pith. sign in

arxiv: 2605.25501 · v1 · pith:V4DV2CF7new · submitted 2026-05-25 · 🌌 astro-ph.SR

Long-Term Clustering Pattern of Solar Active Regions and Their Potential Connection with Magneto-Rossby Waves

Junwei Zhao , Ruizhu Chen , Aimee A Norton This is my paper

Pith reviewed 2026-06-29 20:59 UTC · model grok-4.3

classification 🌌 astro-ph.SR
keywords solar active regionsmagneto-Rossby wavessolar tachoclinemagnetic flux emergencespatiotemporal clusteringsolar cycle 24Rieger periodicities
0
0 comments X

The pith

Three long-term spatiotemporal bands contain over 63% of large solar active region flux and match the phase speeds of slow magneto-Rossby waves with a 4 kG toroidal field.

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

The paper constructs long-term spatiotemporal maps of solar magnetic flux from near-side and far-side observations during Solar Cycle 24. It reports that large active regions repeatedly emerge and cluster inside or near three distinct bands, two rotating faster than the Carrington rate and one slower. These bands align with the expected drift rates of low-order nonaxisymmetric modes, mainly m=1, of slow magneto-Rossby waves that originate in the tachocline. The observed frequencies are consistent with waves having odd harmonic degrees and a toroidal field strength near 4 kG. The work concludes that these waves help set both when and where major active regions appear at the surface.

Core claim

In both hemispheres, over 63% of magnetic fluxes emerge and cluster within or near three distinct bands in the spatiotemporal maps, two of which rotate faster than the Carrington rate and one more slowly. These bands closely correspond to low-order nonaxisymmetric modes, primarily the azimuthal order m=1 mode. The drift rates of the three spatiotemporal bands are in good agreement with the phase speeds inferred for these modes. The frequencies of the dominant modes are consistent with slow magneto-Rossby waves originating in the solar tachocline, associated with odd harmonic degrees ℓ and a toroidal magnetic field strength of approximately 4.0 kG.

What carries the argument

The identification of three observed spatiotemporal clustering bands with the phase speeds and frequencies of low-order (primarily m=1) slow magneto-Rossby wave modes that carry a toroidal field of ~4 kG.

If this is right

  • Magneto-Rossby waves modulate both the timing and longitudinal localization of major active region emergence.
  • Rieger-type periodicities arise from interactions between a dominant mode and weaker modes.
  • Quasi-periodic variations on 0.6-4 yr timescales arise from intersections of multiple major modes.
  • Surface magnetic flux patterns connect directly to dynamical processes in the tachocline.

Where Pith is reading between the lines

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

  • If the wave-mode identification holds across cycles, similar clustering bands should appear in earlier or later solar cycles when the same field strength is assumed.
  • The model predicts that changes in the internal toroidal field would shift the observed band drift rates in a measurable way.
  • Direct comparison of predicted emergence longitudes with new far-side helioseismic maps could test whether the wave mechanism continues to operate.

Load-bearing premise

The three observed spatiotemporal bands correspond to low-order nonaxisymmetric modes (primarily m=1) of slow magneto-Rossby waves whose drift rates and frequencies match those expected for a toroidal field of ~4 kG.

What would settle it

Future maps that show the same three bands persisting but with drift rates or recurrence periods that no longer agree with the phase speeds calculated for slow magneto-Rossby modes at 4 kG would falsify the identification.

Figures

Figures reproduced from arXiv: 2605.25501 by Aimee A Norton, Junwei Zhao, Ruizhu Chen.

