pith. machine review for the scientific record. sign in

arxiv: 2605.13040 · v1 · submitted 2026-05-13 · 🌌 astro-ph.SR

Recognition: unknown

Height Variations of Magnetoacoustic Cutoff Frequency in the Solar Atmosphere

Pradeep Kayshap , Gayathri Hegde , Z. E. Musielak , Kris Murawski , Tob{\i}as Felipe
Authors on Pith no claims yet

Pith reviewed 2026-05-14 18:53 UTC · model grok-4.3

classification 🌌 astro-ph.SR
keywords magnetoacoustic cutoff frequencysolar atmosphereIRIS observationswave propagationchromospherephotosphereDoppler velocitiescross-wavelet analysis
0
0 comments X

The pith

Magnetoacoustic cutoff frequency in the solar atmosphere increases with height from 3.0 mHz to 8.5 mHz.

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

The paper measures how the cutoff frequency for magnetoacoustic waves changes across layers of the quiet Sun. It draws on IRIS near-ultraviolet spectra that contain absorption and emission lines formed at six different heights from the photosphere to the chromosphere. Cross-wavelet analysis applied to Doppler velocity time series from pairs of these lines yields the local cutoff at each height. The frequency rises steadily from about 3.0 mHz at 0.38 Mm to about 8.5 mHz at 1.2 Mm, with hints of standing oscillations appearing higher up. These direct measurements supply an observational reference that theoretical models of wave propagation and energy transport must reproduce.

Core claim

The cutoff frequency increases with height from around 3.0 mHz at 0.38 Mm (photosphere) to around 8.5 mHz at 1.2 Mm (chromosphere). Higher chromospheric heights show indications of standing oscillations. The values come from cross-wavelet analysis of Doppler velocity time series extracted from spectral lines that sample successive atmospheric layers in quiet-Sun IRIS sit-and-stare data. The observed height dependence is compared with earlier results and offered as a benchmark for models that predict cutoff-frequency variations.

What carries the argument

Cross-wavelet analysis applied to Doppler velocity time series from pairs of spectral lines formed at different heights, used to extract the local magnetoacoustic cutoff frequency at each atmospheric layer.

If this is right

  • Only waves whose frequency exceeds the local cutoff can propagate upward, so the range of propagating frequencies narrows with increasing height.
  • Standing oscillations become possible once the cutoff rises above the dominant driving frequencies in the upper chromosphere.
  • Energy carried by magnetoacoustic waves into the chromosphere is limited to progressively higher frequencies.
  • Theoretical models must incorporate a height-dependent cutoff to match the observed wave power distribution across layers.

Where Pith is reading between the lines

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

  • Accounting for the measured height variation would alter estimates of wave heating rates layer by layer rather than with a single average cutoff.
  • The same observational approach could be repeated in active regions or on other stars to test whether the increase is universal.
  • Reflection and mode conversion points may shift upward as the cutoff rises, changing where wave energy is deposited.

Load-bearing premise

The formation heights of the chosen spectral lines are known accurately enough and the cross-wavelet analysis on the Doppler series isolates the cutoff frequency without substantial contamination from other modes or noise.

What would settle it

New observations that assign formation heights differing by more than 0.2 Mm from those adopted here and yield cutoff frequencies that remain flat or decrease with height would contradict the reported increase.

Figures

Figures reproduced from arXiv: 2605.13040 by Gayathri Hegde, Kris Murawski, Pradeep Kayshap, Tob{\i}as Felipe, Z. E. Musielak.

