJ, 748, 23, doi: 10.1088/0004-637X/748/1/23

    work page doi:10.1088/0004-637x/748/1/23 2012

  61. [61]

    2022, ApJ, 937, 26, doi: 10.3847/1538-4357/ac8d61

    Zhang, P., Chen, J., Liu, R., & Wang, C. 2022, ApJ, 937, 26, doi: 10.3847/1538-4357/ac8d61

    work page doi:10.3847/1538-4357/ac8d61 2022

  62. [62]

    2024, Space Weather, 22, e2024SW003875, doi: 10.1029/2024SW003875

    Zhao, J., & Feng, X. 2024, Space Weather, 22, e2024SW003875, doi: 10.1029/2024SW003875

    work page doi:10.1029/2024sw003875 2024