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The Sun at millimeter wavelengths V. Magnetohydrodynamic waves in a fibrillar structure

T0 review · 4 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read ALMA observations of a long-lived dark fibril show magnetohydrodynamic oscillations in brightness temperature, transverse displacement, and width, with median periods of about 240, 225, and 272 seconds.

desk verdict First ALMA dark-fibril wave detection is plausible, but the mode identification rests on unresolved bundles and phase lags too small to measure reliably. read the letter →

arxiv 2411.14190 v1 pith:6QXN4XKG submitted 2024-11-21 astro-ph.SR

Maryam Saberi , Shahin Jafarzadeh , Sven Wedemeyer , Ricardo Gafeira , Mikolaj Szydlarski , David Jess , Marco Stangalini This is my paper · ORCID
classification astro-ph.SR
keywords magnetohydrodynamicwavessolarchromospheredarkfibrilsALMABand6kinkmodessausagewaveletanalysis
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

This paper reports the detection of magnetohydrodynamic (MHD) waves in a long-lived dark fibril, a thread-like magnetic structure in the solar chromosphere, using ALMA Band 6 observations at 1.25 mm with a 2 second cadence. Brightness temperature, transverse displacement, and width all oscillate at periods of roughly three to five minutes, with median values of 240, 225, and 272 seconds respectively. Wavelet cross-spectra between seven artificial slits placed across the fibril show both standing and propagating waves, with the phase-lag distributions dominated by in-phase and anti-phase relationships. The authors interpret the displacement oscillations as MHD kink modes and the width oscillations as sausage modes. The wider point is that ALMA can sample dynamic dark fibrillar structures well enough to support wave-mode identification, despite earlier doubts about contrast and resolution.

What carries the argument

The central objects are the dark fibril itself and the seven artificial slits placed perpendicular to its axis, spaced 510 km apart. Gaussian fits along each slit yield the fibril's position (transverse displacement), the full width at half maximum (which represents the fibril's width), and the brightness temperature at the centroid. The load-bearing analysis is a Morlet wavelet and cross-wavelet decomposition: periods come from the wavelet power spectra, and the phase lag between consecutive slits at the same period is converted into a travel time $\tau = \phi P/2\pi$ and hence a phase speed over the known 510 km slit separation. In-phase and anti-phase lags identify standing waves, while intermediate lags identify propagation.

What would settle it

A high-resolution co-observation that resolves the fibril into separate threads would settle whether the cross-slit phase lags describe one waveguide, because the lags would break apart if the structure is a blend. A long time series showing stable $180^\circ$ phase jumps at fixed nodes along the fibril would directly confirm the standing-wave interpretation.

Watch

Extended reading notes

Core claim

On the authors' own terms, the discovery is that a single long-lived dark fibril seen in ALMA Band 6 continuum exhibits coherent oscillations in brightness temperature, horizontal displacement, and width at multiple locations along its length, with median periods of $240 \pm 114$ s, $225 \pm 102$ s, and $272 \pm 118$ s. The phase relationships between consecutive slits are predominantly $0^\circ$ and $180^\circ$, which the authors read as a prevalence of standing waves, while the remaining phase angles imply a population of oppositely propagating waves with median absolute phase speeds of $74 \pm 204$, $52 \pm 197$, and $28 \pm 254$ km/s for the three observables. In the standard MHD wave classification, the transverse displacement is consistent with kink modes and the width pulsations with sausage modes. The authors therefore conclude that ALMA, despite prior doubts, can effectively sample fibrillar structures in the upper chromosphere and provide a new window on wave dynamics there.

Load-bearing premise

The interpretation assumes the dark feature is a single magnetic tube, so the phase delays measured between slits are travel times of waves along that one tube rather than a mixture of unresolved threads or artifacts from the interpolation across calibration gaps.

