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Active regions that break Joy's or Hale's laws produce more and stronger X-class flares than fully normal ones.

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2026-07-14 07:53 UTC pith:BPMBP7FW

load-bearing objection Clean four-quadrant census of 64 X-class events shows AJ/AHJ configs produce more and stronger flares than NHJ, but the sample is only X-producers so the title’s “favoring” claim overreaches. the 3 major comments →

arxiv 2607.10980 v1 pith:BPMBP7FW submitted 2026-07-13 astro-ph.SR

Magnetic field configuration favoring X-class solar flares: violation of Joy's and Hale's laws

S. Liu , J.T. Su , M. Zhang , J.X. Wang This is my paper
classification astro-ph.SR
keywords solar flaressolar magnetic fieldssolar active regionsJoy's lawHale's lawmagnetic tiltX-class flaresdelta sunspots
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper argues that the magnetic tilt of a sunspot group is a practical indicator of whether an active region will produce major X-class flares. Using vector magnetograms, the authors classify each region's global tilt into four quadrants according to whether it obeys both Hale's polarity law and Joy's tilt law, only one, or neither. Regions that follow both laws produce fewer and weaker X-class events; regions that violate Joy's law (and especially those that violate both laws) produce more flares per region and systematically higher peak classes. Even the globally normal regions that still manage an X-class flare all show localized tilt anomalies or strong shear near the flare site. The result supplies a simple geometric diagnostic—global or local departure from the classical laws—that can flag elevated free-energy storage and therefore elevated eruptive risk.

Core claim

Among 39 active regions that produced 64 X-class flares, global violation of Joy's law (anti-Joy, yellow quadrant) or of both Hale's and Joy's laws (black quadrant) is associated with higher flare counts per region and higher mean flare class than fully compliant (green) configurations; every green region that still flared also harbored local tilt anomalies or strong opposite-polarity shear.

What carries the argument

Four-quadrant tilt classification: the flux-weighted vector from positive to negative polarity centroid is placed in a 0–360° polar scheme that simultaneously encodes compliance with Hale's polarity law and Joy's tilt law (green = both obeyed, yellow = anti-Joy, red = anti-Hale, black = both violated).

Load-bearing premise

The sample contains only regions already known to have produced at least one X-class flare, so the claimed preference for anomalous tilt cannot yet be compared against the baseline rate of the same tilt classes among ordinary, non-X-class active regions.

What would settle it

Compute the same four-quadrant tilt statistics on a matched control sample of active regions that never produced an X-class flare; if the anti-Joy and black fractions (and the local-anomaly rate inside green regions) are statistically identical to those in the X-class sample, the claimed association collapses.

Watch this falsifier — get emailed when new claim-graph text bears on it.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper studies the link between photospheric magnetic tilt and X-class flare productivity using 64 X-class flares from 39 active regions (2008–2025) with SHARP vector magnetograms. Global tilt is classified into four quadrants (NHJ/green, AJ/yellow, AH/red, AHJ/black) according to compliance with Hale’s and Joy’s laws by hemisphere and cycle. Within this X-class-selected sample the authors report 18 NHJ regions producing 24 flares (mean class X1.54), 18 AJ regions producing 36 flares (mean X2.66), and 3 AHJ regions producing 4 flares (mean X2.85), with X5+ events confined to AJ/AHJ. They further show that all 18 globally NHJ regions harbor local shear or local anti-Joy features near the flare sites. The central claim is that global or local violations of Hale/Joy laws are strongly associated with higher X-class occurrence and intensity and are therefore key indicators of major flare activity.

Significance. If the association holds under proper controls, the four-quadrant tilt taxonomy would supply a simple, observationally accessible morphological diagnostic that unifies global and local non-potentiality and could be used for real-time flare-risk ranking. The work is concrete: it supplies a fully tabulated sample (Table 1), explicit centroid-based tilt definition, time-series examples (Figs. 2–4), and a clear intensity hierarchy (Fig. 5). The local-tilt census inside NHJ regions is a useful observational contribution even if the global statistics remain conditional. The result is therefore of genuine interest to solar-flare physics and space-weather forecasting, provided the language of “favoring” is brought into line with what the sample design can actually support.

