pith. machine review for the scientific record. sign in

arxiv: 2605.10892 · v1 · submitted 2026-05-11 · 🌌 astro-ph.SR

Recognition: 2 theorem links

· Lean Theorem

Magnetic Evolution of Highly-Sheared Region in Active Region 13842 Producing Large X9.0 Flare

Authors on Pith no claims yet

Pith reviewed 2026-05-12 03:34 UTC · model grok-4.3

classification 🌌 astro-ph.SR
keywords solar active regionsmagnetic flux ropespolarity inversion linessolar flaresflux cancellationphotospheric evolutionX-class flares
0
0 comments X

The pith

Persistent flux emergences in crossing directions rapidly build a collisional shearing PIL that forms magnetic flux ropes and drives multiple large flares.

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

The paper tracks the photospheric evolution of active region 13842 from late September 2024 onward. A positive pore drifts north while negative patches emerge east of the main sunspot and push it west, creating a narrow, highly sheared polarity inversion line where same-polarity patches also rear-end the pore from behind. Frequent cancellations along this line coincide with quick growth of free magnetic energy and repeated formation of magnetic flux ropes, culminating in the cycle's largest X9.0 flare plus several other major events within two days. The authors note that the high-free-energy area and total free energy in the PIL region shrink before each flare, consistent with the initial rise of the rope.

Core claim

Persistent flux emergences with cross separation directions facilitates rapid formation of collisional shearing PIL and frequent flux cancellations, leading to repeated MFR formations and multiple large flares in a relatively short time.

What carries the argument

The collisional shearing polarity inversion line (PIL) formed when oppositely directed flux emergences push same-polarity patches into each other, driving shear, cancellations, and free-energy buildup.

If this is right

  • Repeated MFR formation can occur on timescales of hours to a day when shearing PILs are refreshed by ongoing emergences.
  • Shrinkage of the high-free-energy photospheric area can precede eruption by serving as a signature of the rope's initial ascent.
  • Multiple X-class flares can cluster within two days when the same collisional PIL is maintained by sequential same-polarity patches.

Where Pith is reading between the lines

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

  • Monitoring the relative motion directions of emerging flux patches could help forecast when a region will switch from isolated to repeated flaring.
  • The observed precursor shrinkage of free-energy area may be testable in other events using vector magnetograms taken at higher cadence.
  • If cross-directed emergences are the key driver, regions with aligned emergence directions should show slower PIL formation and fewer clustered flares.

Load-bearing premise

That the observed photospheric shearing, cancellations, and free-energy accumulation directly caused the MFR formation and flares rather than merely correlating with unseen coronal processes.

What would settle it

A similar active region with persistent cross-directed emergences but no detectable MFR formation or major flares in the subsequent 48 hours would falsify the causal link.

Figures

Figures reproduced from arXiv: 2605.10892 by Chuan Li, Guiping Zhou, Leping Li, Shihao Rao, Shuhong Yang, Shuo Yang, Ting Li, Xiaofeng Liu, Yijun Hou, Yilin Guo, Yingjie Cai.