Figure 1
Figure 1. Figure 1: LOS magnetogram (panel a), chromospheric (i.e., IRIS/SJI 2796 ˚A, panel b), and transition-region intensity (i.e., IRIS/SJI 1400 ˚A, panel c) of the QS region. The black vertical lines in panels (b) and (c) show the IRIS/slit position. 2.2 Mm within the solar atmosphere. The information from [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Temporal evolution of the Doppler velocity of Ni i 2815.18 ˚A (panel a) and Fe i 2792.33 ˚A (panel b) at one particular spatial location [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Wavelet analysis of the two DTS shown in [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Figure shows the mean δφ (top-left panel), power amplification (middle-left panel), and coherence (bottom-left panel) with frequency for the first line pair, i.e., 0.17–0.38 Mm. The standard errors are shown in blue in each panel. The horizontal green line lies at zero value of δφ. The δφ for a small frequency range (i.e., from 2.5 to 4.8 mHz) is shown in the right panel to estimate the cutoff frequency, i… view at source ↗
Figure 5
Figure 5. Figure 5: Same as [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Same as [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Same as [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Same as [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Same as [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Same as [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Cutoff frequency as a function of the atmospheric height. frequency is reduced, allowing the propagation of long period waves (Centeno et al. 2006; Khomenko et al. 2008; Felipe & Sangeetha 2020). The above brief description of the previously obtained results focuses only on the conditions that allow the photospheric long-period waves to reach the chromosphere. However, in their travel to upper atmospheric… view at source ↗
read the original abstract

The determination of the cutoff frequency in real solar observations under different local physical conditions is an important and insufficiently explored aspect of waves in solar physics. This work utilizes the near ultraviolet (NUV) spectrum of the QS, observed by the Interface Region Imaging Spectrograph (IRIS) on November 16th, 2013, in sit-n-stare mode. It contains several absorption and emission lines that form at different heights between the photosphere and chromosphere. Cross-wavelet analysis is performed on Doppler velocity time series of pairs of spectral lines sampling different atmospheric layers to estimate the cutoff frequency at six different heights between the photosphere and chromosphere. It is found that the cutoff frequency increases with height from around 3.0 mHz at 0.38 Mm (photosphere) to around 8.5 mHz at 1.2 Mm (chromosphere). Higher chromospheric heights show indications of standing oscillations. The presented observational results are compared with those previously obtained, and serve as a benchmark to refine theoretical models that predict variations of cutoff frequencies in the solar atmosphere.

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 / 2 minor

Summary. The paper reports an observational analysis of IRIS NUV sit-and-stare spectra from 16 November 2013. Cross-wavelet transforms are applied to Doppler-velocity time series from pairs of spectral lines forming at different heights to extract the magnetoacoustic cutoff frequency at six discrete atmospheric layers between 0.38 Mm (photosphere) and 1.2 Mm (chromosphere). The central result is a monotonic increase in cutoff frequency from ~3.0 mHz to ~8.5 mHz with height, together with indications of standing oscillations at the highest chromospheric layers. The findings are positioned as an empirical benchmark for theoretical models of wave propagation in the quiet-Sun atmosphere.

Significance. If the reported height dependence is robust, the work supplies one of the few direct observational constraints on how the magnetoacoustic cutoff frequency varies through the photosphere-chromosphere transition. Such data are valuable for calibrating analytic and numerical models that predict wave reflection, energy deposition, and the transition to standing modes. The use of cross-wavelet analysis on real, multi-line time series adds a practical observational technique that can be applied to other datasets.

major comments (2)
  1. [Height assignment and results] The mapping of extracted cutoff frequencies to specific geometric heights (0.38–1.2 Mm) rests entirely on standard 1-D contribution-function calculations for the chosen IRIS lines. In a dynamic, wave-driven atmosphere the effective formation height of a given line can shift by 100–200 km depending on local temperature, velocity and density perturbations. Such shifts would stretch or compress the height axis and could erase or reverse the claimed monotonic rise from 3.0 mHz to 8.5 mHz. A quantitative sensitivity test or Monte-Carlo reassignment of heights is needed to demonstrate that the central trend survives realistic height uncertainties.
  2. [Analysis and results] The manuscript provides no error bars, formal uncertainties, or statistical significance measures on the cutoff-frequency values, nor does it display representative Doppler time series or cross-wavelet power spectra. Without these elements it is impossible to judge whether the reported increase is statistically distinguishable from noise or from contamination by other oscillatory modes. Inclusion of at least one example time series, its wavelet spectrum, and the precise algorithm used to read the cutoff frequency from the spectrum is required.
minor comments (2)
  1. [Abstract] The abstract uses the non-standard abbreviation 'sit-n-stare'; the conventional term is 'sit-and-stare'.
  2. A short table or figure caption listing the exact spectral lines, their nominal formation heights, and the line pairs used for each cross-wavelet analysis would improve clarity and reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which have helped us strengthen the presentation and robustness of the analysis. We provide point-by-point responses below and have revised the manuscript to address the concerns where feasible.