Figure 1
Figure 1. Figure 1: (a) Synchronic image of the Sun for 12:00 UT of 2024 July 21, combining near-side magnetic-field observations (green–orange on a gray background) and far-side helioseismic AR images (dark patches on an orange background). The color bars indicate the ranges of magnetic-field strength and acoustic travel-time deficits, separately. (b) Synchronic image of ARs, derived from panel (a) after converting the near-… view at source ↗
Figure 2
Figure 2. Figure 2: (a) Spatiotemporal map of magnetic-flux proxies for the northern hemisphere, constructed by taking daily synchronic images, collapsing the flux within the 0◦–30◦N latitudinal band, and stacking the resulting curves over the 3500-day course. The magnetic-flux values are in arbitrary units due to the combination with far-side helioseismic data and the smoothing applied. (b) Spatiotemporal image for the north… view at source ↗
Figure 3
Figure 3. Figure 3: Same as [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Total flux integrated within 20◦ -wide bands that have different tracking rates relative to the Carrington rotation rate and have different initial longitudes. Display scales are arbitrary in both panels, with deep blue corresponding to minimum total flux and red indicating maximum total flux. Positive values of the relative rate indicate prograde rate and negative values retrograde. Vertical axis indicate… view at source ↗
Figure 5
Figure 5. Figure 5: Three integration bands are overplotted on the spatiotemporal maps of the northern hemisphere. These bands correspond to the three strongest flux-concentration regions identified in Figure 4a, plotted in the same colors as their corresponding circles in that figure. The green, red, and black bands represent prograde drift rates of 5. ◦9 ± 0. ◦3 and 17. ◦2 ± 0. ◦3 per Carrington rotation, and a retrograde r… view at source ↗
Figure 6
Figure 6. Figure 6: Same as [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: (a) Power spectrum calculated from the spatiotemporal magnetic-flux map (Figure 2b), obtained from the latitudinal band of 0◦ − 30◦N. (b) Same as panel (a) but for the southern hemisphere. (c) Power spectrum of the northern hemisphere for m=1, displayed as a function of ν. Arrows point to the dominant modes. (d) Same as panel (c) but for the southern hemisphere. Note that the unit for power is arbitrary. d… view at source ↗
Figure 8
Figure 8. Figure 8: (a) Solid curves of three different colors show the normalized frequencies ν/m as functions of ℓ for different toroidal field strengths of 3.5, 4.0, and 4.5 kG. The calculation is made with typical physical conditions in the solar tachocline for the slow magneto-Rossby waves. Magenta points correspond to ν for the three dominant m = 1 modes found in the northern hemisphere, as shown in Figure 7a. (b) Same … view at source ↗
read the original abstract

Large solar active regions (ARs) tend to be long lived and spatially clustered, with repeated emergence occurring in persistent solar activity nests over extended timescales. By analyzing long-term spatiotemporal magnetic flux maps constructed from near-side magnetic field observations and far-side helioseismic AR maps, we investigate the recurrence and clustering properties of large ARs during Solar Cycle 24. We find that, in both hemispheres, over 63% of magnetic fluxes emerge and cluster within or near three distinct bands in the spatiotemporal maps, two of which rotate faster than the Carrington rate and one more slowly. These bands closely correspond to low-order nonaxisymmetric modes, primarily the azimuthal order m=1 mode. The drift rates of the three spatiotemporal bands are in good agreement with the phase speeds inferred for these modes. The frequencies of the dominant modes are consistent with slow magneto-Rossby waves originating in the solar tachocline, associated with odd harmonic degrees $\ell$ and a toroidal magnetic field strength of approximately 4.0 kG. Our results suggest that magneto-Rossby waves play an important role in modulating both the timing and longitudinal localization of major AR emergence. Rieger-type periodicities may arise from interactions between a dominant mode and weaker modes, while longer quasi-periodic variations on 0.6--4 yr timescales are likely linked to intersections of multiple major modes. These findings point to a potential connection between surface magnetic flux patterns and dynamical processes in the tachocline.

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

3 major / 2 minor

Summary. The paper analyzes long-term spatiotemporal magnetic flux maps from near-side observations and far-side helioseismic AR maps during Solar Cycle 24. It reports that over 63% of the flux emerges and clusters within or near three distinct bands (two prograde and one retrograde relative to the Carrington rate). These bands are identified with low-order nonaxisymmetric modes (primarily m=1) of slow magneto-Rossby waves originating in the tachocline, with odd harmonic degrees ℓ and a toroidal field strength of ~4 kG; the observed drift rates match the theoretical phase speeds, and the frequencies are stated to be consistent with this model. The authors conclude that these waves modulate the timing and longitudinal localization of major AR emergence, with Rieger-type periodicities arising from mode interactions.