Figure 1
Figure 1. Figure 1: Major flares produced by AR 13842 from 2024 October 1 to October 3. (a): GOES SXR 1–8 ˚A flux variation. The blue and red vertical dotted lines mark the peak time of major flares produced by AR 13842. (b): SDO/HMI LOS magnetogram displaying photospheric magnetic field of AR 13842. The green square outlines the field of view (FOV) of (e1) and (e2). (c1), (d1), and (e1): SDO/AIA 94 ˚A image, CHASE/HIS Hα ima… view at source ↗
Figure 2
Figure 2. Figure 2: Evolution of photospheric nonpotentiality and three-dimensional (3D) magnetic topology in flaring PIL region of AR 13842. (a1)–(a3): Sequence of free energy density (ρf ree) maps overlaid with the vertical magnetic field contours at ± 1000 G showing the PIL region with high ρf ree at 12:00 UT on September 30, 21:48 UT on October 1, and 12:00 UT on October 3. (b1)–(b3): Top view of sheared arcades and twist… view at source ↗
Figure 3
Figure 3. Figure 3: Rapid magnetic flux emergence with cross separation directions in AR 13842. (a1)–(a3): Sequence of HMI continuum intensity maps overlaid with the LOS magnetic field contours (red and blue curves) showing the magnetic evolution of AR 13842 from September 30 to October 3. P1, N1, p1, and n1 label the main conjugated magnetic polarity pair of AR 13842, and the satellite positive pore and its conjugated negati… view at source ↗
Figure 4
Figure 4. Figure 4: Frequent magnetic flux cancellations occurring in the collisional shearing PIL region. (a1)–(a3): Sequence of HMI LOS magnetograms exhibiting magnetic evolution of the PIL region during the phase of accelerated shearing after October 1. Rectangles with different colors mark six typical flux cancellation events around the PIL region. (b1)–(b3): Sequences of enlarged HMI LOS magnetograms exhibiting six flux … view at source ↗
Figure 5
Figure 5. Figure 5: Rear-end collisions between the same polarities on each side of a highly-sheared PIL in AR 13842. (a1)–(a4): Sequence of HMI continuum intensity maps overlaid with the LOS magnetic field contours (red and blue curves) showing the evolution of photospheric magnetic structures around the flaring sheared PIL. N1 and p1 label the main negative sunspot and the satellite positive pore. N2, N3, N4, and p2 mark th… view at source ↗
Figure 6
Figure 6. Figure 6: Temporal profiles of kinematic parameters of the main sunspot (N1) and the satellite pore (p1), as well as the magnetic parameters of the sheared PIL region with high ρf ree. The green, red, blue, and purple dashed/dotted curves in (a) show time evolutions of normalized rotation angle of the line connecting intensity centroids of N1 and p1, the corresponding angle velocity, displacement distance of N1, and… view at source ↗
Figure 7
Figure 7. Figure 7: Cartoon illustrating the rear-end collisions driven by persistent flux emergences, as well as the rapid formation of a collisional shearing PIL and twisted MFR in AR 13842. The black patches represent the main negative sunspot (N1) and a series of negative magnetic patches (N2, N3, N4) emerged to its east, as well as the conjugated negative polarity (n1) of satellite positive pore (p1). The white patches r… view at source ↗
read the original abstract

Shearing motion and magnetic flux cancellation around the polarity inversion line (PIL) play significant roles in the build-up of free magnetic energy and magnetic flux rope (MFR) in source region of major solar flares. Here we investigate the magnetic evolution of a highly-sheared PIL in active region (AR) 13842, hosting the largest X9.0 flare of Solar Cycle 25. Since 2024 September 29, a positive-polarity pore persistently drifted northward along the western side of the AR's main negative-polarity sunspot. The main sunspot remained stationary until negative-polarity patches successively emerged to its east and approached. Rear-ended by these same-polarity patches, the sunspot then began moving westward toward the opposite-polarity pore around October 1, forming a collisional PIL. Meanwhile, on the PIL's other side, the pore was also rear-ended by same-polarity patches sequentially emerging behind it, accelerating the shearing motion around the PIL, where frequent flux cancellations were also observed. Synchronous rapid accumulation of free magnetic energy and formation of MFR were then observed in the PIL, where multiple major flares successively occurred within two days. Before these large flares, the area and total free energy of the high-free-energy-density PIL region gradually decreased in the photosphere, which could be caused by the initial ascent of MFR before eruption and serve as a precursor of solar eruptions. These results suggest that persistent flux emergences with cross separation directions facilitates rapid formation of collisional shearing PIL and frequent flux cancellations, leading to repeated MFR formations and multiple large flares in a relatively short time.

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 presents an observational study of the magnetic evolution in active region AR 13842, focusing on a highly sheared polarity inversion line (PIL) associated with the X9.0 flare of Solar Cycle 25. It details persistent northward drift of a positive pore, subsequent emergence of same-polarity patches, formation of a collisional shearing PIL, frequent flux cancellations, rapid free-energy accumulation, inferred MFR formation, and multiple major flares within two days. The authors conclude that flux emergences with cross separation directions facilitate rapid collisional shearing and cancellations, leading to repeated MFRs and large flares; they also interpret pre-flare decreases in photospheric high-free-energy area as possible MFR ascent precursors.

