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arxiv: 2312.06787 · v1 · submitted 2023-12-11 · 🌌 astro-ph.SR

Photospheric Lorentz force changes in eruptive and confined solar flares

Samriddhi Sankar Maity , Ranadeep Sarkar , Piyali Chatterjee , Nandita Srivastava This is my paper

Pith reviewed 2026-05-24 05:21 UTC · model grok-4.3

classification 🌌 astro-ph.SR
keywords solar flaresLorentz forcephotosphereeruptive flaresconfined flarespolarity inversion linecoronal mass ejections
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The pith

Confined solar flares show total downward Lorentz force changes below 1.8 × 10^22 dyne, unlike eruptive flares.

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

The paper measures abrupt permanent changes in the photospheric magnetic field during major solar flares by tracking shifts in the downward Lorentz force near polarity inversion lines. It compares vector magnetogram data for 26 eruptive and 11 confined flares stronger than GOES M5 class, plus two synthetic cases from a delta-sunspot simulation. The central result is that every confined event stays below a total integrated force change of 1.8 × 10^22 dyne while eruptive events exceed this value. The size of the force change also scales with the height of coronal reconnection at flare onset. If the distinction holds, the photospheric impulse helps determine whether a flare will launch a coronal mass ejection.

Core claim

Analysis of SHARP vector-magnetograms shows a rapid increase in the horizontal magnetic field along the flaring polarity inversion line together with a significant change in the downward-directed Lorentz force in the same region. All confined events exhibit a total change in Lorentz force of less than 1.8 × 10^22 dyne. This threshold distinguishes eruptive from confined flares, and the magnitude of the change further depends on reconnection height in the corona.

What carries the argument

Total change in downward-directed Lorentz force integrated over a localized area around the polarity inversion line encompassing the flare site.

If this is right

  • Eruptive flares transmit a larger upward impulse from the photosphere that can drive a coronal mass ejection.
  • The 1.8 × 10^22 dyne threshold supplies a practical diagnostic for classifying flare eruptivity from surface magnetic data.
  • The Lorentz force change correlates with reconnection height, linking photospheric and coronal dynamics during the flare.
  • Synthetic delta-sunspot simulations reproduce the same pattern of force changes seen in the observations.

Where Pith is reading between the lines

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

  • Real-time tracking of photospheric Lorentz force near polarity inversion lines could supply an early indicator of whether an ongoing flare will produce an ejection.
  • Applying the same measurement to weaker flares would test whether the threshold scales with flare magnitude.
  • The reconnection-height dependence points to a direct energy-transfer pathway that MHD models could target for verification.
  • Automated detection of the integration area around the polarity inversion line might reduce selection uncertainty in future applications.

Load-bearing premise

The 37 selected M5+ flares and the precise areas chosen around each polarity inversion line are representative and free of projection or data-processing artifacts that would systematically alter the integrated force for one class versus the other.

What would settle it

Detection of even one confined flare exceeding 1.8 × 10^22 dyne total Lorentz force change, or one eruptive flare staying below it, in a comparable set of HMI magnetograms would falsify the threshold distinction.

Figures

Figures reproduced from arXiv: 2312.06787 by Nandita Srivastava, Piyali Chatterjee, Ranadeep Sarkar, Samriddhi Sankar Maity.