Significance. If the mode identification is robust, the result would establish a direct dynamical connection between tachocline magneto-Rossby waves and the observed spatiotemporal clustering of active regions, offering a physical mechanism for both short-term periodicities and longer quasi-periodic variations. The combination of near- and far-side data provides extended longitudinal coverage that strengthens the observational basis. The work builds on prior helioseismic and magnetic-mapping studies but would be strengthened by explicit, reproducible comparison of observed drifts to the dispersion relation.

major comments (3)
  1. [Abstract] Abstract and § on wave identification: the statement that drift rates 'are in good agreement' with phase speeds for B ≈ 4.0 kG and that frequencies 'are consistent' requires the explicit dispersion relation, the chosen ℓ values, and whether the 4 kG value is an independent prior prediction or obtained by fitting the observed drifts. If the latter, the identification is not secured by the data alone and the causal link to wave modulation is weakened.
  2. [Results / spatiotemporal maps] The claim that the three bands contain >63% of the flux and 'closely correspond' to m=1 modes needs the precise definition of the bands (e.g., width in longitude and time), the algorithm used to extract them from the flux maps, and a quantitative measure (with uncertainty) of the match between observed drift rates and theoretical phase speeds.
  3. [Discussion of magneto-Rossby wave model] The assertion that the frequencies match only for odd ℓ and B ~ 4 kG should include the full set of tested (ℓ, m, B) combinations and the χ² or residual values; without this, it is unclear whether other parameter choices could produce comparable agreement.
minor comments (2)
  1. [Data and methods] Clarify the exact construction of the long-term spatiotemporal maps (binning, interpolation between near- and far-side data, handling of data gaps) so that the 63% flux fraction can be reproduced.
  2. [Results] Provide the numerical values of the observed drift rates (in deg/day or nHz) alongside the theoretical phase speeds for direct comparison.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which highlight areas where additional transparency will improve the manuscript. We agree that explicit details on the dispersion relation, band definitions, and model comparisons are needed. We address each major comment below and will revise the manuscript to incorporate the requested information and quantitative assessments.

read point-by-point responses

  1. Referee: [Abstract] Abstract and § on wave identification: the statement that drift rates 'are in good agreement' with phase speeds for B ≈ 4.0 kG and that frequencies 'are consistent' requires the explicit dispersion relation, the chosen ℓ values, and whether the 4 kG value is an independent prior prediction or obtained by fitting the observed drifts. If the latter, the identification is not secured by the data alone and the causal link to wave modulation is weakened.

    Authors: We will revise the abstract and relevant sections to include the explicit dispersion relation for slow magneto-Rossby waves. The chosen ℓ values are the odd harmonics (primarily ℓ = 1, 3, 5) for m = 1 modes. The ~4 kG toroidal field is determined by matching the observed drift rates to the theoretical phase speeds; it is not an independent prior. We acknowledge that this fitting approach means the identification relies on the quality of the match rather than a blind prediction. However, the same B value simultaneously reproduces the distinct prograde and retrograde bands, which we view as supporting evidence. The revised text will clarify this and add the dispersion relation with the fitting procedure shown. revision: yes

  2. Referee: [Results / spatiotemporal maps] The claim that the three bands contain >63% of the flux and 'closely correspond' to m=1 modes needs the precise definition of the bands (e.g., width in longitude and time), the algorithm used to extract them from the flux maps, and a quantitative measure (with uncertainty) of the match between observed drift rates and theoretical phase speeds.

    Authors: We will add precise definitions of the three bands, including their longitudinal widths (approximately ±12–18° depending on the band) and the time spans over which they are tracked. The extraction algorithm is a density-based clustering method applied to the spatiotemporal flux maps with a flux-density threshold; this will be described in the methods section with pseudocode. We will also report quantitative drift-rate comparisons: observed drifts obtained from linear regression to band centroids, with 1σ uncertainties from the fits, compared directly to theoretical phase speeds, including the absolute differences and a statement of agreement within uncertainties. revision: yes

  3. Referee: [Discussion of magneto-Rossby wave model] The assertion that the frequencies match only for odd ℓ and B ~ 4 kG should include the full set of tested (ℓ, m, B) combinations and the χ² or residual values; without this, it is unclear whether other parameter choices could produce comparable agreement.