Significance. If the causal interpretation holds, the work provides a detailed timeline of photospheric drivers for rapid energy build-up and multiple large flares, adding a concrete case to the literature on flare precursors and potentially informing prediction models. The synchronization of emergence, shearing, cancellation, and energy rise is a useful observational benchmark. However, the significance remains limited to descriptive insights because the central claims rely on correlations without quantitative tests or coronal confirmation, reducing its impact to incremental rather than transformative.

major comments (2)
  1. [Abstract] Abstract: The claim that 'persistent flux emergences with cross separation directions facilitates rapid formation of collisional shearing PIL and frequent flux cancellations, leading to repeated MFR formations and multiple large flares' asserts causality. The evidence consists solely of temporal correlations in HMI magnetograms and free-energy maps derived from standard extrapolations; no error analysis, statistical comparison to non-flaring regions, or explicit tests excluding alternative drivers (subsurface flows, unseen coronal reconnection) are presented to support the causal inference.
  2. [Results/Discussion] Results/Discussion (pre-flare energy decrease): The interpretation that the gradual decrease in area and total free energy of the high-free-energy-density PIL region before flares is caused by initial MFR ascent lacks supporting coronal EUV/X-ray imaging or forward modeling to distinguish ascent from cancellation, flux dispersal, or extrapolation bias.
minor comments (2)
  1. Clarify the exact time cadence and spatial resolution of the free-energy calculations and how the 'high-free-energy-density' threshold is defined, as these details affect the robustness of the precursor claim.
  2. The abstract and text use 'synchronous' for energy accumulation and MFR formation; provide quantitative timing offsets and uncertainties to avoid implying perfect simultaneity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We appreciate the referee's detailed and constructive feedback on our manuscript. Below, we provide point-by-point responses to the major comments, indicating revisions made to address the concerns.

read point-by-point responses
  1. Referee: [Abstract] Abstract: The claim that 'persistent flux emergences with cross separation directions facilitates rapid formation of collisional shearing PIL and frequent flux cancellations, leading to repeated MFR formations and multiple large flares' asserts causality. The evidence consists solely of temporal correlations in HMI magnetograms and free-energy maps derived from standard extrapolations; no error analysis, statistical comparison to non-flaring regions, or explicit tests excluding alternative drivers (subsurface flows, unseen coronal reconnection) are presented to support the causal inference.

    Authors: We agree that our analysis relies on detailed temporal correlations observed in the HMI magnetograms and the derived free-energy maps from potential field extrapolations. As this is a single-event case study, we do not perform statistical comparisons to non-flaring regions or explicit tests for alternative drivers, which would require a larger sample or additional modeling not feasible here. We have revised the abstract to use more cautious phrasing, replacing 'facilitates ... leading to' with 'are consistent with ... and may contribute to' to better reflect the observational nature of the inferences. We have also added a sentence in the discussion acknowledging the correlative nature of the conclusions and the need for future statistical studies. revision: yes

  2. Referee: [Results/Discussion] Results/Discussion (pre-flare energy decrease): The interpretation that the gradual decrease in area and total free energy of the high-free-energy-density PIL region before flares is caused by initial MFR ascent lacks supporting coronal EUV/X-ray imaging or forward modeling to distinguish ascent from cancellation, flux dispersal, or extrapolation bias.

    Authors: We concur that the interpretation of the pre-flare decrease in photospheric high-free-energy area as a possible MFR ascent precursor is based on timing and lacks direct coronal confirmation or forward modeling in this study. We have revised the relevant sections in Results and Discussion to present this as one possible explanation, explicitly discussing alternative possibilities such as flux cancellation, dispersal, or artifacts from the extrapolation method. We have also added references to similar observations in the literature where such decreases have been noted. Unfortunately, the available data for this event did not include suitable high-cadence EUV or X-ray imaging to further constrain the interpretation. revision: yes

Circularity Check

0 steps flagged

No significant circularity; purely observational analysis using standard independent methods

full rationale

The paper is an observational study tracking photospheric vector magnetogram evolution (HMI data) in AR 13842, documenting pore motions, same-polarity emergences, collisional PIL formation, flux cancellations, and free-energy accumulation. Free-energy values and MFR inferences rely on standard NLFFF/potential-field extrapolations that are computed from the observed photospheric boundary conditions and are not fitted or defined in terms of the subsequent flare outcomes. No equations, parameters, or uniqueness theorems are introduced that reduce by construction to the target claims; the central suggestion of causal facilitation is presented as an interpretive correlation rather than a derived prediction. No self-citations serve as load-bearing premises, and no ansatzes or renamings of known results are smuggled in. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central narrative rests on standard solar-physics assumptions about how photospheric motions and cancellations translate into coronal free energy and MFRs; no new entities or fitted parameters are introduced in the abstract.

