Pith. sign in

REVIEW 3 major objections 7 minor 84 references

Investigation on the Relation between Active Regions' Compliance with Empirical Laws and Flare Productivity

T0 review · 3 major / 7 minor · reviewed 2026-07-10 · glm-5.2

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Flare power follows magnetic size, not rule compliance

desk verdict Solid negative finding on empirical-law compliance vs. flare productivity, with one positive exception that needs the same confound check the authors already applied elsewhere. read the letter →

arxiv 2607.08053 v1 pith:3VQPKPNU submitted 2026-07-09 astro-ph.SR

Jinhui Pan , Rui Liu , Jiangtao Su , Jie Jiang This is my paper · ORCID
classification astro-ph.SR PACS 96.60.qe96.60.ph96.60.Ly
keywords flarecomplianceempiricallawsmagneticproductivitycycledistance
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Solar active regions follow several empirical patterns — Hale's polarity law, Joy's tilt law, and the hemispheric helicity rule — that describe how magnetic field configurations are organized on the Sun. Whether an active region breaks or obeys these rules tells us something about the turbulent conditions the magnetic flux tube experienced while rising through the solar interior. This paper asks a direct question: do rule-following active regions produce more flares than rule-breaking ones? Using automated detection on magnetograms spanning Solar Cycle 24 and the ascending phase of Cycle 25, the authors classify over 2,600 active regions by their compliance with all three laws and compare each region's flare productivity, measured by a daily flare index built from GOES C-class-and-above events. The answer is largely negative. Flare productivity shows no significant difference across compliance groups, with one cycle-specific exception: in Cycle 24, regions that obeyed Hale's and Joy's laws but violated the hemispheric helicity rule showed elevated flaring, though the effect size was small. What does separate flare-productive from flare-quiet regions is simpler and more physical: a minimum spatial extent (centroid distance above 50.5 Mm between opposite polarities) and a minimum total unsigned magnetic flux (above 0.58 × 10^22 Mx). Below these thresholds, the median flare index drops to zero. The authors conclude that flare productivity is governed by whether a magnetic system is large and strong enough to store free energy, not by whether its configuration respects the statistical patterns imposed by the solar dynamo and Coriolis force.

What carries the argument

The argument is carried by three measured quantities: the tilt angle (computed from flux-weighted polarity centroids in heliographic coordinates, classifying compliance with Hale's and Joy's laws), the force-free parameter alpha_best (a least-squares fit of the current-to-field ratio across the active region, classifying compliance with the hemispheric helicity rule), and the flare index (a weighted daily rate of C, M, and X-class flares normalized by the time span of flaring activity). The statistical engine is the Mann-Whitney U test, a nonparametric rank-based comparison that handles the heavily zero-inflated, highly skewed flare index distribution without assuming normality. The dual-thi

What would settle it

If a reanalysis using time-resolved compliance labels (updated daily rather than majority-voted) found that flare-productive regions systematically shift their compliance class in the days preceding major flares, the conclusion that compliance is irrelevant to flaring would be weakened, because the relevant configuration would be the pre-flare one, not the disk-transit average.

Watch

Extended reading notes

Core claim

The paper's central negative result is that compliance with Hale's law, Joy's law, and the hemispheric helicity rule does not reliably predict flare productivity. The one statistically significant exception — Cycle 24 regions obeying Hale's and Joy's laws but violating the hemispheric helicity rule — showed higher flaring, but the effect size was below 0.1, and the authors attribute part of this signal to the uncontrolled variable of magnetic complexity (delta-type spot configurations). The positive discovery is the identification of dual empirical thresholds — 50.5 Mm in centroid distance and 0.58 × 10^22 Mx in total unsigned magnetic flux — below which binned median flare index is zero. In

Load-bearing premise

The study assigns each active region a single compliance label by majority vote across all its daily detections during disk transit. If flare-productive regions evolve more rapidly — through flux cancellation, rotation, or polarity migration — their majority-vote label may not capture the magnetic configuration actually present at the time of flare triggering, which could blur the comparison between compliance groups.