Editorial extensions

If this is right

  • ALMA's 2 s cadence can resolve wave periods of a few minutes in dark fibrillar structures, opening a new diagnostic for the upper chromosphere.
  • Dark fibrils support both standing and propagating waves, with periods of 200 to 300 s, extending earlier MHD wave detections in bright structures to different structures and heights.
  • The dominance of in-phase and anti-phase relations implies standing waves are at least as important as propagating waves in these upper-chromospheric waveguides, so energy transport estimates must account for both.
  • Transverse displacement oscillations (kink modes) and width oscillations (sausage modes) coexist in the same structure, meaning both transverse and compressional energy channels are active.
  • The inferred phase speeds (median absolute values of 28 to 74 km/s) are consistent with slow-mode or kink speeds in upper-chromospheric fibrils and can serve as input for future mode-identification models.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the dark feature is actually an unresolved bundle of threads, the reported phase speeds would be averages over several waveguides; resolving the threads observationally could split the broad speed distributions into distinct components.
  • A standing kink and sausage mode pair with known periods and phase relations could be used to estimate the Alfvén speed and hence the magnetic field strength in the upper chromosphere, which is a concrete target for future ALMA campaigns.
  • Using ALMA sub-bands or multi-band co-observations would add height discrimination, because the same fibril seen at different formation heights should show a phase offset if waves propagate upward.
  • The coexistence of oppositely propagating waves hints that some apparent standing patterns may be transient interference rather than true eigenmodes; a longer continuous time series would distinguish sustained standing modes from beating of counter-propagating packets.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The paper analyzes a 2-s cadence ALMA Band 6 time series of a dark fibrillar structure in a plage region. Using seven artificial slits perpendicular to the fibril, the authors measure brightness temperature, horizontal displacement (Gaussian centroid), and width (FWHM) from Gaussian fits, and apply Morlet wavelet analysis to each time series. They report median oscillation periods of 240 +/- 114 s (brightness temperature), 225 +/- 102 s (displacement), and 272 +/- 118 s (width). Wavelet cross-power spectra between consecutive slits yield phase lags that are predominantly in-phase/anti-phase, interpreted as standing waves, with a minority of other phase lags interpreted as oppositely propagating waves with median absolute phase speeds of 74 +/- 204, 52 +/- 197, and 28 +/- 254 km/s. The authors identify the transverse displacement and width oscillations as kink and sausage modes, respectively, and conclude that ALMA can effectively sample dynamic dark fibrils.

Significance. If the period detections are robust, this is one of the first studies of MHD waves in dark fibrils with ALMA, offering a new observing window into upper-chromospheric wave dynamics. The paper's explicit use of 95% confidence contours, cone-of-influence exclusion, and detrending/apodization is commendable, and the authors are appropriately cautious in describing mode identification as 'likely' or 'suggesting.' However, the mode identification and phase-speed estimates rest on the assumption that the tracked object is a single coherent waveguide, which the authors themselves question in Section 3, and the phase-speed distributions have very large dispersions. Thus the significance is high if the assumptions hold, but the current evidence for the specific MHD modes is not yet strong.

major comments (4)
  1. [Section 3, first paragraph] The paper's own statement that 'we find a few extended dark structures, likely due to unresolved individual fibrils' directly undercuts the central assumption that the tracked feature is a single coherent waveguide. If the 'fibril' is a blend of several unresolved threads, the Gaussian centroid and FWHM derived in Section 3.1 will fluctuate as the relative intensities of the threads vary, producing apparent transverse and width oscillations and cross-slit phase lags that are not due to MHD wave propagation. The authors should test this possibility explicitly, for example by fitting a two-component Gaussian model, by comparing the centroid and FWHM variations with total intensity fluctuations, or by checking whether the oscillations are coherent across more than two consecutive slits. Without such a test, the mode identifications in Section 4 (kink and sausage) are not supported.
  2. [Section 3.2.2, Eq. (1), Table 2] For the reported median phase speeds (28–74 km/s) and periods (225–272 s), the expected phase lag between adjacent slits (510 km apart) is only about 0.07–0.20 rad (4°–12°). The wavelet cross-spectrum phase uncertainty for a 1568-s series with four linearly interpolated calibration gaps is not quantified and is likely comparable to or larger than these small lags. The very large standard deviations in Table 2 (197–254 km/s, several times the medians) suggest that the phase measurements are noise-dominated. The authors should provide an estimate of the phase uncertainty (e.g., via bootstrap or Monte Carlo) and determine whether the observed phase-lag distribution is statistically distinguishable from a uniform (noise) distribution.
  3. [Section 2 (data reduction), Section 3.2] The four calibration breaks (each 1.75–2.25 min) were linearly interpolated before the wavelet analysis. Interpolation across gaps can inject spurious power and phase structure at periods comparable to the gap length (105–135 s), a range where the width period distribution in Fig. 4 shows secondary peaks. The robustness of the period and phase results to this interpolation should be tested, for instance by repeating the analysis on continuous segments only or by injecting synthetic gaps into a known signal. This is particularly important because the cross-slit phase lags used for the phase-speed estimates are small.
  4. [Section 4 (Discussion)] The identification of kink and sausage modes rests on the assumption that the observed displacement and width oscillations are wave-induced and that the structure is a single flux tube. Given the unresolved-fibril concern raised in Section 3, the conclusions in Section 4 and the abstract ('suggesting the presence of both MHD kink and sausage modes') overstate the certainty of the mode identification. The authors should either provide additional evidence of a single waveguide (e.g., coherent oscillations over multiple slits or a connection to magnetic field extrapolations) or temper the mode-identification claims accordingly.
minor comments (4)
  1. [Abstract and Table 1] The abstract quotes a median period of 240 +/- 114 s for brightness temperature, while Table 1 lists a median of 241 s with a standard deviation of 114 s; please make the numbers consistent.
  2. [Eq. (1)] In Eq. (1), the phase angle phi should be explicitly defined as being in radians; currently it is only implied by the formula.
  3. [Table 2] Table 2 lists 'Right.' and 'Left.' propagation percentages, but the sign convention for positive/negative phase speeds is not defined in the text or caption; please clarify.
  4. [Section 3.2.2] The statement that phase speeds include 'both leftward-propagating and rightward-propagating waves' would benefit from an explicit definition of the propagation direction relative to the slit numbering (slit 1 to slit 7).

