# Appendix B: Optically Thick and Optically Thin Diagnostics of Spectral-Line Doppler Shifts

In this appendix we first describe the general use of the LOS velocity diagnostics using the Doppler shifts of optically thick and optically thin spectral lines. In the later part we focus on the properties of the spectral lines observed by IRIS. It is important to remember that velocities derived from Doppler shifts do not always provide true information about the LOS component of the velocity of the observed plasma structures. This is caused by several factors, from which the most important is the optical thickness of the observed plasma in the observed spectral line.

## B.1 Optically Thick Case

In the optically very thick case, the observed spectral line is produced in a narrow region closest to the observer (with a caveat we will describe later). This means that the Doppler shift of such a spectral line provides information about the true LOS velocity of that particular region. However, we do not gain any insight into the movement of the plasma beyond this region unless the spectral line in question is narrow and thus very sensitive to the velocity. Then we can obtain complex profiles with a contribution from deeper regions. This was demonstrated for example by Heinzel et al. (2014, 2015bb) who showed that the complex, multi-peak Mg II h&k profiles (see Fig. 14) observed in prominences by IRIS can be explained by the presence of different plasma structures moving with different LOS velocities. Multi-peaked Mg II h&k profiles were also produced by Tei et al. (2020) and Gunár et al. (2022) using multi-thread models with stochastic LOS dynamics. We note that the decreased intensity of the side peaks (Fig. 14) can be explained by the Doppler dimming effect in the Mg II h&k lines described for example by Heinzel et al. (2015bb). While we do not focus on the Doppler dimming/brightening effect here, we note that this effect may also influence the Doppler-shift analysis of the LOS velocities by modifying the complexity of the line profile asymmetries.

We should now ask why we can obtain information from the plasma located beyond the first plasma structure even in optically very thick case? This is due to the fact that the observed plasma is optically very thick only near the centre of a spectral line. The optical thickness decreases away from the line centre to values well below unity in far wings. Therefore, in the wings of optically thick spectral lines we can ‘see beyond’ the first structure in which the centre of the line is formed. If the difference between the LOS velocities

<figure><img src="image_18.png" /><figcaption>**Fig. 14** Left: An example of observed multi-peaked Mg II k profile obtained by IRIS (adapted from Schmieder et al. 2014b). Right: Simulated multi-peaked Mg II k profile (adapted from Heinzel et al. 2015bb)</figcaption></figure>
# Appendix B: Optically Thick and Optically Thin Diagnostics of Spectral-Line Doppler Shifts

In this appendix we first describe the general use of the LOS velocity diagnostics using the Doppler shifts of optically thick and optically thin spectral lines. In the later part we focus on the properties of the spectral lines observed by IRIS. It is important to remember that velocities derived from Doppler shifts do not always provide true information about the LOS component of the velocity of the observed plasma structures. This is caused by several factors, from which the most important is the optical thickness of the observed plasma in the observed spectral line.

## B.1 Optically Thick Case

In the optically very thick case, the observed spectral line is produced in a narrow region closest to the observer (with a caveat we will describe later). This means that the Doppler shift of such a spectral line provides information about the true LOS velocity of that particular region. However, we do not gain any insight into the movement of the plasma beyond this region unless the spectral line in question is narrow and thus very sensitive to the velocity. Then we can obtain complex profiles with a contribution from deeper regions. This was demonstrated for example by Heinzel et al. (2014, 2015bb) who showed that the complex, multi-peak Mg II h&k profiles (see Fig. 14) observed in prominences by IRIS can be explained by the presence of different plasma structures moving with different LOS velocities. Multi-peaked Mg II h&k profiles were also produced by Tei et al. (2020) and Gunár et al. (2022) using multi-thread models with stochastic LOS dynamics. We note that the decreased intensity of the side peaks (Fig. 14) can be explained by the Doppler dimming effect in the Mg II h&k lines described for example by Heinzel et al. (2015bb). While we do not focus on the Doppler dimming/brightening effect here, we note that this effect may also influence the Doppler-shift analysis of the LOS velocities by modifying the complexity of the line profile asymmetries.

We should now ask why we can obtain information from the plasma located beyond the first plasma structure even in optically very thick case? This is due to the fact that the observed plasma is optically very thick only near the centre of a spectral line. The optical thickness decreases away from the line centre to values well below unity in far wings. Therefore, in the wings of optically thick spectral lines we can ‘see beyond’ the first structure in which the centre of the line is formed. If the difference between the LOS velocities

<figure><img src="image_18.png" /><figcaption>**Fig. 14** Left: An example of observed multi-peaked Mg II k profile obtained by IRIS (adapted from Schmieder et al. 2014b). Right: Simulated multi-peaked Mg II k profile (adapted from Heinzel et al. 2015bb)</figcaption></figure>
of individual plasma structures causes a Doppler shift comparable or larger than the FWHM (Full Width at Half-Maximum) of the considered spectral line in a single structure, then we can easily identify individual components of complex, multi-peak observed profiles, such as in the case of Heinzel et al. (2015bb, Fig. 1) or Ruan et al. (2018, Fig. 14). On the other hand, if the difference between the LOS velocities of these plasma structures is significantly smaller than the FWHM of a single structure, the resulting spectral line profile will appear strongly asymmetric or reversed. The LOS velocity derived from the Doppler shift of an entire line profile in such a case does not convey information about the absolute LOS velocity of the nearest, or any other individual plasma structure, but of a superposition of all of them. Therefore, if such an asymmetric profile is analysed in the context of a single moving plasma structure, the obtained Doppler-shift velocity does not provide a truly accurate measurement. The difference between the true LOS velocities of individual plasma structures and the apparent Doppler-shift velocity derived from their superposition may be significant.

The described analysis of the optically thick spectral lines is further complicated by the fact that such spectral lines, for example Mg II h&k or hydrogen Lyman lines, are often naturally reversed due to the behaviour of their source functions. This means that it may be impossible to distinguish between a two-component spectral line formed when two independent plasma structures move with different LOS velocities and a single-component but naturally reversed spectral line from a single plasma structure. An example may be found in Gunár et al. (2008), where the authors studied asymmetries of hydrogen Lyman line profiles caused by movement of multiple prominence plasma structures with stochastic LOS velocities. These authors showed that the strong and sometimes even opposite asymmetries in different Lyman lines can be caused by realistic, relatively low stochastic LOS velocities of individual fine structures and not by several times larger LOS velocity of a supposedly uniform plasma structure. However, we note that it might be possible to distinguish between multi-component and single-component cases when two (or more) spectral lines are analysed together. An example of such a pair of spectral lines are Mg II h&k and C II lines observed by IRIS.