Editorial extensions

If this is right

  • Flare forecasting models that weight compliance with empirical laws as a feature may gain little predictive power; replacing or supplementing such features with simple flux and spatial-extent thresholds could improve performance.
  • The Cycle 24 exception — regions with standard bipolar orientation but anomalous twist showing elevated flaring — is consistent with flare trigger models where opposite-signed helicity interaction drives reconnection, and warrants targeted study with helicity injection measurements.
  • The finding that compliance rates increase with centroid distance and are higher during the ascending phase of a solar cycle constrains flux-emergence simulations: models must reproduce not just the average tilt or twist but also how compliance depends on flux-tube strength and cycle phase.
  • The dual-threshold result provides a concrete, testable separability criterion: if an active region falls below both the 50.5 Mm and 0.58 × 10^22 Mx thresholds, its median flare productivity is statistically zero, regardless of magnetic configuration.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 7 minor

Summary. This manuscript presents a comprehensive statistical analysis of 2616 active regions (ARs) spanning Solar Cycle 24 and the ascending phase of Cycle 25, investigating whether compliance with Hale's law, Joy's law, and the Hemispheric Helicity Rule (HHR) correlates with flare productivity as measured by the flare index (FI). ARs are detected automatically from MDI and HMI magnetograms using the deep-learning-based SARD model, cross-matched with NOAA SRS records. Tilt angles are computed from flux-weighted polarity centroids, magnetic twist is estimated via the force-free parameter alpha_best, and flare productivity is quantified using GOES C-class-and-above events. The authors find that the majority of ARs comply with all three empirical laws (~67%), that compliance rates increase with centroid distance and (for Hale's law) with unsigned flux, and that overall FI does not differ significantly across compliance groups. The one exception is that SC24 ARs obeying Hale's and Joy's laws but violating the HHR (NOR|0) show statistically higher FI. The authors also identify empirical thresholds (50.5 Mm centroid distance, 0.58x10^22 Mx unsigned flux) below which median FI drops to zero. The central conclusion is that flare productivity depends on magnetic system size and strength rather than on compliance with empirical laws.

Significance. The study addresses a well-motivated question with a large, well-curated dataset and appropriate non-parametric statistical methods. The use of the Mann-Whitney U test with effect sizes is well-suited to the highly skewed FI distribution. The systematic uncertainty estimation via threshold variation, patch-size variation, and cycle-boundary variation is commendable and adds robustness. The identification of empirical flux and distance thresholds for flare productivity is a useful, falsifiable result. The transparent acknowledgment that the AHJ group's elevated FI in SC24 is likely a magnetic-complexity confound rather than an intrinsic property demonstrates scientific honesty. The negative central claim is inherently non-circular and well-supported by the data.

major comments (3)
  1. §3.2, Table 2: The paper identifies a statistically significant result that SC24 NOR|0 ARs (obeying Hale's and Joy's laws but violating HHR) exhibit higher FI than other groups (z = -2.333 for NOR|1 vs NOR|0; z = 2.273 for NOR|0 vs 'Other'). The authors interpret this physically via helicity annihilation (§4, citing Kusano et al. 2003). However, the paper itself demonstrates that the elevated FI of the AHJ group in SC24 is confounded by a disproportionate presence of delta-type (magnetically complex) ARs—4 of 36 AHJ ARs are delta-type with high FI, while SC25 AHJ ARs lack delta-types and are quiescent. The critical gap is that this same delta-type confound check is performed for AHJ but NOT for the NOR|0 group (n=257 in SC24). If the NOR|0 group also contains a disproportionate number of delta-type ARs, the significant z-score could be driven by magnetic complexity rather than HHR-violat
  2. §2, paragraph beginning 'SARD is applied to each LoS magnetogram': The majority-vote assignment of a single compliance label per AR across all disk-transit detections assumes that temporal evolution of tilt, twist, and polarity configuration during disk passage does not systematically bias the classification in a manner correlated with flare productivity. Flare-productive ARs may evolve more rapidly through flux cancellation, rotation, or emergence of new flux, potentially shifting their majority-vote label away from the configuration relevant at the time of flare triggering. The authors should discuss this potential confound and, if feasible, quantify how often ARs change compliance status across detections. If the fraction of 'flipping' ARs is small, a sensitivity check excluding them would strengthen the analysis.
  3. §3.3, Figure 7: The empirical thresholds (50.5 Mm, 0.58x10^22 Mx) are derived from the same dataset used to evaluate their discriminative power. The reported 60.9-62.8% true-positive rate and 72.1-72.7% precision are in-sample performance metrics and will be optimistically biased. The authors should either (a) use a cross-validation or split-sample approach to estimate out-of-sample performance, or (b) explicitly state that these thresholds are descriptive rather than predictive and require validation on independent data.
minor comments (7)
  1. §2: The flux imbalance ratio threshold R > 0.5 for flagging unipolar ARs is stated without justification. A brief citation or sensitivity note would help the reader assess robustness.
  2. Table 1: The HHR compliance rate for the full sample is listed as 67.3% in the table but 67.5% in the abstract and conclusion text. Please reconcile.
  3. Figure 2 caption: The tilt-angle ranges for each classification (NOR, AH, AJ, AHJ) are described in the text but the figure annotation is referenced as 'annotated in the figure'—ensure the ranges are clearly legible in the final figure.
  4. §3.2: The phrase 'the correlation between the AR types and the flare productivity is quite weak, as indicated by the ES values (all less than 0.1)' should note that this applies to the HHR-only and three-law tests, but the AH vs AHJ test in SC24 has ES = 0.306 (medium), which is not negligible.
  5. §4, final paragraph: 'minimal spacial scale' should read 'minimal spatial scale'.
  6. References: Li (2018a) and Li (2018b) appear to be the same paper (same ApJ reference, same doi). Please verify and consolidate.
  7. Figure 7a: The color-coded FI values span several orders of magnitude; consider using a logarithmic color scale to improve visibility of the moderate-FI ARs.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the paper's central claim is a negative statistical result that cannot be forced by construction