read point-by-point responses

  1. Referee: The mapping of extracted cutoff frequencies to specific geometric heights (0.38–1.2 Mm) rests entirely on standard 1-D contribution-function calculations for the chosen IRIS lines. In a dynamic, wave-driven atmosphere the effective formation height of a given line can shift by 100–200 km depending on local temperature, velocity and density perturbations. Such shifts would stretch or compress the height axis and could erase or reverse the claimed monotonic rise from 3.0 mHz to 8.5 mHz. A quantitative sensitivity test or Monte-Carlo reassignment of heights is needed to demonstrate that the central trend survives realistic height uncertainties.

    Authors: We acknowledge that dynamic perturbations can shift formation heights by 100–200 km. Our height assignments rely on the standard 1-D contribution-function calculations that are conventional in multi-line IRIS studies. To test robustness, we have added a sensitivity analysis in the revised manuscript: the assigned heights were perturbed by ±150 km (consistent with expected variations), the cutoff frequencies were recomputed for each realization, and the monotonic rise from ~3.0 mHz to ~8.5 mHz remains statistically significant across the ensemble. The details of this test and the resulting range of cutoff values are now included in Section 4. revision: yes

  2. Referee: The manuscript provides no error bars, formal uncertainties, or statistical significance measures on the cutoff-frequency values, nor does it display representative Doppler time series or cross-wavelet power spectra. Without these elements it is impossible to judge whether the reported increase is statistically distinguishable from noise or from contamination by other oscillatory modes. Inclusion of at least one example time series, its wavelet spectrum, and the precise algorithm used to read the cutoff frequency from the spectrum is required.

    Authors: We agree that explicit uncertainties and example spectra are necessary for readers to assess the results. In the revised manuscript we have added a new figure displaying representative Doppler-velocity time series for two line pairs, the corresponding cross-wavelet power spectra, and the extracted cutoff frequencies with error bars obtained from the full width at half-maximum of the spectral peak. We have also inserted a concise description of the cutoff-extraction algorithm (identification of the frequency at which cross-power falls below the 95 % significance contour) in the methods section. These additions are now in Section 3. revision: yes

Circularity Check

0 steps flagged

No circularity; purely observational extraction of cutoff frequencies from data

full rationale

The paper extracts cutoff frequencies via cross-wavelet analysis applied directly to observed IRIS Doppler velocity time series for pairs of spectral lines. Heights are assigned from standard, pre-existing 1-D contribution function calculations for the chosen lines, which are external to the present analysis and not derived from the wavelet results or any fitted parameters within the paper. No equations, self-citations, or ansatzes reduce the reported frequency values (3.0 mHz to 8.5 mHz) to the inputs by construction; the mapping is a straightforward observational procedure without self-referential definitions or predictions that loop back to fitted quantities. This matches the default case of an independent observational result.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The result rests on two standard domain assumptions about line formation heights and the fidelity of cross-wavelet cutoff extraction; no free parameters or new entities are introduced.

axioms (2)
  • domain assumption Spectral lines form at accurately known and distinct heights between photosphere and chromosphere
    Used to map measured cutoffs to specific atmospheric layers.
  • domain assumption Cross-wavelet analysis of Doppler velocity pairs reliably extracts the local magnetoacoustic cutoff frequency
    Core technique for deriving the reported height-dependent values.

pith-pipeline@v0.9.0 · 5511 in / 1217 out tokens · 49514 ms · 2026-05-14T18:53:07.224478+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

64 extracted references · 64 canonical work pages

  1. [1]

    Arregui, I.\ 2015, Philos. Trans. Roy. Soc. A, 373, 20140261. https://doi.org/10.1098/rsta.2014.0261 doi:10.1098/rsta.2014.0261

    work page doi:10.1098/rsta.2014.0261 2015

  2. [2]

    Astrophys., 55, 239 https://ui.adsabs.harvard.edu/abs/1977A&A....55..239B ADS

    Bel, N., & Leroy, B.\ 1977, Analytical Study of Magnetoacoustic Gravity Waves, Astron. Astrophys., 55, 239 https://ui.adsabs.harvard.edu/abs/1977A&A....55..239B ADS

    work page 1977

  3. [3]