major comments (3)
  1. §2.3 sample definition and §3.3 / Fig. 5 statistics: the entire analysis is conditioned on ARs already known to have produced ≥1 X-class flare (plus limb and SHARP constraints). Consequently the paper reports only P(quadrant | X-class producer) and the intensity ranking among those producers. It cannot establish the relative risk P(X-class | AJ)/P(X-class | NHJ) or the base rates of AJ/AHJ among ordinary or non-flaring ARs. The stronger claims in the abstract, title, and §4.2 (“strongly associated with increased flare occurrence”, “key indicators”, “favoring”) therefore over-reach the design. Either a control sample of non-X or non-flaring ARs with the same tilt classification must be added, or the language must be restricted throughout to conditional statements about intensity and multiplicity among known X-class producers.
  2. §3.2 local-tilt census of the 18 NHJ regions: the claim that local tilt anomalies or strong shear are “universally present” and “contribute to X-class flare production” is likewise conditioned on the same X-class selection. Without a parallel census of local tilts in non-X NHJ regions, necessity or sufficiency cannot be demonstrated. The three-category breakdown (12 clear local AJ, 2 local normal + shear, 4 complex) is valuable descriptive material, but the causal language should be softened and the selection bias acknowledged.
  3. §2.4 and Fig. 1 quadrant boundaries: the angular partitions that define the four colors are stated only by schematic and by the labels NHJ/AJ/AH/AHJ. Because the free parameter of the classification is precisely these angular cuts (and the choice of which sub-region is “local”), the manuscript should give explicit numerical ranges (or a reproducible algorithm) for each hemisphere and cycle so that the classification can be independently verified and sensitivity to boundary placement assessed.
minor comments (5)
  1. Table 1: several rows list two sunspot types separated by a slash (e.g., βγ/βγ); the meaning of the dual classification should be stated in the caption or text.
  2. Fig. 5(a): overlapping arrows at similar latitudes make individual events hard to distinguish; a supplementary table or interactive version would help.
  3. Abstract and §4.2: “violation of Hale’s or Joy’s law … are strongly associated” has subject–verb disagreement; also “globally normal (Green quadrant) regions” should consistently use the NHJ acronym introduced in §2.4.
  4. §3.1 / Fig. 3: the two X-class flares attributed to AR 13663 that appear in the GOES panel of AR 13664 should be flagged more clearly in the figure legend to avoid confusion.
  5. References: a few recent statistical studies of anti-Hale/anti-Joy flare productivity (beyond those already cited) could be added for completeness, but this is optional.

Circularity Check

0 steps flagged

Observational classification study with independent GOES and SHARP inputs; no derivation reduces to its own inputs by construction.

full rationale

The paper defines four tilt quadrants from the classical Hale and Joy polarity/tilt rules (Figure 1, §2.4) and measures the global (and local) tilt angle of each active region from SHARP CEA magnetograms via flux-weighted centroids (Eq. 1). Flare times and GOES classes are taken from an independent data stream. The statistics in §3.3 / Figure 5 simply count how many of the 64 X-class events fall into each pre-defined quadrant and report mean flare class per quadrant. No free parameter is fitted to the flare data and then re-used as a “prediction,” no uniqueness theorem is imported from the authors’ prior work, and no known empirical pattern is merely renamed. The only mild self-referential element is the sample definition itself (§2.3): the 39 ARs are selected because they already produced at least one X-class flare. That selection limits the causal claim that can be drawn (conditional distributions only), but it is a selection bias, not a circular derivation. Consequently the circularity score is 1 (minor framing, no load-bearing circular step).

Axiom & Free-Parameter Ledger

2 free parameters · 4 axioms · 1 invented entities

The paper is empirical. Load-bearing content is the Hale/Joy classification rules (domain standard), the flux-weighted centroid definition of global tilt, the exclusive X-class-producer sample, and the four-quadrant taxonomy introduced as an organizational device. No free physical constants are fitted; no new particles or forces are postulated. The main fragility is sample construction and the untested leap from “among X-class producers, anomalous tilt is over-represented in strong events” to “anomalous tilt favors X-class flares.”