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: periods and phase speeds are measured quantities obtained with standard wavelet analysis, and the kink/sausage labels are conventional interpretations of independently measured fluctuations.

full rationale

The paper's derivation chain is observational: ALMA Band 6 time series are reduced, Gaussian fits provide brightness temperature, centroid position, and FWHM at seven slits along a dark fibril, and Morlet wavelet and cross-power spectra yield periods, phase lags, and phase speeds. No free parameter is fitted to the data and then presented as a prediction; no equation defines an output quantity in terms of the claimed conclusion. The propagation-time formula tau = phi P / (2 pi) with a fixed slit separation is a direct measurement relation, not a circular construct. The identification of transverse displacement oscillations as kink modes and width oscillations as sausage modes is a standard observational classification based on the definitions of those modes, rather than a derivation that assumes the conclusion. Self-citations, including the tracking method of Gafeira et al. (2017a,b), the magnetic topology work of Jafarzadeh et al. (2021), and the SoAP reduction pipeline, are methodological or contextual and are not used to force the central claim. The paper itself notes that the extended dark structures are 'likely due to unresolved individual fibrils' and that calibration breaks were linearly interpolated; these are acknowledged limitations that affect the robustness of the mode interpretation and phase-speed estimates, but they do not make the argument circular. The central results are self-contained measurements with standard external analysis tools, so the circularity burden is minimal.

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

No free parameters are fitted to the data and no new physical entities are introduced. The quantitative claims rest on domain assumptions about structural coherence, the faithfulness of Gaussian slit fits, and the meaning of wavelet phase lags, plus a standard-math assumption about the wavelet significance test.

assumptions (4)
  • domain assumption The dark structure is a single coherent magnetic waveguide whose cross-slit phase lags represent wave propagation along the fibril.
    Section 3 states the data contain 'a few extended dark structures, likely due to unresolved individual fibrils'; if the structure is a blend of threads, phase speeds lose their waveguide meaning.
  • domain assumption Centroid and FWHM from a Gaussian fit to each slit cross-section faithfully measure transverse displacement and width of the fibril.
    Section 3.1 defines these observables from Gaussian fitting; no validation against synthetic images or higher-resolution data is provided.
  • domain assumption Wavelet phase differences of 0 and ±180 between consecutive slits indicate standing waves, while intermediate phases indicate propagation.
    Section 3.2 uses this interpretation; global brightness fluctuations or noise could mimic the same phase relationships, and the paper does not test this.
  • standard math The Torrence & Compo (1998) wavelet significance test against red noise is valid for this time series.
    Section 3.2 relies on 95% confidence contours and CoI exclusion for a 1568 s series with four interpolated calibration gaps.