## B.2 Optically Thin Case

In the optically thin case the information about the LOS movement of all plasma structures propagates through the entire observed medium and is integrated into the final spectral line profile. This means that the resulting profile contains a superposition of Doppler shifts from all individual plasma structures. If these structures again move with sufficiently different LOS velocities (producing Doppler shifts comparable or larger than the FWHM of a single structure) we will observe clearly separated individual spectral line components. We are then able to derive the true LOS velocities of individual plasma structures. However, if these structures move with LOS velocities which do not cause sufficiently large Doppler shifts, the resulting profile will be broadened and generally asymmetric. Moreover, we can imagine a simple scenario in which two “identical” plasma structures move with equal but opposite LOS velocities. In such a case, the resulting spectral profile might be even symmetric and centred around the zero (rest) wavelength. This means that we would not measure any Doppler shift and thus assume that we observe a single, stationary plasma structure while we are observing two structures with potentially significant LOS velocities. Such scenario was discussed for example by Gunár et al. (2012). Of course, in reality the situation in observations is even more complex. This simple example just illustrates that information about the LOS velocities derived from Doppler shifts is not always robust.
of individual plasma structures causes a Doppler shift comparable or larger than the FWHM (Full Width at Half-Maximum) of the considered spectral line in a single structure, then we can easily identify individual components of complex, multi-peak observed profiles, such as in the case of Heinzel et al. (2015bb, Fig. 1) or Ruan et al. (2018, Fig. 14). On the other hand, if the difference between the LOS velocities of these plasma structures is significantly smaller than the FWHM of a single structure, the resulting spectral line profile will appear strongly asymmetric or reversed. The LOS velocity derived from the Doppler shift of an entire line profile in such a case does not convey information about the absolute LOS velocity of the nearest, or any other individual plasma structure, but of a superposition of all of them. Therefore, if such an asymmetric profile is analysed in the context of a single moving plasma structure, the obtained Doppler-shift velocity does not provide a truly accurate measurement. The difference between the true LOS velocities of individual plasma structures and the apparent Doppler-shift velocity derived from their superposition may be significant.

The described analysis of the optically thick spectral lines is further complicated by the fact that such spectral lines, for example Mg II h&k or hydrogen Lyman lines, are often naturally reversed due to the behaviour of their source functions. This means that it may be impossible to distinguish between a two-component spectral line formed when two independent plasma structures move with different LOS velocities and a single-component but naturally reversed spectral line from a single plasma structure. An example may be found in Gunár et al. (2008), where the authors studied asymmetries of hydrogen Lyman line profiles caused by movement of multiple prominence plasma structures with stochastic LOS velocities. These authors showed that the strong and sometimes even opposite asymmetries in different Lyman lines can be caused by realistic, relatively low stochastic LOS velocities of individual fine structures and not by several times larger LOS velocity of a supposedly uniform plasma structure. However, we note that it might be possible to distinguish between multi-component and single-component cases when two (or more) spectral lines are analysed together. An example of such a pair of spectral lines are Mg II h&k and C II lines observed by IRIS.

## B.2 Optically Thin Case

In the optically thin case the information about the LOS movement of all plasma structures propagates through the entire observed medium and is integrated into the final spectral line profile. This means that the resulting profile contains a superposition of Doppler shifts from all individual plasma structures. If these structures again move with sufficiently different LOS velocities (producing Doppler shifts comparable or larger than the FWHM of a single structure) we will observe clearly separated individual spectral line components. We are then able to derive the true LOS velocities of individual plasma structures. However, if these structures move with LOS velocities which do not cause sufficiently large Doppler shifts, the resulting profile will be broadened and generally asymmetric. Moreover, we can imagine a simple scenario in which two “identical” plasma structures move with equal but opposite LOS velocities. In such a case, the resulting spectral profile might be even symmetric and centred around the zero (rest) wavelength. This means that we would not measure any Doppler shift and thus assume that we observe a single, stationary plasma structure while we are observing two structures with potentially significant LOS velocities. Such scenario was discussed for example by Gunár et al. (2012). Of course, in reality the situation in observations is even more complex. This simple example just illustrates that information about the LOS velocities derived from Doppler shifts is not always robust.
From the differences between optically thin and thick cases it is clear that in many circumstances we will obtain different LOS velocities derived from Doppler shifts when different optically thick and optically thin spectral lines are used. This is illustrated for example by the work of Ruan et al. (2018), which shows that the LOS velocities derived from Doppler shifts of the Mg II h&k profiles observed by IRIS can be different (often larger) than those derived from the Hα observations. This again demonstrates that the LOS velocity diagnostics employing the analysis of the spectral-line Doppler shifts need to be approached with caution and only detailed radiative-transfer simulations can help to distinguish various situations.

**Acknowledgements** This paper stemmed from the discussions held at ISSI during two meetings of the International Team 374 ("Solving the prominence paradox", led by N. Labrosse) in February 2017 and March 2018. We acknowledge fruitful discussions with all who participated in these meetings including L. Green, S. Gunár, P. Heinzel, S. Ječič, J.M. Jenkins, T.A. Kucera, N. Labrosse, P.J. Levens, A. López Ariste, M. Luna, D.H. Mackay, O. Panasenco, T. Rees-Crockford, A. Rodger, T. Roudier, B. Schmieder, S. Wedemeyer, and M. Zapiór.

We thank I. Ugarte-Urra for providing the Hinode/EIS deconvolution routine used in Warren et al. (2018). Hinode is a Japanese mission developed and launched by ISAS/JAXA, with NAOJ as domestic partner and NASA and STFC (UK) as international partners. It is operated by these agencies in cooperation with ESA and NSC (Norway).

**Author Contribution** Petr Heinzel, Therese A. Kucera, Peter J. Levens, Arturo López Ariste, Duncan H. Mackay, Maciej Zapiór contributed equally to this work.

**Funding** Open access publishing supported by the National Technical Library in Prague. S. Gunár and P. Heinzel acknowledge the support from grant 22-34841S of the Czech Science Foundation (GAČR). S. Gunár, P. Heinzel, and M. Zapiór acknowledge the support from the project RVO:67985815 of the Astronomical Institute of the Czech Academy of Sciences. N. Labrosse acknowledges support from STFC grant ST/T000422/1. M. Luna acknowledges support through the Ramón y Cajal fellowship RYC2018-026129-I from the Spanish Ministry of Science and Innovation, the Spanish National Research Agency (Agencia Estatal de Investigación), the European Social Fund through Operational Program FSE 2014 of Employment, Education and Training and the Universitat de les Illes Balears. This publication is part of the R + D + i project PID2020-112791GB-I00, financed by MCIN/AEI/10.13039/501100011033. T. Kucera acknowledges support of the NASA Heliophysics ISFM program. D.H.M. would like to thank the STFC for support via consolidated grant ST/W001195/1.

## Declarations

**Competing Interests** The authors are not aware of any conflicts of interest (financial or otherwise) in connection with the presented work.

**Open Access** This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

## References

Antolin P, Okamoto TJ, De Pontieu B, Uitenbroek H, Van Doorsselaere T, Yokoyama T (2015) Resonant absorption of transverse oscillations and associated heating in a solar prominence. II. Numerical aspects. Astrophys J 809:72. https://doi.org/10.1088/0004-637X/809/1/72. arXiv:1506.09108 [astro-ph.SR]
From the differences between optically thin and thick cases it is clear that in many circumstances we will obtain different LOS velocities derived from Doppler shifts when different optically thick and optically thin spectral lines are used. This is illustrated for example by the work of Ruan et al. (2018), which shows that the LOS velocities derived from Doppler shifts of the Mg II h&k profiles observed by IRIS can be different (often larger) than those derived from the Hα observations. This again demonstrates that the LOS velocity diagnostics employing the analysis of the spectral-line Doppler shifts need to be approached with caution and only detailed radiative-transfer simulations can help to distinguish various situations.

**Acknowledgements** This paper stemmed from the discussions held at ISSI during two meetings of the International Team 374 ("Solving the prominence paradox", led by N. Labrosse) in February 2017 and March 2018. We acknowledge fruitful discussions with all who participated in these meetings including L. Green, S. Gunár, P. Heinzel, S. Ječič, J.M. Jenkins, T.A. Kucera, N. Labrosse, P.J. Levens, A. López Ariste, M. Luna, D.H. Mackay, O. Panasenco, T. Rees-Crockford, A. Rodger, T. Roudier, B. Schmieder, S. Wedemeyer, and M. Zapiór.