free parameters (2)
  • Quadrant angular boundaries (0–360° partitions by hemisphere and cycle)
    Boundaries follow standard Hale/Joy expectations rather than a fit, but the discrete four-bin partition is a modeling choice that affects how borderline tilts are labeled; no sensitivity to boundary shifts is shown.
  • Choice of which sub-region constitutes the “local” tilt in NHJ ARs
    Local bipoles are identified by eye in case studies (e.g., NOAA 11158); no automated criterion is given, so the 12/18 “clear local anomalous tilt” count depends on analyst judgment.
axioms (4)
  • domain assumption Hale’s polarity law and Joy’s tilt law correctly define the expected leading/following polarity and equatorward tilt for each hemisphere and solar cycle.
    Used as the ground truth for green/yellow/red/black labeling throughout §2.4 and Fig. 1.
  • domain assumption The flux-weighted centroid vector from positive to negative polarity (Eq. 1) is an adequate scalar proxy for the global magnetic tilt relevant to free-energy storage and flaring.
    All global statistics rest on this single angle; multipolar complexity is collapsed into one number.
  • ad hoc to paper Restricting the sample to ARs that produced ≥1 X-class flare, off-limb-safe, with SHARP coverage, yields a set from which relative productivity by tilt quadrant can be inferred.
    §2.3 selection criteria; without a control sample this axiom carries the causal language of the title and abstract.
  • domain assumption Tilt quadrant at (or near) flare time, plus hemisphere and cycle, correctly classifies the configuration that mattered for that flare.
    Table 1 and Fig. 5(a) assign one quadrant per flare from the time series; rapid evolution or multi-bipole cancellation could mislabel some events.
invented entities (1)
  • Four-color tilt quadrant taxonomy (NHJ green / AJ yellow / AH red / AHJ black) independent evidence
    purpose: Unify simultaneous compliance checks against Hale’s and Joy’s laws into a single discrete label for statistical comparison of flare productivity.
    Organizational device built from standard laws; not a new physical object, but the paper’s central analytic invention. Independent evidence is the same public magnetograms anyone can re-bin.

pith-pipeline@v1.1.0-grok45 · 19519 in / 3685 out tokens · 38637 ms · 2026-07-14T07:53:18.089521+00:00 · methodology

0 comments
read the original abstract

We investigate the statistical relationship between magnetic tilt angle and X-class flare productivity using 39 flare-productive active regions that produced 64 X-class flares. By classifying global magnetic tilt properties into four quadrants based on compliance with Hale's and Joy's laws, we identify their distinctive flare productivity characteristics. The Green quadrant (following both laws) contains 18 active regions producing 24 X-class flares, while the Yellow quadrant (following Hale's law but violating Joy's law) shows significantly enhanced productivity with 18 active regions producing 36 X-class flares. The Black quadrant (violating both laws), though containing only 3 active regions, produces 4 X-class flares. More importantly, flares in both the Yellow and Black quadrants exhibit systematically higher flare classes compared to those in the Green quadrant. Our statistical analysis demonstrates that violation of Hale's or Joy's law at the global scale are strongly associated with increased flare occurrence and flare intensity. Furthermore, examination of globally normal (Green quadrant) regions reveals that localized tilt anomalies are universally present and also contribute to X-class flare production. These results establish that abnormal magnetic tilt configurations - whether occurring at the global or local scale - are key indicators of major flare activity.

Figures

Figures reproduced from arXiv: 2607.10980 by J.T. Su, J.X. Wang, M. Zhang, S. Liu.

Figure 1
Figure 1. Figure 1: The definition of four color-coded quadrants for magnetic tilts, in both northern and southern hemispheres and in both solar cycles 24 and 25. The horizontal line indicates the solar equator, north is upward. Plus and minus signs (+/−) denote the positive and negative polarity sunspots. The vector line with arrow indicates the magnetic tilt angle. The four color-coded quadrants with the tilts range from 0◦… view at source ↗
Figure 2
Figure 2. Figure 2: Magnetic field configuration and tilt analysis of NOAA 11158 and NOAA 13664. Panels (a)-(c) depict tilts of regional magnetic features, whereas panel (d) shows the global tilt of the entire active region, for NOAA 11158. Panels (e)-(h) are for NOAA 13664. The grayscale background image in each panel shows the radial magnetic field distribution. The blue line outlines the solar equator direction (east to th… view at source ↗
Figure 3
Figure 3. Figure 3: (a, c) Temporal evolution of magnetic tilt angles for NOAA 11158 (a) and NOAA 13664 (c). For NOAA 11158, both the global tilt (labeled ”global”) and a local anti-Joy tilt (labeled ”local”) are shown. For NOAA 13664, only the global tilt is displayed. Tilt angles are color-coded according to the quadrant classification in [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Magnetic field configuration and local tilt analysis of NOAA 11283 and NOAA 11875. Panels (a)-(c) depict tilts of regional magnetic features, whereas panel (d) shows the global tilt of the entire active region for NOAA 11283. Panels (e)-(h) show the global tilt evolution for NOAA 11875. The grayscale background image in each panel shows the radial magnetic field distribution. The blue line outlines the sol… view at source ↗
Figure 5
Figure 5. Figure 5: (a) Time-latitude plot of magnetic tilt angles for each of X-class flare listed in [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗

discussion (0)

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Works this paper leans on

49 extracted references · 19 canonical work pages · 1 internal anchor

  1. [1]

    Benz, A. O. 2017, Living Reviews in Solar Physics, 14, 2, doi: 10.1007/s41116-016-0004-3

    doi:10.1007/s41116-016-0004-3 2017

  2. [2]

    G., & Ilonidis, S

    Bobra, M. G., & Ilonidis, S. 2016, ApJ, 821, 127, doi: 10.3847/0004-637X/821/2/127

    doi:10.3847/0004-637x/821/2/127 2016

  3. [3]

    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

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

  4. [4]

    M., Tomczyk, S., Kubo, M., et al

    Borrero, J. M., Tomczyk, S., Kubo, M., et al. 2011, SoPh, 273, 267, doi: 10.1007/s11207-010-9515-6

    doi:10.1007/s11207-010-9515-6 2011

  5. [5]

    H., Jiang, J., Schüssler, M., & Gizon, L

    Cameron, R. H., Jiang, J., Schüssler, M., & Gizon, L. 2014, Journal of Geophysical Research (Space Physics), 119, 680, doi: 10.1002/2013JA019498

    work page doi:10.1002/2013ja019498 2014

  6. [6]

    C., & Pevtsov, A

    Canfield, R. C., & Pevtsov, A. A. 1998, in Astronomical Society of the Pacific Conference Series, Vol. 140, Synoptic Solar Physics, ed. K. S. Balasubramaniam, J. Harvey, & D. Rabin, 131

    1998

  7. [7]

    2015, ApJ, 809, 34, doi: 10.1088/0004-637X/809/1/34 13

    Chintzoglou, G., Patsourakos, S., & Vourlidas, A. 2015, ApJ, 809, 34, doi: 10.1088/0004-637X/809/1/34 13

    work page doi:10.1088/0004-637x/809/1/34 2015

  8. [8]

    G., Linton, M

    Fan, Y., Zweibel, E. G., Linton, M. G., & Fisher, G. H. 1999, ApJ, 521, 460, doi: 10.1086/307533

    work page doi:10.1086/307533 1999

  9. [9]

    2015, ApJ, 806, 79, doi: 10.1088/0004-637X/806/1/79

    Fang, F., & Fan, Y. 2015, ApJ, 806, 79, doi: 10.1088/0004-637X/806/1/79

    doi:10.1088/0004-637x/806/1/79 2015

  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

    doi:10.1007/s11214-010-9701-8 2011

  11. [11]

    Garcia, H. A. 1994, SoPh, 154, 275, doi: 10.1007/BF00681100

    doi:10.1007/bf00681100 1994

  12. [12]

    K., Bloomfield, D

    Georgoulis, M. K., Bloomfield, D. S., Piana, M., et al. 2021, Journal of Space Weather and Space Climate, 11, 39, doi: 10.1051/swsc/2021023

    doi:10.1051/swsc/2021023 2021

  13. [13]

    M., Thalmann, J

    Green, L. M., Thalmann, J. K., Valori, G., et al. 2022, ApJ, 937, 59, doi: 10.3847/1538-4357/ac88cb

    work page doi:10.3847/1538-4357/ac88cb 2022

  14. [14]

    E., Ellerman, F., Nicholson, S

    Hale, G. E., Ellerman, F., Nicholson, S. B., & Joy, A. H. 1919, ApJ, 49, 153, doi: 10.1086/142452

    doi:10.1086/142452 1919

  15. [15]