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Pith. "Pith review of The Sun at millimeter wavelengths V. Magnetohydrodynamic waves in a fibrillar structure." pith.science (2026). https://pith.science/paper/6QXN4XKG

@misc{pith2026241114190,
  author       = {Pith},
  title        = {Pith review of: The Sun at millimeter wavelengths V. Magnetohydrodynamic waves in a fibrillar structure},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6QXN4XKG}},
  note         = {Machine review of arXiv:2411.14190}
}
abstract

Magnetohydrodynamic (MHD) waves, playing a crucial role in transporting energy through the solar atmosphere, manifest in various chromospheric structures. Here, we investigated MHD waves in a long-lasting dark fibril using high-temporal-resolution (2~s cadence) Atacama Large Millimeter/submillimeter Array (ALMA) observations in Band 6 (centered at 1.25~mm). We detected oscillations in brightness temperature, horizontal displacement, and width at multiple locations along the fibril, with median periods and standard deviations of $240\pm114$~s, $225\pm102$~s, and $272\pm118$~s, respectively. Wavelet analysis revealed a combination of standing and propagating waves, suggesting the presence of both MHD kink and sausage modes. Less dominant than standing waves, oppositely propagating waves exhibit phase speeds (median and standard deviation of distributions) of $74\pm204$~km/s, $52\pm197$~km/s, and $28\pm254$~km/s for the three observables, respectively. This work demonstrates ALMA's capability to effectively sample dynamic fibrillar structures, despite previous doubts, and provides valuable insights into wave dynamics in the upper chromosphere.

Figures

Figures reproduced from arXiv: 2411.14190 by the authors.

Figure 1
Figure 1. Upper left panel: A brightness temperature (T [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Wavelet power spectra (left and middle columns) and wavelet cross-power spectra (right column) for oscillations in bright [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Normalized distributions of phase differences between oscillations in brightness temperature (left), horizontal displacement (middle), and width (right) at pairs of consecutive slits along the fibril. 0 100 200 300 400 500 600 700 0.0 0.2 0.4 0.6 0.8 1.0 Brightness Temperature 0 100 200 300 400 500 600 700 Period (s) 0.0 0.2 0.4 0.6 0.8 1.0 Normalised histogram frequency Horizontal Displacement 0 100 200 300 400 500… view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Normalized distributions of oscillation periods in brightness temperature, horizontal displacement, and width derived from [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: Normalized distributions of absolute phase speeds for oscillations in brightness temperature, horizontal displacement, and [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

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Works this paper leans on

71 extracted references · 59 canonical work pages

  1. [1]

    B., Brevis, W., Fedun, V ., et al

    Albidah, A. B., Brevis, W., Fedun, V ., et al. 2021, Philosophical Transactions of the Royal Society of London Series A, 379, 20200181

    work page 2021

  2. [2]

    B., Fedun, V ., Aldhafeeri, A

    Albidah, A. B., Fedun, V ., Aldhafeeri, A. A., et al. 2022, ApJ, 927, 201

    work page 2022

  3. [3]

    & Erdélyi, R

    Allcock, M. & Erdélyi, R. 2017, Sol. Phys., 292, 35

    work page 2017

  4. [4]

    & Erdélyi, R

    Allcock, M. & Erdélyi, R. 2018, ApJ, 855, 90

    work page 2018

  5. [5]

    2021, ApJ, 907, 16

    Baker, D., Stangalini, M., Valori, G., et al. 2021, ApJ, 907, 16

    work page 2021

  6. [6]

    Unveiling the True Nature of Plasma Dynamics from the Reference Frame of a Super-penumbral Fibril

    Bate, W., Jess, D. B., Grant, S. D. T., et al. 2024, arXiv e-prints, arXiv:2405.15584

    work page Pith review arXiv 2024

  7. [7]

    B., Nakariakov, V

    Bate, W., Jess, D. B., Nakariakov, V . M., et al. 2022, ApJ, 930, 129

    work page 2022

  8. [8]

    J., Carlsson, M., Hansteen, V

    Bogdan, T. J., Carlsson, M., Hansteen, V . H., et al. 2003, ApJ, 599, 626 Brajša, R., Skoki´c, I., Sudar, D., et al. 2021, A&A, 651, A6 Brajša, R., Sudar, D., Benz, A. O., et al. 2018, A&A, 613, A17

    work page 2003

Show all 71 references
  1. [9]