Figure 1
Figure 1. Figure 1: Illustrations of two eruptive events to identify the regions of interest (RoIs) of the magnetic imprints (MIs). The panels a and b are AIA 1600˚A images of the two flaring events occurred on 2011 February 13 at 17:38 UT and 2011 September 06 at 22:20 UT respectively. The panels c and d represent the radial magnetic field Br whose strength is indicated by colorbars. The horizontal component of the magnetic … view at source ↗
Figure 2
Figure 2. Figure 2: Similar to figure 1 but for confined events occurred on (a), (c) 2013 November 01 at 19:53 UT and (b), (d) 2015 March 12 at 14:08 UT. Stokes parameters at six wavelengths centered on Fe I 6173 ˚A absorption line with a bandwidth of 76 ˚A. Based on these observations, the photospheric vector magnetic field is derived by inverting full set of Stokes parameters using the Milne-Eddington inversion approach (Bo… view at source ↗
Figure 3
Figure 3. Figure 3: Temporal evolution of average horizontal magnetic fields (blue) and vertical Lorentz force (red) calculated by Lorentz force (solid) and horizontal magnetic field (dashed) contouring method. The panels a and b represent eruptive, whereas the panels c and d represent confined events. The shaded region corresponds to the duration of field change. The vertical error bars represents the fluctuations at a 3σ le… view at source ↗
Figure 4
Figure 4. Figure 4: Scatter plot of (a) Average horizontal magnetic field change δBh vs logarithmic flare strength and (b) Vertical Lorentz force change δFz vs logarithmic flare strength for RoIs identified based on the difference maps of horizontal magnetic field. Filled and empty symbols correspond to the eruptive and confined flares, respectively. The triangular and circular symbols are for X-class and M-class flares, resp… view at source ↗
Figure 5
Figure 5. Figure 5: Similar to [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: A sketch of the magnetic field configuration of (a) eruptive event with higher Lorentz force change and (b) eruptive event with lower Lorentz force change. Red and blue filled regions are positive and negative polarity regions whereas solid lines refer to the magnetic field lines. The X mark represents the location of the reconnection site and the downward arrow implies the direction of vertical Lorentz fo… view at source ↗
Figure 7
Figure 7. Figure 7: Illustrations demonstrating the calculation of ribbon distances for two events. Panels a and b represent the photospheric magnetic field maps for the two events occurred on 2013-11-08 04:23 UT and 2014-09-10 17:41 UT respectively. The red/blue colors represent the positive/negative polarities of Br plotted within a range of ±500 Gauss. The yellow line is indicative of the polarity inversion line (PIL) and … view at source ↗
Figure 8
Figure 8. Figure 8: Scatter plot of vertical Lorentz force change vs ribbon distance. The values of Lorentz force change shown in the figure are estimated using the method based on the Lorentz force difference maps. Filled and empty symbols correspond to the eruptive and confined flares, respectively. The triangular and circular symbols imply X-class and M-class flares, respectively. The horizontal dashed line is drawn to ill… view at source ↗
Figure 9
Figure 9. Figure 9: (a) Illustration of the vertical magnetic field Bz for the B-class synthetic flare events and (b) the corresponding temporal evolution of average horizontal magnetic fields (blue) and vertical Lorentz force (red). (c) and (d) Same as (a) and (b) but for the synthetic C-class flare. The green contours in (a) and (c) mark the region where significant change in Lorentz force occurs. The strength of the vertic… view at source ↗
Figure 10
Figure 10. Figure 10: Height–time diagram of Lorentz force from the 3D MHD simulation to show its downward propagation. The dashed vertical lines represent the time of the two synthetic flares. The arrow is for guiding the eye towards the propa￾gation direction of the Lorentz force. force (Fz), and this may be one of the factors contribut￾ing to the observed variations during such events. 3.3. Downward propagation of the Loren… view at source ↗
read the original abstract