axioms (2)
  • domain assumption Photospheric magnetic field evolution can be directly interpreted as the build-up of coronal free magnetic energy and flux ropes
    Invoked throughout the abstract when linking observed shearing and cancellation to MFR formation and flares.
  • domain assumption Standard magnetohydrodynamic interpretations of flux cancellation and shearing apply without significant projection or resolution effects
    Required to treat the observed pore and sunspot motions as the direct drivers.

pith-pipeline@v0.9.0 · 5635 in / 1376 out tokens · 32155 ms · 2026-05-12T03:34:23.617074+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

54 extracted references · 54 canonical work pages

  1. [1]

    2020, ApJ, 894, 29, doi: 10.3847/1538-4357/ab85ca

    Bamba, Y., Inoue, S., & Imada, S. 2020, ApJ, 894, 29, doi: 10.3847/1538-4357/ab85ca

  2. [2]

    2026, Research in Astronomy and Astrophysics, 26, 047001, doi: 10.1088/1674-4527/ae3a65

    Cai, Y., Hou, Y., Ding, H., Li, T., & Liu, J. 2026, Research in Astronomy and Astrophysics, 26, 047001, doi: 10.1088/1674-4527/ae3a65

  3. [3]

    2024, ApJ, 975, 69, doi: 10.3847/1538-4357/ad793b Castellanos Dur´ an, J

    Cai, Y., Hou, Y., Li, T., & Liu, J. 2024, ApJ, 975, 69, doi: 10.3847/1538-4357/ad793b Castellanos Dur´ an, J. S., Kleint, L., & Calvo-Mozo, B. 2018, ApJ, 852, 25, doi: 10.3847/1538-4357/aa9d37

  4. [4]

    2023, ApJL, 950, L3, doi: 10.3847/2041-8213/acda2e

    Chen, F., Rempel, M., & Fan, Y. 2023, ApJL, 950, L3, doi: 10.3847/2041-8213/acda2e

  5. [5]

    D., et al

    Cheng, X., Zhang, J., Ding, M. D., et al. 2013, ApJL, 769, L25, doi: 10.1088/2041-8205/769/2/L25

  6. [6]

    2019, ApJ, 871, 67, doi: 10.3847/1538-4357/aaef30

    Kazachenko, M. 2019, ApJ, 871, 67, doi: 10.3847/1538-4357/aaef30

  7. [7]

    D., Fang, C., & Yun, H

    Ding, M. D., Fang, C., & Yun, H. S. 1999, ApJ, 512, 454, doi: 10.1086/306776

  8. [8]

    2025, ApJL, 985, L16, doi: 10.3847/2041-8213/add32c

    Ding, T., Zhang, J., & Hou, Y. 2025, ApJL, 985, L16, doi: 10.3847/2041-8213/add32c

  9. [9]

    H., Bercik, D

    Fisher, G. H., Bercik, D. J., Welsch, B. T., & Hudson, H. S. 2012, SoPh, 277, 59, doi: 10.1007/s11207-011-9907-2

  10. [10]

    R., Hudson, H

    Fletcher, L., Dennis, B. R., Hudson, H. S., et al. 2011, SSRv, 159, 19, doi: 10.1007/s11214-010-9701-8

  11. [11]

    D., Schmieder, B., D´ emoulin, P., & Li, H

    Guo, Y., Ding, M. D., Schmieder, B., D´ emoulin, P., & Li, H. 2012, ApJ, 746, 17, doi: 10.1088/0004-637X/746/1/17

  12. [12]

    2019, ApJ, 871, 4, doi: 10.3847/1538-4357/aaf4f4

    Hou, Y., Li, T., Yang, S., & Zhang, J. 2019, ApJ, 871, 4, doi: 10.3847/1538-4357/aaf4f4

  13. [13]