    H., Ugarte-Urra, I., & Warren, H

    Brooks, D. H., Ugarte-Urra, I., & Warren, H. P. 2015, Nature Communications, 6, 5947

    2015

  2. [10]

    E., Reardon, K

    Chai, Y ., Gary, D. E., Reardon, K. P., & Yurchyshyn, V . 2022, ApJ, 924, 100

    2022

  3. [11]

    R., Auffret, H., & Priest, E

    Choudhuri, A. R., Auffret, H., & Priest, E. R. 1993, Sol. Phys., 143, 49 da Silva Santos, J. M., de la Cruz Rodríguez, J., Leenaarts, J., et al. 2020a, A&A, 634, A56 da Silva Santos, J. M., de la Cruz Rodríguez, J., White, S. M., et al. 2020b, A&A, 643, A41

    1993

  4. [12]

    1990, IEEE Transactions on Information Theory, 36, 961 De Pontieu, B., Hansteen, V

    Daubechies, I. 1990, IEEE Transactions on Information Theory, 36, 961 De Pontieu, B., Hansteen, V . H., Rouppe van der V oort, L., van Noort, M., &

    1990

  5. [13]

    2007a, ApJ, 655, 624 De Pontieu, B., McIntosh, S

    Carlsson, M. 2007a, ApJ, 655, 624 De Pontieu, B., McIntosh, S. W., Carlsson, M., et al. 2007b, Science, 318, 1574 De Pontieu, B., Title, A. M., Lemen, J. R., et al. 2014, Sol. Phys., 289, 2733

    2014

  6. [14]

    Edwin, P. M. & Roberts, B. 1983, Sol. Phys., 88, 179

    1983

  7. [15]

    Eklund, H., Wedemeyer, S., Szydlarski, M., Jafarzadeh, S., & Guevara Gómez, J. C. 2020, A&A, 644, A152 Erdélyi, R. & Zsámberger, N. K. 2024, Symmetry, 16

    2020

  8. [16]

    Gabriel, A. H. 1976, Philosophical Transactions of the Royal Society of London Series A, 281, 339

    1976

  9. [17]

    A., Jess, D

    Gilchrist-Millar, C. A., Jess, D. B., Grant, S. D. T., et al. 2021, Philosophical Transactions of the Royal Society of London Series A, 379, 20200172

    2021

  10. [18]

    Giovanelli, R. G. & Jones, H. P. 1982, Sol. Phys., 79, 267

    1982

  11. [19]

    Grant, S. D. T., Jess, D. B., Moreels, M. G., et al. 2015, ApJ, 806, 132

    2015

  12. [20]

    Grant, S. D. T., Jess, D. B., Zaqarashvili, T. V ., et al. 2018, Nature Physics, 14, 480 Guevara Gómez, J. C., Jafarzadeh, S., Wedemeyer, S., et al. 2023, A&A, 671, A69 Guevara Gómez, J. C., Jafarzadeh, S., Wedemeyer, S., & Szydlarski, M. 2022, A&A, 665, L2 Guevara Gómez, J. C...

    2018

  13. [21]

    W., Bolding, J., Clark, R., et al

    Harvey, J. W., Bolding, J., Clark, R., et al. 2011, in AAS/Solar Physics Division

    2011

  14. [22]

    2009, ApJ, 705, L217

    He, J., Marsch, E., Tu, C., & Tian, H. 2009, ApJ, 705, L217

    2009

  15. [23]

    Henriques, V . M. J., Jafarzadeh, S., Guevara Gómez, J. C., et al. 2022, A&A, 659, A31

    2022

  16. [24]

    J., Jess, D

    Houston, S. J., Jess, D. B., Keppens, R., et al. 2020, ApJ, 892, 49

    2020

  17. [25]

    Jafarzadeh, S., Schiavo, L. A. C. A., Fedun, V ., et al. 2024, A&A, 688, A2

    2024

  18. [26]

    2021, Philosophical Transactions of the Royal Society of London Series A, 379, 20200174

    Jafarzadeh, S., Wedemeyer, S., Fleck, B., et al. 2021, Philosophical Transactions of the Royal Society of London Series A, 379, 20200174