We thank I. Ugarte-Urra for providing the Hinode/EIS deconvolution routine used in Warren et al. (2018). Hinode is a Japanese mission developed and launched by ISAS/JAXA, with NAOJ as domestic partner and NASA and STFC (UK) as international partners. It is operated by these agencies in cooperation with ESA and NSC (Norway).

**Author Contribution** Petr Heinzel, Therese A. Kucera, Peter J. Levens, Arturo López Ariste, Duncan H. Mackay, Maciej Zapiór contributed equally to this work.

**Funding** Open access publishing supported by the National Technical Library in Prague. S. Gunár and P. Heinzel acknowledge the support from grant 22-34841S of the Czech Science Foundation (GAČR). S. Gunár, P. Heinzel, and M. Zapiór acknowledge the support from the project RVO:67985815 of the Astronomical Institute of the Czech Academy of Sciences. N. Labrosse acknowledges support from STFC grant ST/T000422/1. M. Luna acknowledges support through the Ramón y Cajal fellowship RYC2018-026129-I from the Spanish Ministry of Science and Innovation, the Spanish National Research Agency (Agencia Estatal de Investigación), the European Social Fund through Operational Program FSE 2014 of Employment, Education and Training and the Universitat de les Illes Balears. This publication is part of the R + D + i project PID2020-112791GB-I00, financed by MCIN/AEI/10.13039/501100011033. T. Kucera acknowledges support of the NASA Heliophysics ISFM program. D.H.M. would like to thank the STFC for support via consolidated grant ST/W001195/1.

## Declarations

**Competing Interests** The authors are not aware of any conflicts of interest (financial or otherwise) in connection with the presented work.

**Open Access** This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

## References

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Arregui I, Oliver R, Ballester JL (2018) Prominence oscillations. Living Rev Sol Phys 15:3. https://doi.org/10.1007/s41116-018-0012-6

Aulanier G, Démoulin P (1998) 3-D magnetic configurations supporting prominences. I. The natural presence of lateral feet. Astron Astrophys 329:1125–1137

Barczynski K, Schmieder B, Peat AW, Labrosse N, Mein P, Mein N (2021) Spectro-imagery of an active tornado-like prominence: formation and evolution. Astron Astrophys 653:A94. https://doi.org/10.1051/0004-6361/202140976. arXiv:2106.04259 [astro-ph.SR]

Bemporad A (2011) Prominence 3D reconstruction in the STEREO era: a review. J Atmos Sol-Terr Phys 73(10):1117–1128. https://doi.org/10.1016/j.jastp.2010.12.007

Berger TE, Shine RA, Slater GL, Tarbell TD, Title AM, Okamoto TJ, Ichimoto K, Katsukawa Y, Suematsu Y, Tsuneta S, Lites BW, Shimizu T (2008) Hinode SOT observations of solar quiescent prominence dynamics. Astrophys J Lett 676:L89–L92. https://doi.org/10.1086/587171

Bonet JA, Márquez I, Sánchez Almeida J, Cabello I, Domingo V (2008) Convectively driven vortex flows in the sun. Astrophys J Lett 687(2):L131. https://doi.org/10.1086/593329. arXiv:0809.3885 [astro-ph]

Casini R, Bevilacqua R, López Ariste A (2005) Principal component analysis of the He I D3 polarization profiles from solar prominences. Astrophys J 622(2):1265–1274. https://doi.org/10.1086/428283

Casini R, López Ariste A, Paletou F, Léger L (2009) Multi-line Stokes inversion for prominence magnetic-field diagnostics. Astrophys J 703(1):114–120. https://doi.org/10.1088/0004-637X/703/1/114. arXiv:0906.2144 [astro-ph.IM]

Chae J (2010) Dynamics of vertical threads and descending knots in a hedgerow prominence. Astrophys J 714:618–629. https://doi.org/10.1088/0004-637X/714/1/618

Chae J, Moon YJ, Park YD (2005) The magnetic structure of filament barbs. Astrophys J 626:574–578. https://doi.org/10.1086/429797

Chen H, Zhang J, Ma S, Yan X, Xue J (2017) May. solar tornadoes triggered by interaction between filaments and EUV jets. Astrophys J Lett 841(1):L13. https://doi.org/10.3847/2041-8213/aa71a2

Chen H, Zhang J, De Pontieu B, Ma S, Kliem B, Priest E (2020) Coronal mini-jets in an activated solar tornado-like prominence. Astrophys J 899(1):19. https://doi.org/10.3847/1538-4357/ab9cad. arXiv:2006.08252 [astro-ph.SR]

Culhane JL, Harra LK, James AM, Al-Janabi K, Bradley LJ, Chaudry RA, Rees K, Tandy JA, Thomas P, Whillock MCR, Winter B, Doschek GA, Korendyke CM, Brown CM, Myers S, Mariska J, Seely J, Lang J, Kent BJ, Shaughnessy BM, Young PR, Simnett GM, Castelli CM, Mahmoud S, Mapson-Menard H, Probyn BJ, Thomas RJ, Davila J, Dere K, Windt D, Shea J, Hagood R, Moye R, Hara H, Watanabe T, Matsuzaki K, Kosugi T, Hansteen V, Wikstol Ø (2007) The EUV imaging spectrometer for hinode. Sol Phys 243:19–61. https://doi.org/10.1007/s01007-007-0293-1

De Pontieu B, Title AM, Lemen JR, Kushner GD, Akin DJ, Allard B, Berger T, Boerner P, Cheung M, Chou C, Drake JF, Duncan DW, Freeland S, Heyman GF, Hoffman C, Hurlburt NE, Lindgren RW, Mathur D, Rehse R, Sabolish D, Seguin R, Schrijver CJ, Tarbell TD, Wülser JP, Wolfson CJ, Yanari C, Mudge J, Nguyen-Phuc N, Timmons R, van Bezooijen R, Weingrod I, Brookner R, Butcher G, Dougherty B, Eder J, Knagenhjelm V, Larsen S, Mansir D, Phan L, Boyle P, Cheimets PN, DeLuca EE, Golub L, Gates R, Hertz E, McKillop S, Park S, Perry T, Podgorski WA, Reeves K, Saar S, Testa P, Tian H, Weber M, Dunn C, Eccles S, Jaeggli SA, Kankelborg CC, Mashburn K, Pust N, Springer L, Carvalho R, Kleint L, Marmie J, Mazmanian E, Pereira TMD, Sawyer S, Strong J, Worden SP, Carlsson M, Hansteen VH, Leenaarts J, Wiesmann M, Aloise J, Chu KC, Bush RI, Scherrer PH, Brekke P, Martinez-Sykora J, Lites BW, McIntosh SW, Uitenbroek H, Okamoto TJ, Gummin MA, Auker G, Jerram P, Pool P, Waltham N (2014) The Interface Region Imaging Spectrograph (IRIS). Sol Phys 289:2733–2779. https://doi.org/10.1007/s11207-014-0485-y

Delaboudinière JP, Artzner GE, Brunaud J, Gabriel AH, Hochedez JF, Millier F, Song XY, Au B, Dere KP, Howard RA, Kreplin R, Michels DJ, Moses JD, Defise JM, Jamar C, Rochus P, Chauvineau JP, Marioge JP, Catura RC, Lemen JR, Shing L, Stern RA, Gurman JB, Neupert WM, Maucherat A, Clette F, Cugnon P, van Dessel EL (1995) EIT: extreme-ultraviolet imaging telescope for the SOHO mission. Sol Phys 162:291–312. https://doi.org/10.1007/BF00733432

Dudík J, Aulanier G, Schmieder B, Bommier V, Roudier T (2008) Topological departures from translational invariance along a filament observed by THEMIS. Sol Phys 248:29–50. https://doi.org/10.1007/s11207-008-9155-2