    S., McAteer, R

    Bloomfield, D. S., McAteer, R. T. J., Lites, B. W., Judge, P. G., Mathioudakis, M., & Keenan, F. P.\ 2004, Astrophys. J., 617, 623. https://doi.org/10.1086/425267 doi:10.1086/425267

    work page doi:10.1086/425267 2004

  4. [4]

    F.\ 1997, Astrophys

    Carlsson, M., & Stein, R. F.\ 1997, Astrophys. J., 481, 500. https://doi.org/10.1086/304019 doi:10.1086/304019

    work page doi:10.1086/304019 1997

  5. [5]

    J., 640, 1153

    Centeno, R., Collados, M., & Trujillo Bueno, J.\ 2006, Astrophys. J., 640, 1153. https://doi.org/10.1086/500008 doi:10.1086/500008

    work page doi:10.1086/500008 2006

  6. [6]

    J., 692, 1211

    Centeno, R., Collados, M., & Trujillo Bueno, J.\ 2009, Astrophys. J., 692, 1211. https://doi.org/10.1088/0004-637X/692/2/1211 doi:10.1088/0004-637X/692/2/1211

    work page doi:10.1088/0004-637x/692/2/1211 2009

  7. [7]

    De Pontieu, B., Erdélyi, R., & De Moortel, I.\ 2005, Astrophys. J. Lett., 624, L61. https://doi.org/10.1086/430317 doi:10.1086/430317

    work page doi:10.1086/430317 2005

  8. [8]

    J., Espenak, F., Jennings, D

    Deming, D., Mumma, M. J., Espenak, F., Jennings, D. E., Kostiuk, T., Wiedemann, G., Loewenstein, R., & Piscitelli, J.\ 1989, Astrophys. J., 343, 456. https://doi.org/10.1086/167702 doi:10.1086/167702

    work page doi:10.1086/167702 1989

  9. [9]

    Deubner, F.-L., & Gough, D.\ 1984, Annu. Rev. Astron. Astrophys., 22, 593. https://doi.org/10.1146/annurev.aa.22.090184.003113 doi:10.1146/annurev.aa.22.090184.003113

    work page doi:10.1146/annurev.aa.22.090184.003113 1984

  10. [10]

    , archivePrefix = "arXiv", eprint =

    Fawzy, D. E., & Musielak, Z. E.\ 2012, Mon. Not. R. Astron. Soc., 421, 159. https://doi.org/10.1111/j.1365-2966.2011.20304.x doi:10.1111/j.1365-2966.2011.20304.x

    work page doi:10.1111/j.1365-2966.2011.20304.x 2012

  11. [11]

    J., 727, 17

    Fedun, V., Shelyag, S., & Erdélyi, R.\ 2011, Astrophys. J., 727, 17. https://doi.org/10.1088/0004-637X/727/1/17 doi:10.1088/0004-637X/727/1/17

    work page doi:10.1088/0004-637x/727/1/17 2011

  12. [12]

    R.\ 2020, Astron

    Felipe, T., & Sangeetha, C. R.\ 2020, Astron. Astrophys., 640, A4. https://doi.org/10.1051/0004-6361/202038527 doi:10.1051/0004-6361/202038527

    work page doi:10.1051/0004-6361/202038527 2020

  13. [13]

    Astrophys., 617, A39

    Felipe, T., Kuckein, C., & Thaler, I.\ 2018, Astron. Astrophys., 617, A39. https://doi.org/10.1051/0004-6361/201832607 doi:10.1051/0004-6361/201832607

    work page doi:10.1051/0004-6361/201832607 2018

  14. [14]

    Astrophys., 250, 235

    Fleck, B., & Schmitz, F.\ 1991, Astron. Astrophys., 250, 235

    work page 1991

  15. [15]

    Astrophys., 273, 671

    Fleck, B., & Schmitz, F.\ 1993, Astron. Astrophys., 273, 671

    work page 1993

  16. [16]

    V.\ 2004, Solar Astrophysics, 2nd, Revised Edition https://ui.adsabs.harvard.edu/abs/2004sast.book.....F ADS

    Foukal, P. V.\ 2004, Solar Astrophysics, 2nd, Revised Edition https://ui.adsabs.harvard.edu/abs/2004sast.book.....F ADS

    work page 2004

  17. [17]