    2023, The Astrophysical Journal, 959, 69, doi: 10.3847/1538-4357/ad08bd

    Hou, Y., Li, C., Li, T., et al. 2023, ApJ, 959, 69, doi: 10.3847/1538-4357/ad08bd

  14. [14]

    J., Li, T., Song, Z

    Hou, Y. J., Li, T., Song, Z. P., & Zhang, J. 2020, A&A, 640, A101, doi: 10.1051/0004-6361/202038348

  15. [15]

    J., Li, T., & Zhang, J

    Hou, Y. J., Li, T., & Zhang, J. 2016, A&A, 592, A138, doi: 10.1051/0004-6361/201628851

  16. [16]

    J., Zhang, J., Li, T., Yang, S

    Hou, Y. J., Zhang, J., Li, T., Yang, S. H., & Li, X. H. 2018, A&A, 619, A100, doi: 10.1051/0004-6361/201732530

  17. [17]

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

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

  18. [18]

    Ji, H., Wang, H., Liu, C., & Dennis, B. R. 2008, ApJ, 680, 734, doi: 10.1086/587138

  19. [19]

    2018, ApJ, 869, 13, doi: 10.3847/1538-4357/aaeacc

    Jiang, C., Zou, P., Feng, X., et al. 2018, ApJ, 869, 13, doi: 10.3847/1538-4357/aaeacc

  20. [20]

    G., & Zharkova, V

    Kosovichev, A. G., & Zharkova, V. V. 2001, ApJL, 550, L105, doi: 10.1086/319484 12 Hou et al

  21. [21]

    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

  22. [22]

    2022, Science China Physics, Mechanics, and Astronomy, 65, 289602, doi: 10.1007/s11433-022-1893-3

    Li, C., Fang, C., Li, Z., et al. 2022, Science China Physics, Mechanics, and Astronomy, 65, 289602, doi: 10.1007/s11433-022-1893-3

  23. [23]

    2024a, ApJ, 967, 130, doi: 10.3847/1538-4357/ad3fb3

    Li, L., Song, H., Peter, H., et al. 2024a, ApJ, 967, 130, doi: 10.3847/1538-4357/ad3fb3

  24. [24]

    2024b, ApJ, 964, 159, doi: 10.3847/1538-4357/ad2e90

    Li, T., Zheng, Y., Li, X., et al. 2024b, ApJ, 964, 159, doi: 10.3847/1538-4357/ad2e90

  25. [25]

    2024c, ApJL, 972, L1, doi: 10.3847/2041-8213/ad6d6c

    Li, Y., Liu, X., Jing, Z., et al. 2024c, ApJL, 972, L1, doi: 10.3847/2041-8213/ad6d6c

  26. [26]

    2020, ApJ, 899, 34, doi: 10.3847/1538-4357/ab9cbe

    Liu, C., Prasad, A., Lee, J., & Wang, H. 2020, ApJ, 899, 34, doi: 10.3847/1538-4357/ab9cbe

  27. [27]

    2012a, ApJL, 745, L4, doi: 10.1088/2041-8205/745/1/L4

    Liu, C., Deng, N., Liu, R., et al. 2012a, ApJL, 745, L4, doi: 10.1088/2041-8205/745/1/L4

  28. [28]

    2012b, ApJ, 756, 59, doi: 10.1088/0004-637X/756/1/59

    Liu, R., Kliem, B., T¨ or¨ ok, T., et al. 2012b, ApJ, 756, 59, doi: 10.1088/0004-637X/756/1/59

  29. [29]

    S., et al

    Liu, R., Kliem, B., Titov, V. S., et al. 2016, ApJ, 818, 148, doi: 10.3847/0004-637X/818/2/148

  30. [30]

    T., Valori, G., et al

    Liu, Y., Welsch, B. T., Valori, G., et al. 2023, ApJ, 942, 27, doi: 10.3847/1538-4357/aca3a6

  31. [31]

    L., Sterling, A

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

  32. [32]

    D., Thompson , B

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

  33. [33]

    Petrie, G. J. D., & Sudol, J. J. 2010, ApJ, 724, 1218, doi: 10.1088/0004-637X/724/2/1218

  34. [34]

    R., & Forbes , T

    Priest, E. R., & Forbes, T. G. 2002, A&A Rv, 10, 313, doi: 10.1007/s001590100013

  35. [35]