Gibson S (2015) Coronal cavities: observations and implications for the magnetic environment of prominences. In: Vial J-C, Engvold O (eds) Solar prominences. Astrophysics and space science library, vol 415, p 323. Springer, Cham. https://doi.org/10.1007/978-3-319-10416-4_13

Gibson SE (2018) Solar prominences: theory and models. Fleshing out the magnetic skeleton. Living Rev Sol Phys 15:7. https://doi.org/10.1007/s41116-018-0016-2
Gilbert HR, Hansteen VH, Holzer TE (2002) Neutral atom diffusion in a partially ionized prominence plasma. Astrophys J 577(1):464–474. https://doi.org/10.1086/342165

Gilbert H, Kilper G, Alexander D (2007) Observational evidence supporting cross-field diffusion of neutral material in solar filaments. Astrophys J 671(1):978–989. https://doi.org/10.1086/522884

Gunár S, Mackay DH (2015a) 3D whole-prominence fine structure modeling. Astrophys J 803:64. https://doi.org/10.1088/0004-637X/803/2/64

Gunár S, Mackay DH (2015b) 3D whole-prominence fine structure modeling. II. Prominence evolution. Astrophys J 812:93. https://doi.org/10.1088/0004-637X/812/2/93

Gunár S, Heinzel P, Anzer U, Schmieder B (2008) On Lyman-line asymmetries in quiescent prominences. Astron Astrophys 490:307–313. https://doi.org/10.1051/0004-6361/200810127

Gunár S, Schwartz P, Schmieder B, Heinzel P, Anzer U (2010) Statistical comparison of the observed and synthetic hydrogen Lyman line profiles in solar prominences. Astron Astrophys 514:A43. https://doi.org/10.1051/0004-6361/200913411

Gunár S, Mein P, Schmieder B, Heinzel P, Mein N (2012) Dynamics of quiescent prominence fine structures analyzed by 2D non-LTE modelling of the Hα line. Astron Astrophys 543:A93. https://doi.org/10.1051/0004-6361/201218940

Gunár S, Mackay DH, Anzer U, Heinzel P (2013) Non-linear force-free magnetic dip models of quiescent prominence fine structures. Astron Astrophys 551:A3. https://doi.org/10.1051/0004-6361/201220597

Gunár S, Dudík J, Aulanier G, Schmieder B, Heinzel P (2018) Importance of the Hα visibility and projection effects for the interpretation of prominence fine-structure observations. Astrophys J 867:115. https://doi.org/10.3847/1538-4357/aae4e1

Gunár S, Heinzel P, Koza J, Schwartz P (2022) Large impact of the Mg II h and k incident radiation change on results of radiative transfer models and the importance of dynamics. Astrophys J 934(2):133. https://doi.org/10.3847/1538-4357/ac7397

Handy BN, Acton LW, Kankelborg CC, Wolfson CJ, Akin DJ, Bruner ME, Caravalho R, Catura RC, Chevalier R, Duncan DW, Edwards CG, Feinstein CN, Freeland SL, Friedlaender FM, Hoffmann CH, Hurlburt NE, Jurcevich BK, Katz NL, Kelly GA, Lemen JR, Levay M, Lindgren RW, Mathur DP, Meyer SB, Morrison SJ, Morrison MD, Nightingale RW, Pope TP, Rehse RA, Schrijver CJ, Shine RA, Shing L, Strong KT, Tarbell TD, Title AM, Torgerson DD, Golub L, Bookbinder JA, Caldwell D, Cheimets PN, Davis WN, Deluca EE, McMullen RA, Warren HP, Amato D, Fisher R, Maldonado H, Parkinson C (1999) The transition region and coronal explorer. Sol Phys 187(2):229–260. https://doi.org/10.1023/A:1005166902804

Heinzel P, Vial JC, Anzer U (2014) On the formation of Mg ii h and k lines in solar prominences. Astron Astrophys 564:A132. https://doi.org/10.1051/0004-6361/201322886

Heinzel P, Gunár S, Anzer U (2015a) Fast approximate radiative transfer method for visualizing the fine structure of prominences in the hydrogen Hα line. Astron Astrophys 579:A16. https://doi.org/10.1051/0004-6361/201525716

Heinzel P, Schmieder B, Mein N, Gunár S (2015b) Understanding the Mg II and Hα spectra in a highly dynamical solar prominence. Astrophys J 800:L13. https://doi.org/10.1088/2041-8205/800/1/L13

Jenkins JM, Keppens R (2022) Resolving the solar prominence/filament paradox using the magnetic Rayleigh-Taylor instability. Nat Astron. https://doi.org/10.1038/s41550-022-01705-z

Kaiser ML, Kucera TA, Davila JM, Cyr OCSt, Guhathakurta M, Christian E (2008) The STEREO mission: an introduction. Space Sci Rev 136(1–4):5–16. https://doi.org/10.1007/s11214-007-9277-0

Kosugi T, Matsuzaki K, Sakao T, Shimizu T, Sone Y, Tachikawa S, Hashimoto T, Minesugi K, Ohnishi A, Yamada T, Tsuneta S, Hara H, Ichimoto K, Suematsu Y, Shimojo M, Watanabe T, Shimada S, Davis JM, Hill LD, Owens JK, Title AM, Culhane JL, Harra LK, Doschek GA, Golub L (2007) The hinode (Solar-B) mission: an overview. Sol Phys 243:3–17. https://doi.org/10.1007/s11207-007-9014-6

Kucera TA, Andretta V, Poland AI (1998) Neutral hydrogen column depths in prominences using EUV absorption features. Sol Phys 183(1):107–121. https://doi.org/10.1023/A:1005077417572

Kucera TA, Ofman L, Tarbell TD (2018) Motions in prominence barbs observed on the solar limb. Astrophys J 859:121. https://doi.org/10.3847/1538-4357/aae90

Kupryakov YA, Kotrc P, Kashapova LK (2019) On the role of preflares in tornado-type prominences. Astron Astrophys Trans 31(2):177–182

Labrosse N, Heinzel P, Vial J, Kucera T, Parenti S, Gunár S, Schmieder B, Kilper G (2010) Physics of solar prominences: I: spectral diagnostics and non-LTE modelling. Space Sci Rev 151:243–332. https://doi.org/10.1007/s11214-010-9630-6. arXiv:1001.1620 [astro-ph.SR]

Lemen JR, Title AM, Akin DJ, Boerner PF, Chou C, Drake JF, Duncan DW, Edwards CG, Friedlaender FM, Heyman GF, Hurlburt NE, Katz NL, Kushner GD, Levay M, Lindgren RW, Mathur DP, McFeaters EL, Mitchell S, Rehse RA, Schrijver CJ, Springer LA, Stern RA, Tarbell TD, Wuelser JP, Wolfson CJ, Yanari C, Bookbinder JA, Cheimets PN, Caldwell D, Deluca EE, Gates R, Golub L, Park S, Podgorski WA, Bush RI, Scherrer PH, Gummin MA, Smith P, Auker G, Jerram P, Pool P, Soufli R, Windt DL,
Gilbert HR, Hansteen VH, Holzer TE (2002) Neutral atom diffusion in a partially ionized prominence plasma. Astrophys J 577(1):464–474. https://doi.org/10.1086/342165

Gilbert H, Kilper G, Alexander D (2007) Observational evidence supporting cross-field diffusion of neutral material in solar filaments. Astrophys J 671(1):978–989. https://doi.org/10.1086/522884

Gunár S, Mackay DH (2015a) 3D whole-prominence fine structure modeling. Astrophys J 803:64. https://doi.org/10.1088/0004-637X/803/2/64