    2021

  19. [27]

    2019, A&A, 622, A150

    Jafarzadeh, S., Wedemeyer, S., Szydlarski, M., et al. 2019, A&A, 622, A150

    2019

  20. [28]

    B., Jafarzadeh, S., Keys, P

    Jess, D. B., Jafarzadeh, S., Keys, P. H., et al. 2023, Living Reviews in Solar Physics, 20, 1

    2023

  21. [29]

    B., Keys, P

    Jess, D. B., Keys, P. H., Stangalini, M., & Jafarzadeh, S. 2021, Philosophical Transactions of the Royal Society of London Series A, 379, 20200169

    2021

  22. [30]

    B., Morton, R

    Jess, D. B., Morton, R. J., Verth, G., et al. 2015, Space Sci. Rev., 190, 103

    2015

  23. [31]

    B., Pascoe, D

    Jess, D. B., Pascoe, D. J., Christian, D. J., et al. 2012, ApJ, 744, L5

    2012

  24. [32]

    J., Erdélyi, R., et al

    Kuridze, D., Morton, R. J., Erdélyi, R., et al. 2012, ApJ, 750, 51

    2012

  25. [33]

    E., & Fla, T

    Leer, E., Holzer, T. E., & Fla, T. 1982, Space Sci. Rev., 33, 161

    1982

  26. [34]

    R., Title, A

    Lemen, J. R., Title, A. M., Akin, D. J., et al. 2012, Sol. Phys., 275, 17

    2012

  27. [35]

    2019, Advances in Space Research, 63, 1396

    Loukitcheva, M. 2019, Advances in Space Research, 63, 1396

    2019

  28. [36]

    W., de Pontieu, B., Carlsson, M., et al

    McIntosh, S. W., de Pontieu, B., Carlsson, M., et al. 2011, Nature, 475, 477

    2011

  29. [37]

    E., Reardon, K

    Molnar, M. E., Reardon, K. P., Chai, Y ., et al. 2019, ApJ, 881, 99

    2019

  30. [38]

    G., Goossens, M., & Van Doorsselaere, T

    Moreels, M. G., Goossens, M., & Van Doorsselaere, T. 2013, A&A, 555, A75

    2013

  31. [39]

    J., Mooroogen, K., & Henriques, V

    Morton, R. J., Mooroogen, K., & Henriques, V . M. J. 2021, Philosophical Trans- actions of the Royal Society of London Series A, 379, 20200183

    2021

  32. [40]

    J., Verth, G., Fedun, V ., Shelyag, S., & Erdélyi, R

    Morton, R. J., Verth, G., Fedun, V ., Shelyag, S., & Erdélyi, R. 2013, ApJ, 768, 17

    2013

  33. [41]

    J., Verth, G., Hillier, A., & Erdélyi, R

    Morton, R. J., Verth, G., Hillier, A., & Erdélyi, R. 2014, ApJ, 784, 29

    2014

  34. [42]

    J., Verth, G., Jess, D

    Morton, R. J., Verth, G., Jess, D. B., et al. 2012, Nature Communications, 3, 1315

    2012

  35. [43]

    2021, A&A, 656, A87

    Murabito, M., Stangalini, M., Baker, D., et al. 2021, A&A, 656, A87

    2021

  36. [44]

    M., et al

    Murabito, M., Stangalini, M., Laming, J. M., et al. 2024, Phys. Rev. Lett., 132, 215201

    2024

  37. [45]

    Musielak, Z. E. & Ulmschneider, P. 2003, A&A, 406, 725

    2003

  38. [46]

    2022, A&A, 661, A95

    Narang, N., Chandrashekhar, K., Jafarzadeh, S., et al. 2022, A&A, 661, A95

    2022

  39. [47]

    E., Patsourakos, S., & Bastian, T

    Nindos, A., Alissandrakis, C. E., Patsourakos, S., & Bastian, T. S. 2020, A&A, 638, A62

    2020

  40. [48]

    E., & Bastian, T

    Nindos, A., Patsourakos, S., Alissandrakis, C. E., & Bastian, T. S. 2021, A&A, 652, A92

    2021

  41. [49]

    2022, Frontiers in Astronomy and Space Sciences, 9, 981205

    Nindos, A., Patsourakos, S., Jafarzadeh, S., & Shimojo, M. 2022, Frontiers in Astronomy and Space Sciences, 9, 981205