Solar flares are known to leave imprints on the magnetic field at the photosphere, often manifested as an abrupt and permanent change in the downward-directed Lorentz force in localized areas inside the active region. Our study aims to differentiate eruptive and confined solar flares based on the vertical Lorentz force variations. We select 26 eruptive and 11 confined major solar flares (stronger than the GOES M5 class) observed during 2011-2017. We analyze these flaring regions using SHARP vector-magnetograms obtained from the NASA's Helioseismic and Magnetic Imager (HMI). We also compare data corresponding to 2 synthetic flares from a $\delta$--sunspot simulation reported in Chatterjee et al. [Phys. Rev. Lett. 116, 101101 (2016)]. We estimate the change in the horizontal magnetic field and the total Lorentz force integrated over an area around the polarity inversion line (PIL) that encompasses the location of the flare. Our results indicate a rapid increase of the horizontal magnetic field along the flaring PIL, accompanied by a significant change in the downward-directed Lorentz force in the same vicinity. Notably, we find that all the confined events under study exhibit a total change in Lorentz force of < $1.8 \times 10^{22}$ dyne. This threshold plays an important factor in effectively distinguishing eruptive and confined flares. Further, our analysis suggests that the change in total Lorentz force also depends on the reconnection height in the solar corona during the associated flare onset. The results provide significant implications for understanding the flare-related upward impulse transmission for the associated coronal mass ejection.

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 / 1 minor

Summary. The manuscript analyzes HMI vector magnetograms for 26 eruptive and 11 confined M5+ flares (2011-2017) plus two synthetic flares from a δ-sunspot simulation. It reports a rapid increase in horizontal field along the PIL accompanied by a change in downward Lorentz force, finding that every confined event shows a total integrated ΔF_Lorentz < 1.8 × 10^22 dyne while eruptive events exceed this value; the threshold is presented as an effective discriminator, with additional dependence on coronal reconnection height.

Significance. If the separation survives scrutiny of area selection and sample definition, the result supplies an empirical photospheric observable that links force changes to eruptive potential and could inform CME forecasting. Use of public HMI data and direct comparison to simulation output are clear strengths that enhance reproducibility.

major comments (2)
  1. [Abstract and data-analysis description] The central separation at 1.8 × 10^22 dyne is obtained by integrating over 'an area around the PIL that encompasses the location of the flare.' No fixed physical radius, automated contour, or sensitivity test to area variations is described; because eruptive flares systematically occupy larger areas, the integrated quantity can be altered by the area choice itself rather than by the underlying physics. This directly undermines attribution of the clean threshold to the eruptive/confined distinction.
  2. [Results and discussion of the threshold] The threshold is an empirical summary statistic derived from the 37-event sample rather than a pre-specified criterion; with only 11 confined events, no cross-validation or stability test against sample definition or area choice is reported. The separation could therefore be sensitive to the particular flares selected or the precise integration boundaries.
minor comments (1)
  1. [Abstract] The abstract states that the change in total Lorentz force 'also depends on the reconnection height' but provides no quantitative relation or figure; a brief clarification or reference to the relevant panel would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major point below, agreeing where revisions are needed to improve clarity and robustness.

read point-by-point responses

  1. Referee: [Abstract and data-analysis description] The central separation at 1.8 × 10^22 dyne is obtained by integrating over 'an area around the PIL that encompasses the location of the flare.' No fixed physical radius, automated contour, or sensitivity test to area variations is described; because eruptive flares systematically occupy larger areas, the integrated quantity can be altered by the area choice itself rather than by the underlying physics. This directly undermines attribution of the clean threshold to the eruptive/confined distinction.

    Authors: We agree that the integration area requires a more explicit and reproducible definition. The areas were chosen to encompass the observed region of horizontal field increase along the PIL associated with each flare, guided by the spatial extent of the flare ribbons and field changes in the HMI data. In revision we will add a quantitative description of the selection (e.g., contour at a minimum ΔB_h threshold) and include sensitivity tests that vary the area by ±20 % around the nominal choice, showing that the 1.8 × 10^22 dyne separation persists. These changes will be incorporated. revision: yes

  2. Referee: [Results and discussion of the threshold] The threshold is an empirical summary statistic derived from the 37-event sample rather than a pre-specified criterion; with only 11 confined events, no cross-validation or stability test against sample definition or area choice is reported. The separation could therefore be sensitive to the particular flares selected or the precise integration boundaries.