Gunár S, Mackay DH (2015b) 3D whole-prominence fine structure modeling. II. Prominence evolution. Astrophys J 812:93. https://doi.org/10.1088/0004-637X/812/2/93

Gunár S, Heinzel P, Anzer U, Schmieder B (2008) On Lyman-line asymmetries in quiescent prominences. Astron Astrophys 490:307–313. https://doi.org/10.1051/0004-6361/200810127

Gunár S, Schwartz P, Schmieder B, Heinzel P, Anzer U (2010) Statistical comparison of the observed and synthetic hydrogen Lyman line profiles in solar prominences. Astron Astrophys 514:A43. https://doi.org/10.1051/0004-6361/200913411

Gunár S, Mein P, Schmieder B, Heinzel P, Mein N (2012) Dynamics of quiescent prominence fine structures analyzed by 2D non-LTE modelling of the Hα line. Astron Astrophys 543:A93. https://doi.org/10.1051/0004-6361/201218940

Gunár S, Mackay DH, Anzer U, Heinzel P (2013) Non-linear force-free magnetic dip models of quiescent prominence fine structures. Astron Astrophys 551:A3. https://doi.org/10.1051/0004-6361/201220597

Gunár S, Dudík J, Aulanier G, Schmieder B, Heinzel P (2018) Importance of the Hα visibility and projection effects for the interpretation of prominence fine-structure observations. Astrophys J 867:115. https://doi.org/10.3847/1538-4357/aae4e1

Gunár S, Heinzel P, Koza J, Schwartz P (2022) Large impact of the Mg II h and k incident radiation change on results of radiative transfer models and the importance of dynamics. Astrophys J 934(2):133. https://doi.org/10.3847/1538-4357/ac7397

Handy BN, Acton LW, Kankelborg CC, Wolfson CJ, Akin DJ, Bruner ME, Caravalho R, Catura RC, Chevalier R, Duncan DW, Edwards CG, Feinstein CN, Freeland SL, Friedlaender FM, Hoffmann CH, Hurlburt NE, Jurcevich BK, Katz NL, Kelly GA, Lemen JR, Levay M, Lindgren RW, Mathur DP, Meyer SB, Morrison SJ, Morrison MD, Nightingale RW, Pope TP, Rehse RA, Schrijver CJ, Shine RA, Shing L, Strong KT, Tarbell TD, Title AM, Torgerson DD, Golub L, Bookbinder JA, Caldwell D, Cheimets PN, Davis WN, Deluca EE, McMullen RA, Warren HP, Amato D, Fisher R, Maldonado H, Parkinson C (1999) The transition region and coronal explorer. Sol Phys 187(2):229–260. https://doi.org/10.1023/A:1005166902804

Heinzel P, Vial JC, Anzer U (2014) On the formation of Mg ii h and k lines in solar prominences. Astron Astrophys 564:A132. https://doi.org/10.1051/0004-6361/201322886

Heinzel P, Gunár S, Anzer U (2015a) Fast approximate radiative transfer method for visualizing the fine structure of prominences in the hydrogen Hα line. Astron Astrophys 579:A16. https://doi.org/10.1051/0004-6361/201525716

Heinzel P, Schmieder B, Mein N, Gunár S (2015b) Understanding the Mg II and Hα spectra in a highly dynamical solar prominence. Astrophys J 800:L13. https://doi.org/10.1088/2041-8205/800/1/L13

Jenkins JM, Keppens R (2022) Resolving the solar prominence/filament paradox using the magnetic Rayleigh-Taylor instability. Nat Astron. https://doi.org/10.1038/s41550-022-01705-z

Kaiser ML, Kucera TA, Davila JM, Cyr OCSt, Guhathakurta M, Christian E (2008) The STEREO mission: an introduction. Space Sci Rev 136(1–4):5–16. https://doi.org/10.1007/s11214-007-9277-0

Kosugi T, Matsuzaki K, Sakao T, Shimizu T, Sone Y, Tachikawa S, Hashimoto T, Minesugi K, Ohnishi A, Yamada T, Tsuneta S, Hara H, Ichimoto K, Suematsu Y, Shimojo M, Watanabe T, Shimada S, Davis JM, Hill LD, Owens JK, Title AM, Culhane JL, Harra LK, Doschek GA, Golub L (2007) The hinode (Solar-B) mission: an overview. Sol Phys 243:3–17. https://doi.org/10.1007/s11207-007-9014-6

Kucera TA, Andretta V, Poland AI (1998) Neutral hydrogen column depths in prominences using EUV absorption features. Sol Phys 183(1):107–121. https://doi.org/10.1023/A:1005077417572

Kucera TA, Ofman L, Tarbell TD (2018) Motions in prominence barbs observed on the solar limb. Astrophys J 859:121. https://doi.org/10.3847/1538-4357/aae90

Kupryakov YA, Kotrc P, Kashapova LK (2019) On the role of preflares in tornado-type prominences. Astron Astrophys Trans 31(2):177–182

Labrosse N, Heinzel P, Vial J, Kucera T, Parenti S, Gunár S, Schmieder B, Kilper G (2010) Physics of solar prominences: I: spectral diagnostics and non-LTE modelling. Space Sci Rev 151:243–332. https://doi.org/10.1007/s11214-010-9630-6. arXiv:1001.1620 [astro-ph.SR]

Lemen JR, Title AM, Akin DJ, Boerner PF, Chou C, Drake JF, Duncan DW, Edwards CG, Friedlaender FM, Heyman GF, Hurlburt NE, Katz NL, Kushner GD, Levay M, Lindgren RW, Mathur DP, McFeaters EL, Mitchell S, Rehse RA, Schrijver CJ, Springer LA, Stern RA, Tarbell TD, Wuelser JP, Wolfson CJ, Yanari C, Bookbinder JA, Cheimets PN, Caldwell D, Deluca EE, Gates R, Golub L, Park S, Podgorski WA, Bush RI, Scherrer PH, Gummin MA, Smith P, Auker G, Jerram P, Pool P, Soufli R, Windt DL,
Beardsley S, Clapp M, Lang J, Waltham N (2012) The Atmospheric Imaging Assembly (AIA) on the Solar Dynamics Observatory (SDO). Sol Phys 275:17–40. https://doi.org/10.1007/s11207-011-9776-8

Levens PJ (2018) Diagnostics of solar tornado-like prominences. Ph. D. thesis, University of Glasgow. http://theses.gla.ac.uk/id/eprint/8684

Levens PJ, Labrosse N, Fletcher L, Schmieder B (2015) A solar tornado observed by EIS. Plasma diagnostics. Astron Astrophys 582:A27. https://doi.org/10.1051/0004-6361/201425586. arXiv:1508.01377 [astro-ph.SR]

Levens PJ, Schmieder B, Labrosse N, López Ariste A (2016) Structure of prominence legs: plasma and magnetic field. Astrophys J 818:31. https://doi.org/10.3847/0004-637X/818/1/31. arXiv:1512.04727 [astro-ph.SR]

Levens PJ, Schmieder B, López Ariste A, Labrosse N, Dalmasse K, Gelly B (2016) Magnetic field in atypical prominence structures: bubble, tornado, and eruption. Astrophys J 826:164. https://doi.org/10.3847/0004-637X/826/2/164. arXiv:1605.05964 [astro-ph.SR]

Levens PJ, Labrosse N, Schmieder B, López Ariste A, Fletcher L (2017) Comparing UV/EUV line parameters and magnetic field in a quiescent prominence with tornadoes. Astron Astrophys 607:A16. https://doi.org/10.1051/0004-6361/201730808. arXiv:1708.04606 [astro-ph.SR]