full rationale

The paper's derivation chain is self-contained and non-circular. (1) Compliance labels (NOR, AH, AJ, AHJ, HHR|1, HHR|0) are computed from observable magnetic properties—tilt angles via flux-weighted centroids (Eq. 1) and magnetic twist via α_best (Eq. 2)—which are independent of the flare index. (2) The flare index (Eq. 4) is computed from GOES C-class-and-above flare events catalogued in HEK, an independent data source. (3) The Mann-Whitney U test (Eqs. 5–7) is a standard non-parametric test applied to compare FI distributions across compliance groups; no parameter is fitted to the outcome being tested. (4) The empirical thresholds (50.5 Mm, 0.58×10^22 Mx) are derived from binned median FI distributions but are explicitly labeled 'empirical' and not presented as theoretical predictions—they are descriptive observations from the data. (5) Self-citations (Pan et al. 2025a for the SARD detection model; Pan & Liu 2025 for the Mann-Whitney methodology) are methodological tools that are externally verifiable and do not constitute the load-bearing theoretical claim. The central claim is a negative result (no significant FI difference across compliance groups), which is inherently non-circular: it cannot be forced by parameter choices or definitions. No step in the derivation reduces to its own inputs by construction.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new physical entities, particles, or forces. All parameters are standard in solar physics and are either adopted from prior literature or chosen with sensitivity analysis. The free parameters are processing thresholds rather than theoretical fitting parameters. The axioms are domain-standard approximations rather than ad-hoc postulates.

free parameters (5)
  • Magnetic field threshold for polarity centroid and alpha_best = 100 G (fiducial), varied to 150 G
    Chosen to exclude weak-field noise; affects tilt angle and alpha_best computation. Sensitivity is checked but the fiducial value is a free choice.
  • Flux imbalance ratio threshold R = 0.5
    ARs with R>0.5 are flagged as unipolar and excluded. This cutoff is adopted from prior literature (Virtanen et al. 2017) but is a parameter choice affecting sample composition.
  • Longitude range for AR retention = [-30°, 30°]
    Chosen to mitigate projection effects; affects which detections are retained.
  • Number of bins for FI threshold identification = 80 (fiducial), varied 70-90
    Determines the empirical flux and distance thresholds; sensitivity is checked but the bin count is a free parameter.
  • Cycle boundary between SC24 and SC25 = 2019 December 1
    Varied from 2018 Dec to 2020 Dec to estimate uncertainty; the fiducial choice affects cycle-specific statistics.
assumptions (4)
  • domain assumption The force-free approximation (nabla x B = alpha*B) is valid for computing alpha_best as a twist proxy in photospheric vector magnetograms.
    Section 2, Equation 2. The photosphere is not force-free, but alpha_best is used as a proxy following Seehafer 1990 and Leka 1999. This is standard in the field but is an approximation.
  • domain assumption The majority-vote label across multiple disk-transit detections represents the intrinsic compliance state of an AR.
    Section 2, paragraph on SARD application. Assumes temporal evolution does not systematically bias the classification.
  • domain assumption The flare index (FI) as defined in Equation 4 is a valid proxy for flare productivity.
    Section 3.2, Equation 4. FI normalizes by the time range between first and last flare, which may bias ARs with only one flare (tau is undefined or zero).
  • domain assumption GOES C-class-and-above flares from the HEK catalog represent a complete sample of each AR's flare productivity.
    Section 3.2. Assumes complete association of flares to ARs and complete detection above C-class.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Investigation on the Relation between Active Regions' Compliance with Empirical Laws and Flare Productivity." pith.science (2026). https://pith.science/paper/3VQPKPNU

@misc{pith2026260708053,
  author       = {Pith},
  title        = {Pith review of: Investigation on the Relation between Active Regions' Compliance with Empirical Laws and Flare Productivity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3VQPKPNU}},
  note         = {Machine review of arXiv:2607.08053}
}
abstract