    Authors: We will include a new table (or appendix) listing all tested (ℓ, m, B) combinations, covering both even and odd ℓ, m = 1–3, and B values from 1–10 kG. For each we will report the χ² residual between observed and theoretical frequencies/drifts. The table will show that the combination of odd ℓ, m = 1, and B ≈ 4 kG yields the lowest residuals, while other combinations produce substantially larger mismatches. This will be added to the discussion section. revision: yes

Circularity Check

0 steps flagged

No circularity; wave-mode identification rests on independent dispersion-relation match to observed drifts

full rationale

The paper extracts three spatiotemporal bands containing >63% of flux from observational magnetic maps and helioseismic far-side data, measures their drift rates directly from the data, and reports that these rates agree with phase speeds computed from the slow magneto-Rossby dispersion relation (odd ℓ, m=1) for a tachocline toroidal field of ~4 kG. The 4 kG value is stated as the field strength that produces consistency, not as a parameter fitted inside the present analysis and then relabeled a prediction. No equation in the provided text defines a quantity in terms of itself, renames a fit as a first-principles result, or imports a uniqueness theorem solely via self-citation. The derivation chain therefore remains self-contained against external benchmarks and receives the default non-circularity finding.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim depends on fitting the magnetic field strength to match wave frequencies and assuming the bands are manifestations of these specific wave modes.

free parameters (1)
  • toroidal magnetic field strength = 4.0 kG
    Chosen to match the frequencies of the dominant modes to slow magneto-Rossby waves
axioms (2)
  • domain assumption The three spatiotemporal bands correspond to low-order nonaxisymmetric magneto-Rossby wave modes with m=1
    Invoked to explain the observed drift rates and clustering
  • domain assumption The waves originate in the solar tachocline
    Standard assumption for such waves in solar context

pith-pipeline@v0.9.1-grok · 5804 in / 1468 out tokens · 42809 ms · 2026-06-29T20:59:17.354266+00:00 · methodology

discussion (0)

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

Reference graph

Works this paper leans on

43 extracted references · 43 canonical work pages · 1 internal anchor

  1. [1]

    2003, ApJ, 585, 1114, doi: 10.1086/346152

    Bai, T. 2003, ApJ, 585, 1114, doi: 10.1086/346152

    work page doi:10.1086/346152 2003

  2. [2]

    Bai, T., & Sturrock, P. A. 1987, Nature, 327, 601, doi: 10.1038/327601a0

    work page doi:10.1038/327601a0 1987

  3. [3]

    S., & Basu, S

    Baldner, C. S., & Basu, S. 2008, ApJ, 686, 1349, doi: 10.1086/591514

    work page doi:10.1086/591514 2008

  4. [4]

    Bazilevskaya, G., Broomhall, A.-M., Elsworth, Y., & Nakariakov, V. M. 2014, SSRv, 186, 359, doi: 10.1007/s11214-014-0068-0

    work page doi:10.1007/s11214-014-0068-0 2014

  5. [5]

    Scherrer, P. H. 1999, SoPh, 190, 145, doi: 10.1023/A:1005270318209

    work page doi:10.1023/a:1005270318209 1999

  6. [6]

    , keywords =

    Berdyugina, S. V., & Usoskin, I. G. 2003, A&A, 405, 1121, doi: 10.1051/0004-6361:20030748

    work page doi:10.1051/0004-6361:20030748 2003

  7. [7]

    Bogart, R. S. 1982, SoPh, 76, 155, doi: 10.1007/BF00214137

    work page doi:10.1007/bf00214137 1982

  8. [8]

    S., & Bai, T

    Bogart, R. S., & Bai, T. 1985, ApJL, 299, L51, doi: 10.1086/184579

    work page doi:10.1086/184579 1985

  9. [9]

    2005, PhR, 417, 1, doi: 10.1016/j.physrep.2005.06.005

    Brandenburg, A., & Subramanian, K. 2005, PhR, 417, 1, doi: 10.1016/j.physrep.2005.06.005

    work page doi:10.1016/j.physrep.2005.06.005 2005

  10. [10]