Li K, Zhong S (1997) The observations and analyses of an eruptive prominence. Astron Astrophys Suppl Ser 126:241–245. https://doi.org/10.1051/aas:1997261

Li X, Morgan H, Leonard D, Jeska L (2012) A solar tornado observed by AIA/SDO: rotational flow and evolution of magnetic helicity in a prominence and cavity. Astrophys J Lett 752:L22. https://doi.org/10.1088/2041-8205/752/2/L22. arXiv:1205.3819 [astro-ph.SR]

Liakh V, Luna M, Khomenko E (2020) Numerical simulations of large-amplitude oscillations in flux rope solar prominences. Astron Astrophys 637:A75. https://doi.org/10.1051/0004-6361/201937083. arXiv:2003.04343 [astro-ph.SR]

Liakh V, Luna M, Khomenko E (2021) Large-amplitude longitudinal oscillations in solar prominences simulated with different resolutions. Astron Astrophys 654:A145. https://doi.org/10.1051/0004-6361/202141524. arXiv:2108.01143 [astro-ph.SR]

Lin Y, Engvold OR, Wiik JE (2003) Counterstreaming in a large polar crown filament. Sol Phys 216:109–120. https://doi.org/10.1023/A:1026150809598

Lin Y, Engvold O, Rouppe van der Voort L, Wiik JE, Berger TE (2005) Thin threads of solar filaments. Sol Phys 226:239–254. https://doi.org/10.1007/s11207-005-6876-3

Lin Y, Martin SF, Engvold O, Rouppe van der Voort LHM, van Noort M (2008) On small active region filaments, fibrils and surges. Adv Space Res 42:803–811. https://doi.org/10.1016/j.asr.2007.05.052

López Ariste A, Casini R (2005) Inference of the magnetic field in spicules from spectropolarimetry of He I D3. Astron Astrophys 436(1):325–331. https://doi.org/10.1051/0004-6361:20042214

López Ariste A, Aulanier G, Schmieder B, Sainz Dalda A (2006) First observation of bald patches in a filament channel and at a barb endpoint. Astron Astrophys 456(2):725–735. https://doi.org/10.1051/0004-6361:20064923

Luna M, Díaz AJ, Karpen J (2012) The effects of magnetic-field geometry on longitudinal oscillations of solar prominences. Astrophys J 757(1):98. https://doi.org/10.1088/0004-637X/757/1/98

Luna M, Karpen JT, DeVore CR (2012) Formation and evolution of a multi-threaded solar prominence. Astrophys J 746:30. https://doi.org/10.1088/0004-637X/746/1/30. arXiv:1201.3559 [astro-ph.SR]

Luna M, Moreno-Insertis F, Priest E (2015) Are tornado-like magnetic structures able to support solar prominence plasma? Astrophys J 808(1):L23. https://doi.org/10.1088/2041-8205/808/1/L23

Luna M, Terradas J, Khomenko E, Collados M, Vicente Ad (2016) On the robustness of the pendulum model for large-amplitude longitudinal oscillations in prominences. Astrophys J 817(2):157. https://doi.org/10.3847/0004-637X/817/2/157

Luna M, Karpen J, Ballester JL, Muglach K, Terradas J, Kucera T, Gilbert H (2018) GONG catalog of solar filament oscillations near solar maximum. Astrophys J Suppl Ser 236(2):35. https://doi.org/10.3847/1538-4365/aabde7. arXiv:1804.03743 [astro-ph.SR]

Luna M, Priest E, Moreno-Insertis F (2018) Self-similar approach for rotating magnetohydrodynamic solar and astrophysical structures. Astrophys J 863(2):147. https://doi.org/10.3847/1538-4357/aad093

Mackay DH, van Ballegooijen AA (2009) A non-linear force-free field model for the evolving magnetic structure of solar filaments. Sol Phys 260:321–346. https://doi.org/10.1007/s11207-009-9468-9

Mackay DH, Karpen JT, Ballester JL, Schmieder B, Aulanier G (2010) Physics of solar prominences: II—Magnetic structure and dynamics. Space Sci Rev 151:333–399. https://doi.org/10.1007/s11214-010-9628-0. arXiv:1001.1635 [astro-ph.SR]

Martínez González MJ, Manso Sainz R, Asensio Ramos A, Beck C, de la Cruz Rodríguez J, Díaz AJ (2015) Spectro-polarimetric imaging reveals helical magnetic fields in solar prominence feet. Astrophys J 802(1):3. https://doi.org/10.1088/0004-637X/802/1/3. arXiv:1501.03295 [astro-ph.SR]
Beardsley S, Clapp M, Lang J, Waltham N (2012) The Atmospheric Imaging Assembly (AIA) on the Solar Dynamics Observatory (SDO). Sol Phys 275:17–40. https://doi.org/10.1007/s11207-011-9776-8

Levens PJ (2018) Diagnostics of solar tornado-like prominences. Ph. D. thesis, University of Glasgow. http://theses.gla.ac.uk/id/eprint/8684

Levens PJ, Labrosse N, Fletcher L, Schmieder B (2015) A solar tornado observed by EIS. Plasma diagnostics. Astron Astrophys 582:A27. https://doi.org/10.1051/0004-6361/201425586. arXiv:1508.01377 [astro-ph.SR]

Levens PJ, Schmieder B, Labrosse N, López Ariste A (2016) Structure of prominence legs: plasma and magnetic field. Astrophys J 818:31. https://doi.org/10.3847/0004-637X/818/1/31. arXiv:1512.04727 [astro-ph.SR]

Levens PJ, Schmieder B, López Ariste A, Labrosse N, Dalmasse K, Gelly B (2016) Magnetic field in atypical prominence structures: bubble, tornado, and eruption. Astrophys J 826:164. https://doi.org/10.3847/0004-637X/826/2/164. arXiv:1605.05964 [astro-ph.SR]

Levens PJ, Labrosse N, Schmieder B, López Ariste A, Fletcher L (2017) Comparing UV/EUV line parameters and magnetic field in a quiescent prominence with tornadoes. Astron Astrophys 607:A16. https://doi.org/10.1051/0004-6361/201730808. arXiv:1708.04606 [astro-ph.SR]

Li K, Zhong S (1997) The observations and analyses of an eruptive prominence. Astron Astrophys Suppl Ser 126:241–245. https://doi.org/10.1051/aas:1997261

Li X, Morgan H, Leonard D, Jeska L (2012) A solar tornado observed by AIA/SDO: rotational flow and evolution of magnetic helicity in a prominence and cavity. Astrophys J Lett 752:L22. https://doi.org/10.1088/2041-8205/752/2/L22. arXiv:1205.3819 [astro-ph.SR]

Liakh V, Luna M, Khomenko E (2020) Numerical simulations of large-amplitude oscillations in flux rope solar prominences. Astron Astrophys 637:A75. https://doi.org/10.1051/0004-6361/201937083. arXiv:2003.04343 [astro-ph.SR]

Liakh V, Luna M, Khomenko E (2021) Large-amplitude longitudinal oscillations in solar prominences simulated with different resolutions. Astron Astrophys 654:A15. https://doi.org/10.1051/0004-6361/202141524. arXiv:2108.01143 [astro-ph.SR]

Lin Y, Engvold OR, Wiik JE (2003) Counterstreaming in a large polar crown filament. Sol Phys 216:109–120. https://doi.org/10.1023/A:1026150809598

Lin Y, Engvold O, Rouppe van der Voort L, Wiik JE, Berger TE (2005) Thin threads of solar filaments. Sol Phys 226:239–254. https://doi.org/10.1007/s11207-005-6876-3