It remains evasive whether solar active regions (ARs) obeying or violating Hale's polarity law, Joy's tilt law, and the hemispheric helicity rule (HHR) differ in flare productivity. Here we conduct a comprehensive statistical analysis of ARs during the Solar Cycle 24 and the ascending phase of Cycle 25. ARs are automatically detected from full-disk line-of-sight magnetograms acquired by the Michelson Doppler Imager (MDI) and the Helioseismic and Magnetic Imager (HMI). We calculate tilt angles via flux-weighted polarity centroids, estimate magnetic twist by the force-free parameter $\alpha_{\mathrm{best}}$ from HMI vector magnetograms, and measure flare productivity using the flare index (FI) built from GOES C-class-and-above events. Our results substantiate that the majority of ARs follow the aforementioned three empirical laws. The compliance rate tends to be higher for ARs emerging at higher latitudes or having larger centroid distance, while total unsigned magnetic flux exerts limited influence, with a clear positive correlation only for Hale's law. Overall, FI shows no significant discrepancies across different compliance groups, except that Cycle 24 ARs that satisfy Hale's and Joy's laws but violate the HHR exhibit higher FI than other groups. We also identify empirical thresholds for centroid distance and total unsigned flux, above which the median FI of binned ARs becomes nonzero. Combining the flux and distance thresholds effectively separates flare-productive from flare-quiet ARs. We hence conclude that the flare productivity of ARs is not dependent on the compliance with the empirical laws, but more closely associated with sufficiently large and strong magnetic systems.

Figures

Figures reproduced from arXiv: 2607.08053 by the authors.

Figure 1
Figure 1. Data processing pipeline. (a) SARD detection results on the full-disk LoS magnetogram on 2014 October 22, which are calibrated with the AR information from the NOAA SRS catalog. The detected ARs are indicated by yellow bounding boxes (Bbox) , whose centers are marked by red dots, in comparison with the AR locations in the NOAA SRS catalog, as marked by blue asterisks. (b) (Br, Bθ, Bϕ) maps of AR 12192 in the Heliogr… view at source ↗
Figure 2
Figure 2. Definitions of the tilt angles for SC24. The left panel shows the adopted sign convention for the tilt angle, which spans (−180◦ , 180◦ ]. P denotes the positive polarity and N denotes the negative polarity. The right panel illustrates the classification of ARs according to their compliance with Hale’s law and Joy’s law. ‘NOR’ (normal) denotes ARs that obey both Hale’s law and Joy’s law, ‘AH’ (Anti-Hale) denotes ARs… view at source ↗
Figure 3
Figure 3. Frequency distribution of ARs with respect to latitude. The left, middle, and right column show the compliance state with Hale’s law, Joy’s law, and the HHR, respectively, for the full dataset (top row), SC24 (middle row), and SC25 (bottom row). The red (blue) bars, as scaled by the left y-axis, represent the number of ARs that obey (violate) the empirical laws; black dots, as scaled by the right y-axis, show the co… view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Frequency distribution of ARs that obey/violate Hale’s law (top), Joy’s law (middle), and the HHR (bottom), respectively. The red (blue) bars, as scaled by the left y-axis, represent the number of ARs that obey (violate) the empirical laws; black dots, as scaled by the…
Figure 5
Figure 5. Figure 5: Frequency distribution of ARs with respect to centroid distance between opposite polarities. The left, middle, and right column show the compliance state with Hale’s law, Joy’s law, and the HHR, respectively, for the full dataset (top row), SC24 (middle row), and SC25 …
Figure 6
Figure 6. Figure 6: Frequency distribution of ARs with respect to total unsigned magnetic flux. The left, middle, and right column show the compliance state with Hale’s law, Joy’s law, and the HHR, respectively, for the full dataset (top row), SC24 (middle row), and SC25 (bottom row). The…
Figure 7
Figure 7. Figure 7: The distribution of FI with respect to centroid distance and unsigned flux. (a) Scatter plot of unsigned flux versus centroid distance for all ARs, color-coded by FI. The vertical and horizontal dashed lines mark the flux and distance thresholds identified from the bin…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

84 extracted references · 84 canonical work pages

  1. [1]

    1998, ApJL, 496, L43, doi: 10.1086/311232

    Bao, S., & Zhang, H. 1998, ApJL, 496, L43, doi: 10.1086/311232

    work page doi:10.1086/311232 1998

  2. [2]

    C., Schunker, H., Cameron, R

    Baumgartner, C., Birch, A. C., Schunker, H., Cameron, R. H., & Gizon, L. 2022, A&A, 664, A183, doi: 10.1051/0004-6361/202243357

    work page doi:10.1051/0004-6361/202243357 2022

  3. [3]