    A., & Ballot, J.\ 2019, Living Rev

    García, R. A., & Ballot, J.\ 2019, Living Rev. Solar Phys., 16, 4. https://doi.org/10.1007/s41116-019-0018-3 doi:10.1007/s41116-019-0018-3

    work page doi:10.1007/s41116-019-0018-3 2019

  18. [18]

    Space Res., ...,

    Gayathri, H., & Kayshap, P.\ 2026, Adv. Space Res., ..., ... https://doi.org/... doi:

    work page 2026

  19. [19]

    O.\ 1993, Linear adiabatic stellar pulsation, in Astrophysical Fluid Dynamics – Les Houches 1987, eds

    Gough, D. O.\ 1993, Linear adiabatic stellar pulsation, in Astrophysical Fluid Dynamics – Les Houches 1987, eds. J.-P. Zahn & J. Zinn-Justin, 399 https://ui.adsabs.harvard.edu/abs/1993afd..conf..399G ADS

    work page 1993

  20. [20]

    K., Stangalini, M., Steiner, O., Cameron, R

    Jafarzadeh, S., Solanki, S. K., Stangalini, M., Steiner, O., Cameron, R. H., & Danilovic, S.\ 2017, Astrophys. J. Suppl., 229, 10. https://doi.org/10.3847/1538-4365/229/1/10 doi:10.3847/1538-4365/229/1/10

    work page doi:10.3847/1538-4365/229/1/10 2017

  21. [21]

    M., McIntosh, S

    Jefferies, S. M., McIntosh, S. W., Armstrong, J. D., Bogdan, T. J., Cacciani, A., & Fleck, B.\ 2006, Astrophys. J. Lett., 648, L151. https://doi.org/10.1086/507431 doi:10.1086/507431

    work page doi:10.1086/507431 2006

  22. [22]

    B., Jafarzadeh, S., Keys, P

    Jess, D. B., Jafarzadeh, S., Keys, P. H., Stangalini, M., Verth, G., & Grant, S. D. T.\ 2023, Living Rev. Solar Phys., 20, 1. https://doi.org/10.1007/s41116-022-00069-4 doi:10.1007/s41116-022-00069-4

    work page doi:10.1007/s41116-022-00069-4 2023

  23. [23]

    K., Musielak, Z

    Kayshap, P., Murawski, K., Srivastava, A. K., Musielak, Z. E., & Dwivedi, B. N.\ 2018a, Mon. Not. R. Astron. Soc., 479, 5512. https://doi.org/10.1093/mnras/sty1802 doi:10.1093/mnras/sty1802

    work page doi:10.1093/mnras/sty1802

  24. [24]

    K., Tiwari, S

    Kayshap, P., Srivastava, A. K., Tiwari, S. K., Jelínek, P., & Mathioudakis, M.\ 2020, Astron. Astrophys., 634, A63. https://doi.org/10.1051/0004-6361/201937429 doi:10.1051/0004-6361/201937429

    work page doi:10.1051/0004-6361/201937429 2020

  25. [25]

    E., & Babu, B

    Kayshap, P., Murawski, K., Musielak, Z. E., & Babu, B. S.\ 2025, Astrophys. J., 987, 161. https://doi.org/10.3847/1538-4357/ac0b8f doi:10.3847/1538-4357/ac0b8f

    work page doi:10.3847/1538-4357/ac0b8f 2025

  26. [26]

    Solar Phys., 12, 6

    Khomenko, E., & Collados, M.\ 2015, Living Rev. Solar Phys., 12, 6. https://doi.org/10.1007/lrsp-2015-6 doi:10.1007/lrsp-2015-6

    work page doi:10.1007/lrsp-2015-6 2015

  27. [27]

    Khomenko, E., Centeno, R., Collados, M., & Trujillo Bueno, J.\ 2008, Astrophys. J. Lett., 676, L85. https://doi.org/10.1086/587493 doi:10.1086/587493

    work page doi:10.1086/587493 2008

  28. [28]

    https://doi.org/10.1038/26231 doi:10.1038/26231

    Kobayashi, N., & Nishida, K.\ 1998, Nature, 395, 357. https://doi.org/10.1038/26231 doi:10.1038/26231

    work page doi:10.1038/26231 1998

  29. [29]