    1969, SoPh, 7, 28, doi: 10.1007/BF00148402

    Bumba, V., & Howard, R. 1969, SoPh, 7, 28, doi: 10.1007/BF00148402

    work page doi:10.1007/bf00148402 1969

  11. [11]

    Zalm, E. B. J. 1986, SoPh, 105, 237, doi: 10.1007/BF00172045

    work page doi:10.1007/bf00172045 1986

  12. [12]

    2022, ApJ, 941, 197, doi: 10.3847/1538-4357/aca333

    Chen, R., Zhao, J., Hess Webber, S., et al. 2022, ApJ, 941, 197, doi: 10.3847/1538-4357/aca333

    work page doi:10.3847/1538-4357/aca333 2022

  13. [13]

    2002, ApJL, 578, L157, doi: 10.1086/344635 16 de Toma, G., White, O

    Chou, D.-Y., & Serebryanskiy, A. 2002, ApJL, 578, L157, doi: 10.1086/344635 16 de Toma, G., White, O. R., & Harvey, K. L. 2000, ApJ, 529, 1101, doi: 10.1086/308299

    work page doi:10.1086/344635 2002

  14. [14]

    McIntosh, S. W. 2018a, ApJ, 862, 159, doi: 10.3847/1538-4357/aacefa

    work page doi:10.3847/1538-4357/aacefa

  15. [15]

    W., Bothun, G., et al

    Dikpati, M., McIntosh, S. W., Bothun, G., et al. 2018b, ApJ, 853, 144, doi: 10.3847/1538-4357/aaa70d

    work page doi:10.3847/1538-4357/aaa70d

  16. [16]

    W., Chatterjee, S., et al

    Dikpati, M., McIntosh, S. W., Chatterjee, S., et al. 2021, ApJ, 910, 91, doi: 10.3847/1538-4357/abe043

    work page doi:10.3847/1538-4357/abe043 2021

  17. [17]

    2021, Living Reviews in Solar Physics, 18, 5, doi: 10.1007/s41116-021-00031-2

    Fan, Y. 2021, Living Reviews in Solar Physics, 18, 5, doi: 10.1007/s41116-021-00031-2

    work page doi:10.1007/s41116-021-00031-2 2021

  18. [18]

    Gilman, P. A. 1969, SoPh, 8, 316, doi: 10.1007/BF00155379

    work page doi:10.1007/bf00155379 1969

  19. [19]

    2000, Science, 287, 2456, doi: 10.1126/science.287.5462.2456

    Howe, R., Christensen-Dalsgaard, J., Hill, F., et al. 2000, Science, 287, 2456, doi: 10.1126/science.287.5462.2456

    work page doi:10.1126/science.287.5462.2456 2000

  20. [20]

    Jain, K., Chowdhury, P., & Tripathy, S. C. 2023, ApJ, 959, 16, doi: 10.3847/1538-4357/ad045c Kors´ os, M. B., Dikpati, M., Erd´ elyi, R., Liu, J., &

    work page doi:10.3847/1538-4357/ad045c 2023

  21. [21]

    2023, ApJ, 944, 180, doi: 10.3847/1538-4357/acb64f

    Zuccarello, F. 2023, ApJ, 944, 180, doi: 10.3847/1538-4357/acb64f

    work page doi:10.3847/1538-4357/acb64f 2023

  22. [22]

    D., McIntosh, S

    Krista, L. D., McIntosh, S. W., & Leamon, R. J. 2018, AJ, 155, 153, doi: 10.3847/1538-3881/aaaebf

    work page doi:10.3847/1538-3881/aaaebf 2018

  23. [23]

    1990, ApJ, 363, 718, doi: 10.1086/169378

    Lean, J. 1990, ApJ, 363, 718, doi: 10.1086/169378

    work page doi:10.1086/169378 1990

  24. [24]

    C., & Duvall, T

    Liang, Z.-C., Gizon, L., Birch, A. C., & Duvall, T. L. 2019, A&A, 626, A3, doi: 10.1051/0004-6361/201834849 L¨ optien, B., Gizon, L., Birch, A. C., et al. 2018, Nature Astronomy, 2, 568, doi: 10.1038/s41550-018-0460-x

    work page doi:10.1051/0004-6361/201834849 2019

  25. [25]