    Authors: The threshold is an empirical discriminator identified from the clear separation in the 37-event sample. With only 11 confined events we recognize the statistical limitations and lack of cross-validation. In the revised manuscript we will expand the discussion to state explicitly that the value is sample-derived, note the modest confined-flare count, and report the area-sensitivity tests described above. We maintain that the observed separation is physically informative for this dataset while agreeing to highlight these caveats. revision: partial

Circularity Check

0 steps flagged

No circularity; purely observational empirical threshold

full rationale

The paper is an observational analysis of HMI vector magnetograms for 37 selected flares (26 eruptive, 11 confined). It computes the integrated change in downward Lorentz force over an area around the PIL and reports that all confined events fall below an empirical threshold of 1.8e22 dyne as a direct summary statistic of the measurements. No equations derive this threshold from prior assumptions or inputs; the separation is a post-hoc observation from the data. The citation to Chatterjee et al. (2016) supplies only supplementary synthetic flare comparisons and does not load-bear the central observational claim. No self-definitional steps, fitted inputs renamed as predictions, or ansatz smuggling occur.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on an empirically fitted threshold derived from the 37-event sample plus the domain assumption that HMI vector fields accurately capture the photospheric Lorentz force change.

free parameters (1)
  • Lorentz-force threshold = 1.8e22 dyne
    The value 1.8 × 10^22 dyne is chosen to separate the two flare classes in the observed sample.
axioms (1)
  • domain assumption SHARP/HMI vector magnetograms provide a faithful representation of the photospheric magnetic field vector without significant projection or calibration artifacts inside the chosen PIL boxes.
    The entire analysis depends on the accuracy of the downloaded magnetograms for computing horizontal-field change and integrated force.

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Works this paper leans on

60 extracted references · 60 canonical work pages

  1. [1]

    Andrews, M. D. 2003, SoPh, 218, 261, doi: 10.1023/B:SOLA.0000013039.69550.bf

    work page doi:10.1023/b:sola.0000013039.69550.bf 2003

  2. [2]

    2016, Nature Physics, 12, 998, doi: 10.1038/nphys3938

    Aulanier, G. 2016, Nature Physics, 12, 998, doi: 10.1038/nphys3938

    work page doi:10.1038/nphys3938 2016

  3. [3]

    2004, Space Weather, 2, S02004, doi: 10.1029/2003SW000044

    Panasyuk, M. 2004, Space Weather, 2, S02004, doi: 10.1029/2003SW000044

    work page doi:10.1029/2003sw000044 2004

  4. [4]

    Barczynski, K., Aulanier, G., Masson, S., & Wheatland, M. S. 2019, ApJ, 877, 67, doi: 10.3847/1538-4357/ab1b3d

    work page doi:10.3847/1538-4357/ab1b3d 2019

  5. [5]

    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

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

  6. [6]

    1964, in NASA Special Publication, Vol

    Carmichael, H. 1964, in NASA Special Publication, Vol. 50, 451 Castellanos Dur´ an, J. S., Kleint, L., & Calvo-Mozo, B. 2018, ApJ, 852, 25, doi: 10.3847/1538-4357/aa9d37

    work page doi:10.3847/1538-4357/aa9d37 1964

  7. [7]

    2016, PhRvL, 116, 101101, doi: 10.1103/PhysRevLett.116.101101

    Chatterjee, P., Hansteen, V., & Carlsson, M. 2016, PhRvL, 116, 101101, doi: 10.1103/PhysRevLett.116.101101

    work page doi:10.1103/physrevlett.116.101101 2016

  8. [8]

    2017, Physics of Plasmas, 24, 090501, doi: 10.1063/1.4993929

    Chen, J. 2017, Physics of Plasmas, 24, 090501, doi: 10.1063/1.4993929

    work page doi:10.1063/1.4993929 2017

  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

    work page doi:10.1007/s11207-011-9907-2 2012

  10. [10]