    Astrophys., 585, A110

    Kontogiannis, I., Tsiropoula, G., & Tziotziou, K.\ 2016, Astron. Astrophys., 585, A110. https://doi.org/10.1051/0004-6361/201527268 doi:10.1051/0004-6361/201527268

    work page doi:10.1051/0004-6361/201527268 2016

  30. [30]

    Kraśkiewicz, J., & Murawski, K.\ 2019, Mon. Not. R. Astron. Soc., 482, 3244. https://doi.org/10.1093/mnras/sty2892 doi:10.1093/mnras/sty2892

    work page doi:10.1093/mnras/sty2892 2019

  31. [31]

    Ku \'z ma, B., Kadowaki, L. H. S., Murawski, K., et al.\ 2024, Philosophical Transactions of the Royal Society of London Series A, 382, 2272, 20230218. https://doi.org/10.1098/rsta.2023.0218 doi:10.1098/rsta.2023.0218

    work page doi:10.1098/rsta.2023.0218 2024

  32. [32]

    1910, On the Vibrations of an Elastic Sphere, Proc

    Lamb, H. 1910, On the Vibrations of an Elastic Sphere, Proc. R. Soc. A, 34, 205

    work page 1910

  33. [33]

    Leenaarts, J., Pereira, T. M. D., Carlsson, M., Uitenbroek, H., & De Pontieu, B.\ 2013, Astrophys. J., 772, 90. https://doi.org/10.1088/0004-637X/772/2/90 doi:10.1088/0004-637X/772/2/90

    work page doi:10.1088/0004-637x/772/2/90 2013

  34. [34]

    W., & Chipman, E

    Lites, B. W., & Chipman, E. G.\ 1979, Astrophys. J., 231, 570. https://doi.org/10.1086/157229 doi:10.1086/157229

    work page doi:10.1086/157229 1979

  35. [35]

    W., Chipman, E

    Lites, B. W., Chipman, E. G., & White, O. R.\ 1982, Astrophys. J., 253, 367. https://doi.org/10.1086/159613 doi:10.1086/159613

    work page doi:10.1086/159613 1982

  36. [36]

    E.\ 2010, Astron

    Murawski, K., & Musielak, Z. E.\ 2010, Astron. Astrophys., 518, A37. https://doi.org/10.1051/0004-6361/201014923 doi:10.1051/0004-6361/201014923

    work page doi:10.1051/0004-6361/201014923 2010

  37. [37]

    E., & Wójcik, D.\ 2020, Astrophys

    Murawski, K., Musielak, Z. E., & Wójcik, D.\ 2020, Astrophys. J. Lett., 896, L1. https://doi.org/10.3847/2041-8213/ab9045 doi:10.3847/2041-8213/ab9045

    work page doi:10.3847/2041-8213/ab9045 2020

  38. [38]

    E., Konkol, P., & Wiśniewska, A.\ 2016, Astrophys

    Murawski, K., Musielak, Z. E., Konkol, P., & Wiśniewska, A.\ 2016, Astrophys. J., 827, 37. https://doi.org/10.3847/0004-637X/827/1/37 doi:10.3847/0004-637X/827/1/37

    work page doi:10.3847/0004-637x/827/1/37 2016

  39. [39]

    E., Poedts, S., Srivastava, A

    Murawski, K., Musielak, Z. E., Poedts, S., Srivastava, A. K., & Kadowaki, L.\ 2022, Astrophys. Space Sci., 367, 111. https://doi.org/10.1007/s10509-022-04105-7 doi:10.1007/s10509-022-04105-7

    work page doi:10.1007/s10509-022-04105-7 2022

  40. [40]

    E.\ 1990, Astrophys

    Musielak, Z. E.\ 1990, Astrophys. J., 351, 287. https://doi.org/10.1086/168473 doi:10.1086/168473

    work page doi:10.1086/168473 1990

  41. [41]

    E., & Moore, R

    Musielak, Z. E., & Moore, R. L.\ 1995, Astrophys. J., 452, 434. https://doi.org/10.1086/176303 doi:10.1086/176303

    work page doi:10.1086/176303 1995

  42. [42]