    A., & Field, G

    Berger, M. A., & Field, G. B. 1984, Journal of Fluid Mechanics, 147, 133, doi: 10.1017/S0022112084002019

    work page doi:10.1017/s0022112084002019 1984

  4. [4]

    A., & Ruzmaikin, A

    Berger, M. A., & Ruzmaikin, A. 2000, J. Geophys. Res., 105, 10481, doi: 10.1029/1999JA900392

    work page doi:10.1029/1999ja900392 2000

  5. [5]

    W., Evenson, P., & Matthaeus, W

    Bieber, J. W., Evenson, P., & Matthaeus, W. H. 1987, Geophys. Res. Lett., 14, 864, doi: 10.1029/GL014i008p00864

    work page doi:10.1029/gl014i008p00864 1987

  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]

    R., & Greisen, E

    Calabretta, M. R., & Greisen, E. W. 2002, A&A, 395, 1077, doi: 10.1051/0004-6361:20021327

    work page doi:10.1051/0004-6361:20021327 2002

  8. [8]

    1995, ApJ, 441, 886, doi: 10.1086/175410

    Caligari, P., Moreno-Insertis, F., & Schussler, M. 1995, ApJ, 441, 886, doi: 10.1086/175410

    work page doi:10.1086/175410 1995

Show all 84 references
  1. [9]

    C., Hudson, H

    Canfield, R. C., Hudson, H. S., & McKenzie, D. E. 1999, Geophys. Res. Lett., 26, 627, doi: 10.1029/1999GL900105

    1999 doi

  2. [10]

    2021, SoPh, 296, 150, doi: 10.1007/s11207-021-01895-1

    Chen, A., Ye, Q., & Wang, J. 2021, SoPh, 296, 150, doi: 10.1007/s11207-021-01895-1

    2021 doi

  3. [11]

    Q., & Wang, J

    Chen, A. Q., & Wang, J. X. 2012, A&A, 543, A49, doi: 10.1051/0004-6361/201118037

    2012 doi

  4. [12]

    1988, Routledge, doi: 10.4324/9780203771587

    Cohen, J. 1988, Routledge, doi: 10.4324/9780203771587

    1988 doi

  5. [13]

    W., & Foreman, D

    Corder, G. W., & Foreman, D. I. 2009, (No Title), doi: 10.1002/9781118165881

    2009 doi

  6. [14]

    K., Krivova, N

    Dasi-Espuig, M., Solanki, S. K., Krivova, N. A., Cameron, R., & Pe˜ nuela, T. 2010, A&A, 518, A7, doi: 10.1051/0004-6361/201014301 D´ emoulin, P., Mandrini, C. H., Van Driel-Gesztelyi, L., Lopez Fuentes, M. C., & Aulanier, G. 2002, SoPh, 207, 87, doi: 10.1023/A:1015531804337 D...

    2010 doi

  7. [15]

    2008, ApJ, 676, 680, doi: 10.1086/527317

    Fan, Y. 2008, ApJ, 676, 680, doi: 10.1086/527317

    2008 doi

  8. [16]

    2003, The Astrophysical Journal, 582, 1206, doi: 10.1086/344798

    Fan, Y., Abbett, W., & Fisher, G. 2003, The Astrophysical Journal, 582, 1206, doi: 10.1086/344798

    2003 doi

  9. [17]

    2014, ApJ, 789, 35, doi: 10.1088/0004-637X/789/1/35

    Fan, Y., & Fang, F. 2014, ApJ, 789, 35, doi: 10.1088/0004-637X/789/1/35

    2014 doi

  10. [18]

    H., & Deluca, E

    Fan, Y., Fisher, G. H., & Deluca, E. E. 1993, ApJ, 405, 390, doi: 10.1086/172370

    1993 doi

  11. [19]

    H., & McClymont, A

    Fan, Y., Fisher, G. H., & McClymont, A. N. 1994, ApJ, 436, 907, doi: 10.1086/174967

    1994 doi

  12. [20]

    G., & Lantz, S

    Fan, Y., Zweibel, E. G., & Lantz, S. R. 1998, ApJ, 493, 480, doi: 10.1086/305122

    1998 doi

  13. [21]

    H., Fan, Y., & Howard, R

    Fisher, G. H., Fan, Y., & Howard, R. F. 1995, ApJ, 438, 463, doi: 10.1086/175090

    1995 doi

  14. [22]

    A., & Hagyard, M

    Gary, G. A., & Hagyard, M. J. 1990, SoPh, 126, 21, doi: 10.1007/BF00158295

    1990 doi

  15. [23]