    Fletcher, L., & Hudson, H. S. 2008, ApJ, 675, 1645, doi: 10.1086/527044

    work page doi:10.1086/527044 2008

  11. [11]

    2012, ApJ, 749, 85, doi: 10.1088/0004-637X/749/1/85

    Gosain, S. 2012, ApJ, 749, 85, doi: 10.1088/0004-637X/749/1/85

    work page doi:10.1088/0004-637x/749/1/85 2012

  12. [12]

    2018, SSRv, 214, 46, doi: 10.1007/s11214-017-0462-5

    Veronig, A. 2018, SSRv, 214, 46, doi: 10.1007/s11214-017-0462-5

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

  13. [13]

    Harrison, R. A. 2003, Advances in Space Research, 32, 2425, doi: 10.1016/j.asr.2003.03.016

    work page doi:10.1016/j.asr.2003.03.016 2003

  14. [14]

    1974, SoPh, 34, 323, doi: 10.1007/BF00153671

    Hirayama, T. 1974, SoPh, 34, 323, doi: 10.1007/BF00153671

    work page doi:10.1007/bf00153671 1974

  15. [15]

    Hudson, H. S. 2000, ApJL, 531, L75, doi: 10.1086/312516

    work page doi:10.1086/312516 2000

  16. [16]

    S., Fisher, G

    Hudson, H. S., Fisher, G. H., & Welsch, B. T. 2008, in Astronomical Society of the Pacific Conference Series, Vol. 383, Subsurface and Atmospheric Influences on Solar Activity, ed. R. Howe, R. W. Komm, K. S. Balasubramaniam, & G. J. D. Petrie, 221

    work page 2008

  17. [17]

    2018, ApJ, 864, 138, doi: 10.3847/1538-4357/aad6e4

    Jing, J., Liu, C., Lee, J., et al. 2018, ApJ, 864, 138, doi: 10.3847/1538-4357/aad6e4

    work page doi:10.3847/1538-4357/aad6e4 2018

  18. [18]

    Kazachenko, M. D. 2023, arXiv e-prints, arXiv:2310.02878, doi: 10.48550/arXiv.2310.02878

    work page doi:10.48550/arxiv.2310.02878 2023

  19. [19]

    D., Albelo-Corchado, M

    Kazachenko, M. D., Albelo-Corchado, M. F., Tamburri, C. A., & Welsch, B. T. 2022, SoPh, 297, 59, doi: 10.1007/s11207-022-01987-6

    work page doi:10.1007/s11207-022-01987-6 2022

  20. [20]

    2017, ApJ, 834, 26, doi: 10.3847/1538-4357/834/1/26

    Kleint, L. 2017, ApJ, 834, 26, doi: 10.3847/1538-4357/834/1/26

    work page doi:10.3847/1538-4357/834/1/26 2017

  21. [21]

    A., & Pneuman, G

    Kopp, R. A., & Pneuman, G. W. 1976, SoPh, 50, 85, doi: 10.1007/BF00206193 Kors´ os, M. B., Chatterjee, P., & Erd´ elyi, R. 2018, ApJ, 857, 103, doi: 10.3847/1538-4357/aab891 Kors´ os, M. B., Ludm´ any, A., Erd´ elyi, R., & Baranyi, T. 2015, ApJL, 802, L21, doi: 10.1088/2041-8205/802/2/L21

    work page doi:10.1007/bf00206193 1976

  22. [22]

    2020, MNRAS, 497, 976, doi: 10.1093/mnras/staa1974

    Kumar, H., & Kumar, B. 2020, MNRAS, 497, 976, doi: 10.1093/mnras/staa1974

    work page doi:10.1093/mnras/staa1974 2020

  23. [23]

    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

  24. [24]

    2011, ApJL, 727, L19, doi: 10.1088/2041-8205/727/1/L19

    Li, Y., Jing, J., Fan, Y., & Wang, H. 2011, ApJL, 727, L19, doi: 10.1088/2041-8205/727/1/L19

    work page doi:10.1088/2041-8205/727/1/l19 2011

  25. [25]