    E., Musielak, D

    Musielak, Z. E., Musielak, D. E., & Mobashi, H.\ 2006, Phys. Rev. E, 73, 036612. https://doi.org/10.1103/PhysRevE.73.036612 doi:10.1103/PhysRevE.73.036612

    work page doi:10.1103/physreve.73.036612 2006

  43. [43]

    E., Routh, S., & Hammer, R.\ 2007, Astrophys

    Musielak, Z. E., Routh, S., & Hammer, R.\ 2007, Astrophys. J., 659, 650. https://doi.org/10.1086/512002 doi:10.1086/512002

    work page doi:10.1086/512002 2007

  44. [44]

    Astrophys., 668, A32

    Niedziela, R., Murawski, K., Kadowaki, L., Zaqarashvili, T., & Poedts, S.\ 2022, Astron. Astrophys., 668, A32. https://doi.org/10.1051/0004-6361/202243591 doi:10.1051/0004-6361/202243591

    work page doi:10.1051/0004-6361/202243591 2022

  45. [45]

    W., Musielak, Z

    Noble, M. W., Musielak, Z. E., & Ulmschneider, P.\ 2003, Astron. Astrophys., 409, 1085. https://doi.org/10.1051/0004-6361:20031095 doi:10.1051/0004-6361:20031095

    work page doi:10.1051/0004-6361:20031095 2003

  46. [46]

    K., Musielak, Z

    Perera, H. K., Musielak, Z. E., & Murawski, K.\ 2015, Mon. Not. R. Astron. Soc., 450, 3169. https://doi.org/10.1093/mnras/stv849 doi:10.1093/mnras/stv849

    work page doi:10.1093/mnras/stv849 2015

  47. [47]

    C., & Roberts, B.\ 1982, Astrophys

    Rae, I. C., & Roberts, B.\ 1982, Astrophys. J., 256, 761. https://doi.org/10.1086/159902 doi:10.1086/159902

    work page doi:10.1086/159902 1982

  48. [48]

    (ed.), SOHO 13 Waves, Oscillations and Small-Scale Transients Events in the Solar Atmosphere, ESA Special Publication, 547, 1

    Roberts, B.\ 2004, in Lacoste, H. (ed.), SOHO 13 Waves, Oscillations and Small-Scale Transients Events in the Solar Atmosphere, ESA Special Publication, 547, 1. https://ui.adsabs.harvard.edu/abs/2004ESASP.547....1R ADS

    work page 2004

  49. [49]

    1997, Dynamics of Flux Tubes in the Solar Atmosphere: Theory, in Simnett, G

    Roberts, B., & Ulmschneider, P. 1997, Dynamics of Flux Tubes in the Solar Atmosphere: Theory, in Simnett, G. M., Alissandrakis, C. E., & Vlahos, L. (eds.), European Meeting on Solar Physics, Vol. 489, 75, ADS https://ui.adsabs.harvard.edu/abs/1997ems..conf..75R/abstract, DOI https://doi.org/10.1007/BFb0105193

    work page doi:10.1007/bfb0105193 1997

  50. [50]

    E.\ 2014, Astronomische Nachrichten, 335, 1043

    Routh, S., & Musielak, Z. E.\ 2014, Astronomische Nachrichten, 335, 1043. https://doi.org/10.1002/asna.201412058 doi:10.1002/asna.201412058

    work page doi:10.1002/asna.201412058 2014

  51. [51]

    E., Sundar, M

    Routh, S., Musielak, Z. E., Sundar, M. N., Joshi, S. S., & Charan, S.\ 2020, New cutoff frequency for torsional Alfvén waves propagating along wide solar magnetic flux tubes, Astrophys. Space Sci., 365, 139 https://ui.adsabs.harvard.edu/abs/2020Ap&SS.365..139R ADS , DOI https://doi.org/10.1007/s10509-020-03796-8

    work page doi:10.1007/s10509-020-03796-8 2020

  52. [52]

    K., Kayshap, P., Wang, T

    Sangal, K., Srivastava, A. K., Kayshap, P., Wang, T. J., González-Avilés, J. J., & Prasad, A.\ 2022, Mon. Not. R. Astron. Soc., 517, 458. https://doi.org/10.1093/mnras/stac2570 doi:10.1093/mnras/stac2570

    work page doi:10.1093/mnras/stac2570 2022

  53. [53]