    2006, The American Statistician, 60, 328, doi: 10.1198/000313006X152649

    Gelman, A., & Stern, H. 2006, The American Statistician, 60, 328, doi: 10.1198/000313006X152649

    2006 doi

  16. [24]

    K., & Rust, D

    Georgoulis, M. K., & Rust, D. M. 2007, ApJL, 661, L109, doi: 10.1086/518718

    2007 doi

  17. [25]

    Glatzmaier, G. A. 1985, ApJ, 291, 300, doi: 10.1086/163069

    1985 doi

  18. [26]

    2005, PASJ, 57, 481, doi: 10.1093/pasj/57.3.481

    Hagino, M., & Sakurai, T. 2005, PASJ, 57, 481, doi: 10.1093/pasj/57.3.481

    2005 doi

  19. [27]

    E., Ellerman, F., Nicholson, S

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

    1919 doi

  20. [28]

    Hathaway, D. H. 2015, Living Reviews in Solar Physics, 12, 4, doi: 10.1007/lrsp-2015-4

    2015 doi

  21. [29]

    H., Wilson, R

    Hathaway, D. H., Wilson, R. M., & Reichmann, E. J. 1994, SoPh, 151, 177, doi: 10.1007/BF00654090

    1994 doi

  22. [30]

    Howard, R. F. 1991, SoPh, 136, 251, doi: 10.1007/BF00146534

    1991 doi

  23. [31]

    2012, SoPh, 275, 67, doi: 10.1007/s11207-010-9624-2

    Hurlburt, N., Cheung, M., Schrijver, C., et al. 2012, SoPh, 275, 67, doi: 10.1007/s11207-010-9624-2

    2012 doi

  24. [32]

    2018, ApJ, 863, 159, doi: 10.3847/1538-4357/aad197

    Jiang, J., Wang, J.-X., Jiao, Q.-R., & Cao, J.-B. 2018, ApJ, 863, 159, doi: 10.3847/1538-4357/aad197

    2018 doi

  25. [33]

    2010, ApJ, 713, 440, doi: 10.1088/0004-637X/713/1/440

    Jing, J., Tan, C., Yuan, Y., et al. 2010, ApJ, 713, 440, doi: 10.1088/0004-637X/713/1/440

    2010 doi

  26. [34]

    2019, The American Statistician, 73, 129, doi: 10.1080/00031305.2018.1518788

    Johnson, V. 2019, The American Statistician, 73, 129, doi: 10.1080/00031305.2018.1518788

    2019 doi arXiv

  27. [35]

    Jouve, L., & Brun, A. S. 2009, ApJ, 701, 1300, doi: 10.1088/0004-637X/701/2/1300

    2009 doi

  28. [36]

    2003, Advances in Space Research, 32, 1931, doi: 10.1016/S0273-1177(03)90628-4

    Kusano, K., Yokoyama, T., Maeshiro, T., & Sakurai, T. 2003, Advances in Space Research, 32, 1931, doi: 10.1016/S0273-1177(03)90628-4

    2003 doi

  29. [37]

    2018, SoPh, 293, 159, doi: 10.1007/s11207-018-1381-7

    Lee, E.-J., Park, S.-H., & Moon, Y.-J. 2018, SoPh, 293, 159, doi: 10.1007/s11207-018-1381-7

    2018 doi

  30. [38]

    Leka, K. D. 1999, SoPh, 188, 21, doi: 10.1023/A:1005130630873

    1999 doi

  31. [40]

    2018b, ApJ, 867, 89, doi: 10.3847/1538-4357/aae31a

    Li, J. 2018b, ApJ, 867, 89, doi: 10.3847/1538-4357/aae31a

    doi

  32. [41]

    Li, J., & Ulrich, R. K. 2012, ApJ, 758, 115, doi: 10.1088/0004-637X/758/2/115

    2012 doi

  33. [42]

    2024, ApJ, 973, 50, doi: 10.3847/1538-4357/ad66bd

    Liu, R., & Wang, W. 2024, ApJ, 973, 50, doi: 10.3847/1538-4357/ad66bd

    2024 doi

  34. [43]

    T., & Sun, X

    Liu, Y., Hoeksema, J. T., & Sun, X. 2014, ApJL, 783, L1, doi: 10.1088/2041-8205/783/1/L1

    2014 doi

  35. [44]

    Liu, Y., & Schuck, P. W. 2012, ApJ, 761, 105, doi: 10.1088/0004-637X/761/2/105

    2012 doi

  36. [45]

    W., Fisher, G

    Longcope, D. W., Fisher, G. H., & Pevtsov, A. A. 1998, ApJ, 507, 417, doi: 10.1086/306312

    1998 doi

  37. [46]