    2022, ApJL, 934, L33, doi: 10.3847/2041-8213/ac83bf

    Liu, L., Zhou, Z., Wang, Y., Sun, X., & Wang, G. 2022, ApJL, 934, L33, doi: 10.3847/2041-8213/ac83bf

    work page doi:10.3847/2041-8213/ac83bf 2022

  26. [26]

    L., Sterling, A

    Moore, R. L., Sterling, A. C., Hudson, H. S., & Lemen, J. R. 2001, ApJ, 552, 833, doi: 10.1086/320559 Pencil Code Collaboration, Brandenburg, A., Johansen, A., et al. 2021, The Journal of Open Source Software, 6, 2807, doi: 10.21105/joss.02807

    work page doi:10.1086/320559 2001

  27. [27]

    D., Thompson, B

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

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

  28. [28]

    Petrie, G. J. D. 2012, ApJ, 759, 50, doi: 10.1088/0004-637X/759/1/50

    work page doi:10.1088/0004-637x/759/1/50 2012

  29. [29]

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

    work page doi:10.3847/1538-4365/aaef2f 2019

  30. [30]

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

    work page doi:10.1088/0004-637x/724/2/1218 2010

  31. [31]

    W., & Toriumi, S

    Reep, J. W., & Toriumi, S. 2017, ApJ, 851, 4, doi: 10.3847/1538-4357/aa96fe

    work page doi:10.3847/1538-4357/aa96fe 2017

  32. [32]

    2000, ApJ, 540, 583, doi: 10.1086/309303

    Sammis, I., Tang, F., & Zirin, H. 2000, ApJ, 540, 583, doi: 10.1086/309303

    work page doi:10.1086/309303 2000

  33. [33]

    2018, SoPh, 293, 16, doi: 10.1007/s11207-017-1235-8

    Sarkar, R., & Srivastava, N. 2018, SoPh, 293, 16, doi: 10.1007/s11207-017-1235-8

    work page doi:10.1007/s11207-017-1235-8 2018

  34. [34]

    Sarkar, R., Srivastava, N., & Veronig, A. M. 2019, The Astrophysical Journal Letters, 885, L17, doi: 10.3847/2041-8213/ab4da2

    work page doi:10.3847/2041-8213/ab4da2 2019

  35. [35]

    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

  36. [36]

    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

    work page doi:10.12942/lrsp-2011-6 2011

  37. [37]

    2000, Journal of Atmospheric and Solar-Terrestrial Physics, 62, 1223, doi: 10.1016/S1364-6826(00)00074-2

    Siscoe, G. 2000, Journal of Atmospheric and Solar-Terrestrial Physics, 62, 1223, doi: 10.1016/S1364-6826(00)00074-2

    work page doi:10.1016/s1364-6826(00)00074-2 2000

  38. [38]

    Sturrock, P. A. 1966, Nature, 211, 695, doi: 10.1038/211695a0

    work page doi:10.1038/211695a0 1966

  39. [39]

    J., & Harvey, J

    Sudol, J. J., & Harvey, J. W. 2005, ApJ, 635, 647, doi: 10.1086/497361

    work page doi:10.1086/497361 2005

  40. [40]

    2017, ApJ, 839, 67, doi: 10.3847/1538-4357/aa69c1 Eruptive and confined flares 19

    Chen, R. 2017, ApJ, 839, 67, doi: 10.3847/1538-4357/aa69c1 Eruptive and confined flares 19

    work page doi:10.3847/1538-4357/aa69c1 2017

  41. [41]

    T., Liu, Y., et al

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

    work page doi:10.1088/0004-637x/748/2/77 2012

  42. [42]

    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

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

  43. [43]

    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

    work page doi:10.1007/s41116-019-0019-7 2019

  44. [44]