    2022

  42. [50]

    2012, A&A, 538, A79

    Nutto, C., Steiner, O., Schaffenberger, W., & Roth, M. 2012, A&A, 538, A79

    2012

  43. [51]

    E., Nindos, A., & Bastian, T

    Patsourakos, S., Alissandrakis, C. E., Nindos, A., & Bastian, T. S. 2020, A&A, 634, A86

    2020

  44. [52]

    D., Thompson, B

    Pesnell, W. D., Thompson, B. J., & Chamberlin, P. C. 2012, Sol. Phys., 275, 3

    2012

  45. [53]

    Pietarila, A., Aznar Cuadrado, R., Hirzberger, J., & Solanki, S. K. 2011, ApJ, 739, 92

    2011

  46. [54]

    M., Gilchrist-Millar, C

    Riedl, J. M., Gilchrist-Millar, C. A., Van Doorsselaere, T., Jess, D. B., & Grant, S. D. T. 2021, A&A, 648, A77

    2021

  47. [55]

    1981, Sol

    Roberts, B. 1981, Sol. Phys., 69, 39 Rouppe van der V oort, L., Leenaarts, J., De Pontieu, B., Carlsson, M., & Vissers, G. 2009, ApJ, 705, 272

    1981

  48. [56]

    Rutten, R. J. 2017, A&A, 598, A89

    2017

  49. [57]

    H., Bush, R

    Schou, J., Scherrer, P. H., Bush, R. I., et al. 2012, Sol. Phys., 275, 229

    2012

  50. [58]

    S., Hales, A

    Shimojo, M., Bastian, T. S., Hales, A. S., et al. 2017, Sol. Phys., 292, 87

    2017

  51. [59]

    Solanki, S. K. 1993, Space Sci. Rev., 63, 1

    1993

  52. [60]

    K., Riethmüller, T

    Solanki, S. K., Riethmüller, T. L., Barthol, P., et al. 2017, ApJS, 229, 2

    2017

  53. [61]

    K., Steiner, O., & Uitenbroeck, H

    Solanki, S. K., Steiner, O., & Uitenbroeck, H. 1991, A&A, 250, 220

    1991

  54. [62]

    Spruit, H. C. 1982, Sol. Phys., 75, 3

    1982

  55. [63]

    2021, Philosophical Transactions of the Royal Society of London Series A, 379, 20200216

    Stangalini, M., Baker, D., Valori, G., et al. 2021, Philosophical Transactions of the Royal Society of London Series A, 379, 20200216

    2021

  56. [64]

    Stangalini, M., Del Moro, D., Berrilli, F., & Je fferies, S. M. 2011, A&A, 534, A65

    2011

  57. [65]

    & Compo, G

    Torrence, C. & Compo, G. P. 1998, Bulletin of the American Meteorological Society, 79, 61

    1998

  58. [66]

    R., & Rosner, R

    Ulmschneider, P., Priest, E. R., & Rosner, R. 1991, in Mechanisms of Chromo- spheric and Coronal Heating (Springer-Verlag, Berlin)

    1991

  59. [67]

    & Jess, D

    Verth, G. & Jess, D. B. 2016, Washington DC American Geophysical Union Geophysical Monograph Series, 216, 431

    2016

  60. [68]

    2016, Space Sci

    Wedemeyer, S., Bastian, T., Brajša, R., et al. 2016, Space Sci. Rev., 200, 1

    2016

  61. [69]

    2020, A&A, 635, A71 Wedemeyer-Böhm, S., Lagg, A., & Nordlund, Å

    Wedemeyer, S., Szydlarski, M., Jafarzadeh, S., et al. 2020, A&A, 635, A71 Wedemeyer-Böhm, S., Lagg, A., & Nordlund, Å. 2009, Space Sci. Rev., 144, 317

    2020

  62. [70]

    M., Iwai, K., Phillips, N

    White, S. M., Iwai, K., Phillips, N. M., et al. 2017, Sol. Phys., 292, 88

    2017

  63. [71]

    & Thompson, A

    Wootten, A. & Thompson, A. R. 2009, IEEE Proceedings, 97, 1463 Article number, page 8 of 8

    2009

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