    W., & Klapper, I

    Longcope, D. W., & Klapper, I. 1997, ApJ, 488, 443, doi: 10.1086/304680 Mu˜ noz-Jaramillo, A., Navarrete, B., & Campusano, L. E. 2021, ApJ, 920, 31, doi: 10.3847/1538-4357/ac133b

    1997 doi

  38. [47]

    J., Brown, B

    Nelson, N. J., Brown, B. P., Sacha Brun, A., Miesch, M. S., & Toomre, J. 2014, SoPh, 289, 441, doi: 10.1007/s11207-012-0221-4

    2014 doi

  39. [48]

    2023, SSRv, 219, 64, doi: 10.1007/s11214-023-01008-3

    Norton, A., Howe, R., Upton, L., & Usoskin, I. 2023, SSRv, 219, 64, doi: 10.1007/s11214-023-01008-3

    2023 doi

  40. [49]

    2025a, SoPh, 300, 111, doi: 10.1007/s11207-025-02525-w

    Pan, J., Liu, J., Fang, S., & Liu, R. 2025a, SoPh, 300, 111, doi: 10.1007/s11207-025-02525-w

    doi

  41. [50]

    2025b, Chinese Journal of Space Science, 45, 1650, doi: 10.11728/cjss2025.06.2025-0086

    Pan, J., LIU, J., & LIU, R. 2025b, Chinese Journal of Space Science, 45, 1650, doi: 10.11728/cjss2025.06.2025-0086

    2025 doi

  42. [51]

    2025, ApJ, 995, 46, doi: 10.3847/1538-4357/ae1d7e

    Pan, J., & Liu, R. 2025, ApJ, 995, 46, doi: 10.3847/1538-4357/ae1d7e

    2025 doi

  43. [52]

    2010, ApJ, 720, 1102, doi: 10.1088/0004-637X/720/2/1102

    Park, S.-H., Chae, J., Jing, J., Tan, C., & Wang, H. 2010, ApJ, 720, 1102, doi: 10.1088/0004-637X/720/2/1102

    2010 doi

  44. [53]

    D., & Kusano, K

    Park, S.-H., Leka, K. D., & Kusano, K. 2020, ApJ, 904, 6, doi: 10.3847/1538-4357/abbb93

    2020 doi

  45. [54]

    D., & Kusano, K

    Park, S.-H., Leka, K. D., & Kusano, K. 2021, ApJ, 911, 79, doi: 10.3847/1538-4357/abea13

    2021 doi

  46. [55]

    2013, ApJ, 778, 13, doi: 10.1088/0004-637X/778/1/13

    Park, S.-H., Kusano, K., Cho, K.-S., et al. 2013, ApJ, 778, 13, doi: 10.1088/0004-637X/778/1/13

    2013 doi

  47. [56]

    Parker, E. N. 1994, ApJ, 433, 867, doi: 10.1086/174695

    1994 doi

  48. [57]

    A., Canfield, R

    Pevtsov, A. A., Canfield, R. C., & Metcalf, T. R. 1995, ApJL, 440, L109, doi: 10.1086/187773

    1995 doi

  49. [58]

    A., & Longcope, D

    Pevtsov, A. A., & Longcope, D. W. 2001, in Astronomical Society of the Pacific Conference Series, Vol. 236, Advanced Solar Polarimetry – Theory, Observation, and Instrumentation, ed. M. Sigwarth, 423

    2001

  50. [59]

    2025, ApJ, 986, 114, doi: 10.3847/1538-4357/add93a

    Qin, L., Jiang, J., & Wang, R. 2025, ApJ, 986, 114, doi: 10.3847/1538-4357/add93a

    2025 doi

  51. [60]

    S., McKillop, S

    Savcheva, A. S., McKillop, S. C., McCauley, P. I., Hanson, E. M., & DeLuca, E. E. 2014, SoPh, 289, 3297, doi: 10.1007/s11207-013-0469-3

    2014 doi

  52. [61]

    H., Schou, J., Bush, R

    Scherrer, P. H., Schou, J., Bush, R. I., et al. 2012, SoPh, 275, 207, doi: 10.1007/s11207-011-9834-2

    2012 doi

  53. [62]

    1990, SoPh, 125, 219, doi: 10.1007/BF00158402

    Seehafer, N. 1990, SoPh, 125, 219, doi: 10.1007/BF00158402

    1990 doi

  54. [63]

    K., Karak, B

    Sreedevi, A., Jha, B. K., Karak, B. B., & Banerjee, D. 2023, ApJS, 268, 58, doi: 10.3847/1538-4365/acec47

    2023 doi

  55. [64]