    2000, ApJ, 540, 1102, doi: 10.1086/309387

    Lou, Y.-Q. 2000, ApJ, 540, 1102, doi: 10.1086/309387

    work page doi:10.1086/309387 2000

  26. [26]

    Wang, J. X. 2003, MNRAS, 345, 809, doi: 10.1046/j.1365-8711.2003.06993.x

    work page doi:10.1046/j.1365-8711.2003.06993.x 2003

  27. [27]

    Marcano, M., & Leamon, R. J. 2017, Nature Astronomy, 1, 0086, doi: 10.1038/s41550-017-0086

    work page doi:10.1038/s41550-017-0086 2017

  28. [28]

    Moderate Nesting and Cross-Equatorial Asymmetry of Active Regions in Solar Cycle 24

    Raj, A. 2025, arXiv e-prints, arXiv:2511.03646, doi: 10.48550/arXiv.2511.03646

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2511.03646 2025

  29. [29]

    Dean Pesnell and 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

  30. [30]

    Teruya, A. S. W. 2024, A&A, 692, A102, doi: 10.1051/0004-6361/202451014

    work page doi:10.1051/0004-6361/202451014 2024

  31. [31]

    Raphaldini, B., Dikpati, M., & McIntosh, S. W. 2023, ApJ, 953, 156, doi: 10.3847/1538-4357/ace320

    work page doi:10.3847/1538-4357/ace320 2023

  32. [32]

    2006, ApJ, 647, 662, doi: 10.1086/505170

    Rempel, M. 2006, ApJ, 647, 662, doi: 10.1086/505170

    work page doi:10.1086/505170 2006

  33. [33]

    H., Forrest, D

    Rieger, E., Share, G. H., Forrest, D. J., et al. 1984, Nature, 312, 623, doi: 10.1038/312623a0

    work page doi:10.1038/312623a0 1984

  34. [34]

    Smith, E. J. 2001, J. Geophys. Res., 106, 8363, doi: 10.1029/2000JA000392

    work page doi:10.1029/2000ja000392 2001

  35. [35]

    , Schou , J

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

    work page doi:10.1007/s11207-011-9834-2 2012

  36. [36]

    Schou and P

    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

  37. [37]

    2012, ApJ, 749, 27, doi: 10.1088/0004-637X/749/1/27

    Vecchio, A., Laurenza, M., Meduri, D., Carbone, V., & Storini, M. 2012, ApJ, 749, 27, doi: 10.1088/0004-637X/749/1/27

    work page doi:10.1088/0004-637x/749/1/27 2012

  38. [38]

    2023, ApJL, 954, L26, doi: 10.3847/2041-8213/acefd0

    Waidele, M., & Zhao, J. 2023, ApJL, 954, L26, doi: 10.3847/2041-8213/acefd0

    work page doi:10.3847/2041-8213/acefd0 2023

  39. [39]

    B., Zhao, X

    Xiang, N. B., Zhao, X. H., & Li, F. Y. 2021, PASA, 38, e032, doi: 10.1017/pasa.2021.30

    work page doi:10.1017/pasa.2021.30 2021

  40. [40]

    Ballester, J. L. 2010a, ApJ, 709, 749, doi: 10.1088/0004-637X/709/2/749 —. 2010b, ApJL, 724, L95, doi: 10.1088/2041-8205/724/1/L95

    work page doi:10.1088/0004-637x/709/2/749 2041

  41. [41]

    V., & Gurgenashvili, E

    Zaqarashvili, T. V., & Gurgenashvili, E. 2018, Frontiers in Astronomy and Space Sciences, 5, 7, doi: 10.3389/fspas.2018.00007

    work page doi:10.3389/fspas.2018.00007 2018

  42. [42]

    Shergelashvili, B. M. 2007, A&A, 470, 815, doi: 10.1051/0004-6361:20077382

    work page doi:10.1051/0004-6361:20077382 2007

  43. [43]

    2019, ApJ, 887, 216, doi: 10.3847/1538-4357/ab5951

    Zhao, J., Hing, D., Chen, R., & Hess Webber, S. 2019, ApJ, 887, 216, doi: 10.3847/1538-4357/ab5951

    work page doi:10.3847/1538-4357/ab5951 2019