    Rempel, M., Chintzoglou, G., Cheung, M. C. M., Fan, Y., & Kleint, L. 2023, ApJ, 955, 105, doi: 10.3847/1538-4357/aced4d

  36. [36]

    H., Bush, R

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

  37. [37]

    Schrijver, C. J. 2007, ApJL, 655, L117, doi: 10.1086/511857

  38. [38]

    2019, ApJL, 885, L11, doi: 10.3847/2041-8213/ab4cf3

    Shen, Y., Qu, Z., Zhou, C., et al. 2019, ApJL, 885, L11, doi: 10.3847/2041-8213/ab4cf3

  39. [39]

    2011, Living Reviews in Solar Physics, 8, 6, doi: 10.12942/lrsp-2011-6

    Shibata, K., & Magara, T. 2011, Living Reviews in Solar Physics, 8, 6, doi: 10.12942/lrsp-2011-6

  40. [40]

    C., & Moore, R

    Sterling, A. C., & Moore, R. L. 2005, ApJ, 630, 1148, doi: 10.1086/432044

  41. [41]

    T., Liu, Y., et al

    Sun, X., Hoeksema, J. T., Liu, Y., et al. 2013, ApJ, 778, 139, doi: 10.1088/0004-637X/778/2/139 —. 2012, ApJ, 748, 77, doi: 10.1088/0004-637X/748/2/77

  42. [42]

    K., et al

    Tian, H., Li, G., Reeves, K. K., et al. 2014, ApJL, 797, L14, doi: 10.1088/2041-8205/797/2/L14

  43. [43]

    2017, ApJ, 834, 56, doi: 10.3847/1538-4357/834/1/56

    Nagashima, K. 2017, ApJ, 834, 56, doi: 10.3847/1538-4357/834/1/56

  44. [44]

    2019, Living Reviews in Solar Physics, 16, 3, doi: 10.1007/s41116-019-0019-7

    Toriumi, S., & Wang, H. 2019, Living Reviews in Solar Physics, 16, 3, doi: 10.1007/s41116-019-0019-7

  45. [45]

    2015, Research in Astronomy and Astrophysics, 15, 145, doi: 10.1088/1674-4527/15/2/001

    Wang, H., & Liu, C. 2015, Research in Astronomy and Astrophysics, 15, 145, doi: 10.1088/1674-4527/15/2/001

  46. [46]

    1996, ApJ, 456, 861, doi: 10.1086/176703

    Wang, J., Shi, Z., Wang, H., & Lue, Y. 1996, ApJ, 456, 861, doi: 10.1086/176703

  47. [47]
  48. [48]

    K., Inhester, B., et al

    Wiegelmann, T., Thalmann, J. K., Inhester, B., et al. 2012, SoPh, 281, 37, doi: 10.1007/s11207-012-9966-z

  49. [49]

    L., Wang, J

    Yan, X. L., Wang, J. C., Pan, G. M., et al. 2018, ApJ, 856, 79, doi: 10.3847/1538-4357/aab153

  50. [50]

    L., Xue, Z

    Yan, X. L., Xue, Z. K., Pan, G. M., et al. 2015, ApJS, 219, 17, doi: 10.1088/0067-0049/219/2/17

  51. [51]

    2017, ApJL, 849, L21, doi: 10.3847/2041-8213/aa9476

    Yang, S., Zhang, J., Zhu, X., & Song, Q. 2017, ApJL, 849, L21, doi: 10.3847/2041-8213/aa9476

  52. [52]

    2020, ApJ, 898, 101, doi: 10.3847/1538-4357/ab9ac7

    Yang, S., Zhang, Q., Xu, Z., et al. 2020, ApJ, 898, 101, doi: 10.3847/1538-4357/ab9ac7

  53. [53]

    M., Yang, S

    Zhang, Q. M., Yang, S. H., Li, T., Hou, Y. J., & Li, Y. 2020, A&A, 636, L11, doi: 10.1051/0004-6361/202038072

  54. [54]

    1973, SoPh, 32, 173, doi: 10.1007/BF00152736

    Zirin, H., & Tanaka, K. 1973, SoPh, 32, 173, doi: 10.1007/BF00152736