    K., Karak, B

    Sreedevi, A., Jha, B. K., Karak, B. B., & Banerjee, D. 2024, ApJ, 966, 112, doi: 10.3847/1538-4357/ad34b8

    2024 doi

  56. [65]

    O., & Kosovichev, A

    Stenflo, J. O., & Kosovichev, A. G. 2012, ApJ, 745, 129, doi: 10.1088/0004-637X/745/2/129

    2012 doi

  57. [66]

    2013, arXiv e-prints, arXiv:1309.2392, doi: 10.48550/arXiv.1309.2392

    Sun, X. 2013, arXiv e-prints, arXiv:1309.2392, doi: 10.48550/arXiv.1309.2392

    2013 doi arXiv

  58. [67]

    2021, Living Reviews in Solar Physics, 18, 4, doi: 10.1007/s41116-021-00030-3

    Temmer, M. 2021, Living Reviews in Solar Physics, 18, 4, doi: 10.1007/s41116-021-00030-3

    2021 doi

  59. [68]

    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

    2005 doi

  60. [69]

    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

    1999 doi

  61. [70]

    2019, Living Reviews in Solar Physics, 16, 3, doi: 10.1007/s41116-019-0019-7 van Driel-Gesztelyi, L., & Green, L

    Toriumi, S., & Wang, H. 2019, Living Reviews in Solar Physics, 16, 3, doi: 10.1007/s41116-019-0019-7 van Driel-Gesztelyi, L., & Green, L. M. 2015, Living Reviews in Solar Physics, 12, 1

    2019 doi

  62. [71]

    Vemareddy, P., Ambastha, A., & Maurya, R. A. 2012, ApJ, 761, 60, doi: 10.1088/0004-637X/761/1/60

    2012 doi

  63. [72]

    Virtanen, I. O. I., Virtanen, I. I., Pevtsov, A. A., Yeates, A., & Mursula, K. 2017, A&A, 604, A8, doi: 10.1051/0004-6361/201730415

    2017 doi

  64. [73]

    2015, Science China

    Wang, J., Zhang, Y., He, H., et al. 2015, Science China

    2015

  65. [74]

    Physics, Mechanics, and Astronomy, 58, 5682, doi: 10.1007/s11433-015-5682-7

    doi

  66. [75]

    2023, ApJS, 268, 55, doi: 10.3847/1538-4365/acef1b

    Wang, R., Jiang, J., & Luo, Y. 2023, ApJS, 268, 55, doi: 10.3847/1538-4365/acef1b

    2023 doi

  67. [76]

    2013, ApJL, 775, L46, doi: 10.1088/2041-8205/775/2/L46

    Wang, Y.-M. 2013, ApJL, 775, L46, doi: 10.1088/2041-8205/775/2/L46

    2013 doi

  68. [77]

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

    1989 doi

  69. [78]

    A., & Fan, Y

    Weber, M. A., & Fan, Y. 2015, SoPh, 290, 1295, doi: 10.1007/s11207-015-0674-3

    2015 doi

  70. [79]

    A., Fan, Y., & Miesch, M

    Weber, M. A., Fan, Y., & Miesch, M. S. 2011, ApJ, 741, 11, doi: 10.1088/0004-637X/741/1/11

    2011 doi

  71. [80]

    A., Fan, Y., & Miesch, M

    Weber, M. A., Fan, Y., & Miesch, M. S. 2013, SoPh, 287, 239, doi: 10.1007/s11207-012-0093-7

    2013 doi

  72. [81]

    W., Norton, A

    Will, L. W., Norton, A. A., & Hoeksema, J. T. 2024, ApJ, 976, 20, doi: 10.3847/1538-4357/ad82e3

    2024 doi

  73. [82]

    R., Altrocki, R

    Wilson, P. R., Altrocki, R. C., Harvey, K. L., Martin, S. F., & Snodgrass, H. B. 1988, Nature, 333, 748, doi: 10.1038/333748a0

    1988 doi

  74. [83]

    Yeates, A. R. 2020, SoPh, 295, 119, doi: 10.1007/s11207-020-01688-y

    2020 doi

  75. [84]

    1988, Science, 242, 1586

    Zirin, H. 1988, Science, 242, 1586

    1988

  76. [85]

    ABN” category integrates ARs classified as AH, AJ, or AHJ. The “Other

    Zirin, H., & Liggett, M. A. 1987, SoPh, 113, 267, doi: 10.1007/BF00147707 12 Figure 1.Data processing pipeline. (a) SARD detection results on the full-disk LoS magnetogram on 2014 October 22, which are calibrated with the AR information from the NOAA SRS catalog. The detected ...

    1987 doi

Pith tools

Reviewed July 10, 2026 · model on record in the stance chip above.