    E., & Nicholson, S

    Hale, G. E., & Nicholson, S. B. 1925, ApJ, 62, 270, doi: 10.1086/142933

    doi:10.1086/142933 1925

  16. [16]

    T., Liu, Y., Hayashi, K., et al

    Hoeksema, J. T., Liu, Y., Hayashi, K., et al. 2014, SoPh, 289, 3483, doi: 10.1007/s11207-014-0516-8

    doi:10.1007/s11207-014-0516-8 2014

  17. [17]

    2024, ApJ, 975, 46, doi: 10.3847/1538-4357/ad7820

    Jin, C., Zhou, G., Ji, H., & Wang, J. 2024, ApJ, 975, 46, doi: 10.3847/1538-4357/ad7820

    work page doi:10.3847/1538-4357/ad7820 2024

  18. [18]

    D., & Barnes, G

    Leka, K. D., & Barnes, G. 2003, ApJ, 595, 1277, doi: 10.1086/377511

    doi:10.1086/377511 2003

  19. [19]

    G., Fisher, G

    Linton, M. G., Fisher, G. H., Dahlburg, R. B., & Fan, Y. 1999, ApJ, 522, 1190, doi: 10.1086/307678

    doi:10.1086/307678 1999

  20. [20]

    T., Valori, G., et al

    Liu, Y., Welsch, B. T., Valori, G., et al. 2023, ApJ, 942, 27, doi: 10.3847/1538-4357/aca3a6 López Fuentes, M. C., Démoulin, P., Mandrini, C. H.,

    doi:10.3847/1538-4357/aca3a6 2023

  21. [21]

    A., & van Driel-Gesztelyi, L

    Pevtsov, A. A., & van Driel-Gesztelyi, L. 2003, A&A, 397, 305, doi: 10.1051/0004-6361:20021487

    work page doi:10.1051/0004-6361:20021487 2003

  22. [22]

    1998, ApJL, 493, L43, doi: 10.1086/311116

    Shibata, K. 1998, ApJL, 493, L43, doi: 10.1086/311116

    work page doi:10.1086/311116 1998

  23. [23]

    Metcalf, T. R. 1994, SoPh, 155, 235, doi: 10.1007/BF00680593

    work page doi:10.1007/bf00680593 1994

  24. [24]

    R., Leka, K

    Metcalf, T. R., Leka, K. D., Barnes, G., et al. 2006, SoPh, 237, 267, doi: 10.1007/s11207-006-0170-x

    doi:10.1007/s11207-006-0170-x 2006

  25. [25]

    K., & Ricca, R

    Moffatt, H. K., & Ricca, R. L. 1992, Proceedings of the Royal Society of London Series A, 439, 411, doi: 10.1098/rspa.1992.0159

    doi:10.1098/rspa.1992.0159 1992

  26. [26]

    2017, SoPh, 292, 167, doi: 10.1007/s11207-017-1194-0

    Charbonneau, P. 2017, SoPh, 292, 167, doi: 10.1007/s11207-017-1194-0

    doi:10.1007/s11207-017-1194-0 2017

  27. [27]

    Petrie, G. J. D. 2019, ApJS, 240, 11, doi: 10.3847/1538-4365/aaef2f

    doi:10.3847/1538-4365/aaef2f 2019

  28. [28]

    2014, Magnetohydrodynamics of the Sun, doi: 10.1017/CBO9781139020732

    Priest, E. 2014, Magnetohydrodynamics of the Sun, doi: 10.1017/CBO9781139020732

    doi:10.1017/cbo9781139020732 2014

  29. [29]

    Richardson, R. S. 1948, ApJ, 107, 78, doi: 10.1086/144988

    work page doi:10.1086/144988 1948

  30. [30]

    H., Bush, R

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

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

  31. [31]

    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

    doi:10.12942/lrsp-2011-6 2011

  32. [32]

    2024, A&A, 686, A148, doi: 10.1051/0004-6361/202348734

    Sun, Z., Li, T., Wang, Q., et al. 2024, A&A, 686, A148, doi: 10.1051/0004-6361/202348734

    doi:10.1051/0004-6361/202348734 2024

  33. [33]