Lin Y, Martin SF, Engvold O, Rouppe van der Voort LHM, van Noort M (2008) On small active region filaments, fibrils and surges. Adv Space Res 42:803–811. https://doi.org/10.1016/j.asr.2007.05.052

López Ariste A, Casini R (2005) Inference of the magnetic field in spicules from spectropolarimetry of He I D3. Astron Astrophys 436(1):325–331. https://doi.org/10.1051/0004-6361:20042214

López Ariste A, Aulanier G, Schmieder B, Sainz Dalda A (2006) First observation of bald patches in a filament channel and at a barb endpoint. Astron Astrophys 456(2):725–735. https://doi.org/10.1051/0004-6361:20064923

Luna M, Díaz AJ, Karpen J (2012) The effects of magnetic-field geometry on longitudinal oscillations of solar prominences. Astrophys J 757(1):98. https://doi.org/10.1088/0004-637X/757/1/98

Luna M, Karpen JT, DeVore CR (2012) Formation and evolution of a multi-threaded solar prominence. Astrophys J 746:30. https://doi.org/10.1088/0004-637X/746/1/30. arXiv:1201.3559 [astro-ph.SR]

Luna M, Moreno-Insertis F, Priest E (2015) Are tornado-like magnetic structures able to support solar prominence plasma? Astrophys J 808(1):L23. https://doi.org/10.1088/2041-8205/808/1/L23

Luna M, Terradas J, Khomenko E, Collados M, Vicente Ad (2016) On the robustness of the pendulum model for large-amplitude longitudinal oscillations in prominences. Astrophys J 817(2):157. https://doi.org/10.3847/0004-637X/817/2/157

Luna M, Karpen J, Ballester JL, Muglach K, Terradas J, Kucera T, Gilbert H (2018) GONG catalog of solar filament oscillations near solar maximum. Astrophys J Suppl Ser 236(2):35. https://doi.org/10.3847/1538-4365/aabde7. arXiv:1804.03743 [astro-ph.SR]

Luna M, Priest E, Moreno-Insertis F (2018) Self-similar approach for rotating magnetohydrodynamic solar and astrophysical structures. Astrophys J 863(2):147. https://doi.org/10.3847/1538-4357/aad093

Mackay DH, van Ballegooijen AA (2009) A non-linear force-free field model for the evolving magnetic structure of solar filaments. Sol Phys 260:321–346. https://doi.org/10.1007/s11207-009-9468-9

Mackay DH, Karpen JT, Ballester JL, Schmieder B, Aulanier G (2010) Physics of solar prominences: II—Magnetic structure and dynamics. Space Sci Rev 151:333–399. https://doi.org/10.1007/s11214-010-9628-0. arXiv:1001.1635 [astro-ph.SR]

Martínez González MJ, Manso Sainz R, Asensio Ramos A, Beck C, de la Cruz Rodríguez J, Díaz AJ (2015) Spectro-polarimetric imaging reveals helical magnetic fields in solar prominence feet. Astrophys J 802(1):3. https://doi.org/10.1088/0004-637X/802/1/3. arXiv:1501.03295 [astro-ph.SR]
Martínez González MJ, Asensio Ramos A, Arregui I, Collados M, Beck C, de la Cruz Rodríguez J (2016) On the magnetism and dynamics of prominence legs hosting tornadoes. Astrophys J 825:119. https://doi.org/10.3847/0004-637X/825/2/119. arXiv:1605.01183 [astro-ph.SR]

Mein P (1991) Solar 2D spectroscopy - a new MSDP instrument. Astron Astrophys 248:669-676

Mghebrishvili I, Zaqarashvili TV, Kukhianidze V, Ramishvili G, Shergelashvili B, Veronig A, Poedts S (2015) Dynamics of a solar prominence tornado observed by SDO/AIA on 2012 November 7-8. Astrophys J 810:89. https://doi.org/10.1088/0004-637X/810/2/89. arXiv:1508.06788 [astro-ph.SR]

Mghebrishvili I, Zaqarashvili TV, Kukhianidze V, Kuridze D, Tsiklauri D, Shergelashvili BM, Poedts S (2018) Association between tornadoes and instability of hosting prominences. Astrophys J 861(2):112. https://doi.org/10.3847/1538-4357/aac823. arXiv:1807.01345 [astro-ph.SR]

Müller D, Cyr OCSt, Zouganelis I, Gilbert HR, Marsden R, Nieves-Chinchilla T, Antonucci E, Auchère F, Berghmans D, Horbury TS, Howard RA, Krucker S, Maksimovic M, Owen CJ, Rochus P, Rodriguez-Pacheco J, Romoli M, Solanki SK, Bruno R, Carlsson M, Fludra A, Harra L, Hassler DM, Livi S, Louarn P, Peter H, Schühle U, Teriaca L, del Toro Iniesta JC, Wimmer-Schweingruber RF, Marsch E, Velli M, De Groof A, Walsh A, Williams D (2020) The Solar Orbiter mission. Science overview. Astron Astrophys 642:A1. https://doi.org/10.1051/0004-6361/202038467. arXiv:2009.00861 [astro-ph.SR]

Nicholson SB (1944) A tornado prominence, June 19, 1944. Publ Astron Soc Pac 56:162. https://doi.org/10.1086/125642

Ofman L, Knizhnik K, Kucera T, Schmieder B (2015) Nonlinear MHD waves in a prominence foot. Astrophys J 813:124. https://doi.org/10.1088/0004-637X/813/2/124. arXiv:1509.07911 [astro-ph.SR]

Öhman Y (1969) Observations of rotational motion in prominences. Sol Phys 9:427-431. https://doi.org/10.1007/BF02391666

Okamoto TJ, Tsuneta S, Berger TE, Ichimoto K, Katsukawa Y, Lites BW, Nagata S, Shibata K, Shimizu T, Shine RA, Suematsu Y, Tarbell TD, Title AM (2007) Coronal transverse magnetohydrodynamic waves in a solar prominence. Science 318:1577. https://doi.org/10.1126/science.1145447. arXiv:0801.1958

Okamoto TJ, Antolin P, De Pontieu B, Uitenbroek H, Van Doorsselaere T, Yokoyama T (2015) Resonant absorption of transverse oscillations and associated heating in a solar prominence. I. Observational aspects. Astrophys J 809:71. https://doi.org/10.1088/0004-637X/809/1/71. arXiv:1506.08965 [astro-ph.SR]

Okamoto TJ, Liu W, Tsuneta S (2016) Helical motions of fine-structure prominence threads observed by hinode and IRIS. Astrophys J 831(2):126. https://doi.org/10.3847/0004-637X/831/2/126. arXiv:1608.00123 [astro-ph.SR]

Orozco Suárez D, Ramos AA, Trujillo Bueno J (2012) Evidence for rotational motions in the feet of a quiescent solar prominence. Astrophys J Lett 761:L25. https://doi.org/10.1088/2041-8205/761/2/L25. arXiv:1211.6980 [astro-ph.SR]

Panasenco O, Martin SF, Velli M (2014) Apparent solar tornado-like prominences. Sol Phys 289:603-622. https://doi.org/10.1007/s11207-013-0337-1. arXiv:1307.2303 [astro-ph.SR]

Panesar NK, Innes DE, Tiwari SK, Low BC (2013) A solar tornado triggered by flares? Astron Astrophys 549:A105. https://doi.org/10.1051/0004-6361/201220503

Parenti S (2014) Solar Prominences: Observations. Living Rev Sol Phys 11:1. https://doi.org/10.12942/lrsp-2014-1

Pesnell WD, Thompson BJ, Chamberlin PC (2012) The Solar Dynamics Observatory (SDO). Sol Phys 275(1-2):3-15. https://doi.org/10.1007/s11207-011-9841-3