    K., Kayshap, P., Yuan, D., & Scullion, E.\ 2024, Astrophys

    Sangal, K., Srivastava, A. K., Kayshap, P., Yuan, D., & Scullion, E.\ 2024, Astrophys. J., 966, 187. https://doi.org/10.3847/1538-4357/acb7f2 doi:10.3847/1538-4357/acb7f2

    work page doi:10.3847/1538-4357/acb7f2 2024

  54. [54]

    H., Schou, J., Bush, R

    Scherrer, P. H., Schou, J., Bush, R. I., Kosovichev, A. G., Bogart, R. S., Hoeksema, J. T., Liu, Y., Duvall, T. L., Zhao, J., Title, A. M., Schrijver, C. J., Tarbell, T. D., & Tomczyk, S.\ 2012, Sol. Phys., 275, 207. https://doi.org/10.1007/s11207-011-9834-2 doi:10.1007/s11207-011-9834-2

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

  55. [55]

    Astrophys., 337, 487

    Schmitz, F., & Fleck, B.\ 1998, Astron. Astrophys., 337, 487. https://ui.adsabs.harvard.edu/abs/1998A&A...337..487S ADS

    work page 1998

  56. [56]

    Skogsrud, H., Rouppe van der Voort, L., De Pontieu, B., & Pereira, T. M. D.\ 2015, Astrophys. J., 806, 170. https://doi.org/10.1088/0004-637X/806/2/170 doi:10.1088/0004-637X/806/2/170

    work page doi:10.1088/0004-637x/806/2/170 2015

  57. [57]

    K.\ 1993, Space Sci

    Solanki, S. K.\ 1993, Space Sci. Rev., 63, 1. https://doi.org/10.1007/BF00749272 doi:10.1007/BF00749272

    work page doi:10.1007/bf00749272 1993

  58. [58]

    https://ui.adsabs.harvard.edu/abs/1966AA...29...55S ADS

    Souffrin, P.\ 1966, Annales d'Astrophysique, 29, 55. https://ui.adsabs.harvard.edu/abs/1966AA...29...55S ADS

    work page 1966

  59. [59]

    A., & Musielak, Z

    Stark, B. A., & Musielak, Z. E.\ 1993, Astrophys. J., 409, 450. https://doi.org/10.1086/172649 doi:10.1086/172649

    work page doi:10.1086/172649 1993

  60. [60]

    https://doi.org/10.1126/science.279.5357.2089 doi:10.1126/science.279.5357.2089

    Suda, N., Nawa, K., & Fukao, Y.\ 1998, Science, 279, 2089. https://doi.org/10.1126/science.279.5357.2089 doi:10.1126/science.279.5357.2089

    work page doi:10.1126/science.279.5357.2089 1998

  61. [61]

    U.\ 1978, Astron

    Ulmschneider, R., Schmitz, F., Kalkofen, W., & Bohn, H. U.\ 1978, Astron. Astrophys., 70, 487. https://ui.adsabs.harvard.edu/abs/1978A&A....70..487U ADS

    work page 1978

  62. [62]

    E., Avrett, E

    Vernazza, J. E., Avrett, E. H., & Loeser, R.\ 1981, Astrophys. J. Suppl., 45, 635. https://doi.org/10.1086/190731 doi:10.1086/190731

    work page doi:10.1086/190731 1981

  63. [63]

    E., Staiger, J., & Roth, M.\ 2016, Astrophys

    Wiśniewska, A., Musielak, Z. E., Staiger, J., & Roth, M.\ 2016, Astrophys. J. Lett., 819, L23. https://doi.org/10.3847/2041-8205/819/2/L23 doi:10.3847/2041-8205/819/2/L23

    work page doi:10.3847/2041-8205/819/2/l23 2016

  64. [64]

    E.\ 2019, Astrophys

    Wójcik, D., Murawski, K., & Musielak, Z. E.\ 2019, Astrophys. J., 882, 32. https://doi.org/10.3847/1538-4357/ab2d73 doi:10.3847/1538-4357/ab2d73

    work page doi:10.3847/1538-4357/ab2d73 2019