    1983, SoPh, 89, 43, doi: 10.1007/BF00211951

    Tang, F. 1983, SoPh, 89, 43, doi: 10.1007/BF00211951

    work page doi:10.1007/bf00211951 1983

  34. [34]

    K., Linan, L., Pariat, E., & Valori, G

    Thalmann, J. K., Linan, L., Pariat, E., & Valori, G. 2019a, ApJL, 880, L6, doi: 10.3847/2041-8213/ab2e73

    work page doi:10.3847/2041-8213/ab2e73 2041

  35. [35]

    K., Moraitis, K., Linan, L., et al

    Thalmann, J. K., Moraitis, K., Linan, L., et al. 2019b, ApJ, 887, 64, doi: 10.3847/1538-4357/ab4e15

    work page doi:10.3847/1538-4357/ab4e15

  36. [36]

    K., Georgoulis, M

    Thalmann, J. K., Georgoulis, M. K., Liu, Y., et al. 2021, ApJ, 922, 41, doi: 10.3847/1538-4357/ac1f93

    work page doi:10.3847/1538-4357/ac1f93 2021

  37. [37]

    2005, SoPh, 229, 63, doi: 10.1007/s11207-005-3524-x

    Tian, L., Alexander, D., Liu, Y., & Yang, J. 2005, SoPh, 229, 63, doi: 10.1007/s11207-005-3524-x

    doi:10.1007/s11207-005-3524-x 2005

  38. [38]

    2001, A&A, 374, 294, doi: 10.1051/0004-6361:20010701

    Tian, L., Bao, S., Zhang, H., & Wang, H. 2001, A&A, 374, 294, doi: 10.1051/0004-6361:20010701

    work page doi:10.1051/0004-6361:20010701 2001

  39. [39]

    2003, A&A, 407, L13, doi: 10.1051/0004-6361:20030977

    Tian, L., & Liu, Y. 2003, A&A, 407, L13, doi: 10.1051/0004-6361:20030977

    work page doi:10.1051/0004-6361:20030977 2003

  40. [40]

    2002, SoPh, 209, 361, doi: 10.1023/A:1021270202680

    Tian, L., Liu, Y., & Wang, J. 2002, SoPh, 209, 361, doi: 10.1023/A:1021270202680

    work page doi:10.1023/a:1021270202680 2002

  41. [41]

    1999, SoPh, 189, 305, doi: 10.1023/A:1005252617906

    Tian, L., Zhang, H., Tong, Y., & Jing, H. 1999, SoPh, 189, 305, doi: 10.1023/A:1005252617906

    doi:10.1023/a:1005252617906 1999

  42. [42]

    2014, SoPh, 289, 3351, doi: 10.1007/s11207-014-0502-1

    Toriumi, S., Iida, Y., Kusano, K., Bamba, Y., & Imada, S. 2014, SoPh, 289, 3351, doi: 10.1007/s11207-014-0502-1

    doi:10.1007/s11207-014-0502-1 2014

  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

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

  44. [44]

    M., & Sheeley, Jr., N

    Wang, Y. M., & Sheeley, Jr., N. R. 1989, SoPh, 124, 81, doi: 10.1007/BF00146521

    doi:10.1007/bf00146521 1989

  45. [45]

    2022, ApJL, 937, L11, doi: 10.3847/2041-8213/ac8fef

    Xu, Z., Yan, X., Yang, L., et al. 2022, ApJL, 937, L11, doi: 10.3847/2041-8213/ac8fef

    work page doi:10.3847/2041-8213/ac8fef 2022

  46. [46]

    Zhang, M., Flyer, N., & Low, B. C. 2006, ApJ, 644, 575, doi: 10.1086/503353

    doi:10.1086/503353 2006

  47. [47]

    Zhang, M., & Low, B. C. 2005, ARA&A, 43, 103, doi: 10.1146/annurev.astro.43.072103.150602

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1146/annurev.astro.43.072103.150602 2005

  48. [48]

    P., Tan, C

    Zhou, G. P., Tan, C. M., Su, Y. N., et al. 2019, ApJ, 873, 23, doi: 10.3847/1538-4357/ab01cf

    work page doi:10.3847/1538-4357/ab01cf 2019

  49. [49]

    1988, Astrophysics of the sun

    Zirin, H. 1988, Astrophysics of the sun

    1988