    P., Malanushenko, O

    Turmon, M., Jones, H. P., Malanushenko, O. V., & Pap, J. M. 2010, SoPh, 262, 277, doi: 10.1007/s11207-009-9490-y

    work page doi:10.1007/s11207-009-9490-y 2010

  45. [45]

    Doddamani, V. H. 2022, ApJ, 927, 86, doi: 10.3847/1538-4357/ac4d8c

    work page doi:10.3847/1538-4357/ac4d8c 2022

  46. [46]

    2006, ApJ, 649, 490, doi: 10.1086/506320

    Wang, H. 2006, ApJ, 649, 490, doi: 10.1086/506320

    work page doi:10.1086/506320 2006

  47. [47]

    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

    work page doi:10.1088/1674-4527/15/2/001 2015

  48. [48]

    2012a, ApJL, 745, L17, doi: 10.1088/2041-8205/745/2/L17

    Wang, S., Liu, C., Liu, R., et al. 2012a, ApJL, 745, L17, doi: 10.1088/2041-8205/745/2/L17

    work page doi:10.1088/2041-8205/745/2/l17 2041

  49. [49]

    2012b, ApJL, 757, L5, doi: 10.1088/2041-8205/757/1/L5

    Wang, S., Liu, C., & Wang, H. 2012b, ApJL, 757, L5, doi: 10.1088/2041-8205/757/1/L5

    work page doi:10.1088/2041-8205/757/1/l5 2041

  50. [50]

    F., & Howard, T

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

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

  51. [51]

    S., Melrose, D

    Wheatland, M. S., Melrose, D. B., & Mastrano, A. 2018, ApJ, 864, 159, doi: 10.3847/1538-4357/aad8ae

    work page doi:10.3847/1538-4357/aad8ae 2018

  52. [52]

    K., & Solanki, S

    Wiegelmann, T., Thalmann, J. K., & Solanki, S. K. 2014, A&A Rv, 22, 78, doi: 10.1007/s00159-014-0078-7

    work page doi:10.1007/s00159-014-0078-7 2014

  53. [53]

    Yadav, R., & Kazachenko, M. D. 2023, ApJ, 944, 215, doi: 10.3847/1538-4357/acaa9d

    work page doi:10.3847/1538-4357/acaa9d 2023

  54. [54]

    Yang, Y.-H., Hsieh, M.-S., Yu, H.-S., & Chen, P. F. 2017, ApJ, 834, 150, doi: 10.3847/1538-4357/834/2/150

    work page doi:10.3847/1538-4357/834/2/150 2017

  55. [55]

    2009, in Universal Heliophysical Processes, ed

    Yashiro, S., & Gopalswamy, N. 2009, in Universal Heliophysical Processes, ed. N. Gopalswamy & D. F

    work page 2009

  56. [56]

    257, 233–243, doi: 10.1017/S1743921309029342

    Webb, Vol. 257, 233–243, doi: 10.1017/S1743921309029342

    work page doi:10.1017/s1743921309029342

  57. [57]

    Howard, R. A. 2005, Journal of Geophysical Research (Space Physics), 110, A12S05, doi: 10.1029/2005JA011151

    work page doi:10.1029/2005ja011151 2005

  58. [58]

    2012, NRIAG Journal of Astronomy and Geophysics, 1, 172, doi: 10.1016/j.nrjag.2012.12.014

    Youssef, M. 2012, NRIAG Journal of Astronomy and Geophysics, 1, 172, doi: 10.1016/j.nrjag.2012.12.014

    work page doi:10.1016/j.nrjag.2012.12.014 2012

  59. [59]

    White, S. M. 2001, ApJ, 559, 452, doi: 10.1086/322405

    work page doi:10.1086/322405 2001

  60. [60]

    Zirin, H., & Liggett, M. A. 1987, SoPh, 113, 267, doi: 10.1007/BF00147707

    work page doi:10.1007/bf00147707 1987