Pettit E (1919) The great eruptive prominences of May 29 and July 15, 1919. Astrophys J 50:206. https://doi.org/10.1086/142496

Pettit E (1925) The forms and motions of the solar prominences. Publications of the Yerkes Observatory 3:4-iii-XXXVII.1

Pettit E (1932) Characteristic features of solar prominences. Astrophys J 76:9. https://doi.org/10.1086/143396

Pettit E (1941) The rotation of a tornado prominence. Publ Astron Soc Pac 53:289. https://doi.org/10.1086/125348

Pettit E (1943) The properties of solar prominences as related to type. In: Contributions from the Mount Wilson Observatory/Carnegie Institution of Washington, vol 679, pp 1-14

Pettit E (1946) Rotation of tornado prominences determined by Doppler effect. Publ Astron Soc Pac 58:150. https://doi.org/10.1086/125796

Pettit E (1950) The evidence for tornado prominences. Publ Astron Soc Pac 62:144. https://doi.org/10.1086/126261

Pike CD, Mason HE (1998) Rotating transition region features observed with the SOHO coronal diagnostic spectrometer. Sol Phys 182:333-348. https://doi.org/10.1023/A:1005065704108

Richardson RS (1940) A tornado prominence of record height. Publ Astron Soc Pac 52:326. https://doi.org/10.1086/125211
Martínez González MJ, Asensio Ramos A, Arregui I, Collados M, Beck C, de la Cruz Rodríguez J (2016) On the magnetism and dynamics of prominence legs hosting tornadoes. Astrophys J 825:119. https://doi.org/10.3847/0004-637X/825/2/119. arXiv:1605.01183 [astro-ph.SR]

Mein P (1991) Solar 2D spectroscopy - a new MSDP instrument. Astron Astrophys 248:669-676

Mghebrishvili I, Zaqarashvili TV, Kukhianidze V, Ramishvili G, Shergelashvili B, Veronig A, Poedts S (2015) Dynamics of a solar prominence tornado observed by SDO/AIA on 2012 November 7-8. Astrophys J 810:89. https://doi.org/10.1088/0004-637X/810/2/89. arXiv:1508.06788 [astro-ph.SR]

Mghebrishvili I, Zaqarashvili TV, Kukhianidze V, Kuridze D, Tsiklauri D, Shergelashvili BM, Poedts S (2018) Association between tornadoes and instability of hosting prominences. Astrophys J 861(2):112. https://doi.org/10.3847/1538-4357/aac823. arXiv:1807.01345 [astro-ph.SR]

Müller D, Cyr OCSt, Zouganelis I, Gilbert HR, Marsden R, Nieves-Chinchilla T, Antonucci E, Auchère F, Berghmans D, Horbury TS, Howard RA, Krucker S, Maksimovic M, Owen CJ, Rochus P, Rodriguez-Pacheco J, Romoli M, Solanki SK, Bruno R, Carlsson M, Fludra A, Harra L, Hassler DM, Livi S, Louarn P, Peter H, Schühle U, Teriaca L, del Toro Iniesta JC, Wimmer-Schweingruber RF, Marsch E, Velli M, De Groof A, Walsh A, Williams D (2020) The Solar Orbiter mission. Science overview. Astron Astrophys 642:A1. https://doi.org/10.1051/0004-6361/202038467. arXiv:2009.00861 [astro-ph.SR]

Nicholson SB (1944) A tornado prominence, June 19, 1944. Publ Astron Soc Pac 56:162. https://doi.org/10.1086/125642

Ofman L, Knizhnik K, Kucera T, Schmieder B (2015) Nonlinear MHD waves in a prominence foot. Astrophys J 813:124. https://doi.org/10.1088/0004-637X/813/2/124. arXiv:1509.07911 [astro-ph.SR]

Öhman Y (1969) Observations of rotational motion in prominences. Sol Phys 9:427-431. https://doi.org/10.1007/BF02391666

Okamoto TJ, Tsuneta S, Berger TE, Ichimoto K, Katsukawa Y, Lites BW, Nagata S, Shibata K, Shimizu T, Shine RA, Suematsu Y, Tarbell TD, Title AM (2007) Coronal transverse magnetohydrodynamic waves in a solar prominence. Science 318:1577. https://doi.org/10.1126/science.1145447. arXiv:0801.1958

Okamoto TJ, Antolin P, De Pontieu B, Uitenbroek H, Van Doorsselaere T, Yokoyama T (2015) Resonant absorption of transverse oscillations and associated heating in a solar prominence. I. Observational aspects. Astrophys J 809:71. https://doi.org/10.1088/0004-637X/809/1/71. arXiv:1506.08965 [astro-ph.SR]

Okamoto TJ, Liu W, Tsuneta S (2016) Helical motions of fine-structure prominence threads observed by hinode and IRIS. Astrophys J 831(2):126. https://doi.org/10.3847/0004-637X/831/2/126. arXiv:1608.00123 [astro-ph.SR]

Orozco Suárez D, Ramos AA, Trujillo Bueno J (2012) Evidence for rotational motions in the feet of a quiescent solar prominence. Astrophys J Lett 761:L25. https://doi.org/10.1088/2041-8205/761/2/L25. arXiv:1211.6980 [astro-ph.SR]

Panasenco O, Martin SF, Velli M (2014) Apparent solar tornado-like prominences. Sol Phys 289:603-622. https://doi.org/10.1007/s11207-013-0337-1. arXiv:1307.2303 [astro-ph.SR]

Panesar NK, Innes DE, Tiwari SK, Low BC (2013) A solar tornado triggered by flares? Astron Astrophys 549:A105. https://doi.org/10.1051/0004-6361/201220503

Parenti S (2014) Solar Prominences: Observations. Living Rev Sol Phys 11:1. https://doi.org/10.12942/lrsp-2014-1

Pesnell WD, Thompson BJ, Chamberlin PC (2012) The Solar Dynamics Observatory (SDO). Sol Phys 275(1-2):3-15. https://doi.org/10.1007/s11207-011-9841-3

Pettit E (1919) The great eruptive prominences of May 29 and July 15, 1919. Astrophys J 50:206. https://doi.org/10.1086/142496

Pettit E (1925) The forms and motions of the solar prominences. Publications of the Yerkes Observatory 3:4-iii-XXXVII.1

Pettit E (1932) Characteristic features of solar prominences. Astrophys J 76:9. https://doi.org/10.1086/143396

Pettit E (1941) The rotation of a tornado prominence. Publ Astron Soc Pac 53:289. https://doi.org/10.1086/125348

Pettit E (1943) The properties of solar prominences as related to type. In: Contributions from the Mount Wilson Observatory/Carnegie Institution of Washington, vol 679, pp 1-14

Pettit E (1946) Rotation of tornado prominences determined by Doppler effect. Publ Astron Soc Pac 58:150. https://doi.org/10.1086/125796

Pettit E (1950) The evidence for tornado prominences. Publ Astron Soc Pac 62:144. https://doi.org/10.1086/126261

Pike CD, Mason HE (1998) Rotating transition region features observed with the SOHO coronal diagnostic spectrometer. Sol Phys 182:333-348. https://doi.org/10.1023/A:1005065704108

Richardson RS (1940) A tornado prominence of record height. Publ Astron Soc Pac 52:326. https://doi.org/10.1086/125211
Rochus P, Auchère F, Berghmans D, Harra L, Schmutz W, Schühle U, Addison P, Appourchaux T, Aznar Cuadrado R, Baker D, Barbay J, Bates D, BenMoussa A, Bergmann M, Beurthe C, Borgo B, Bonte K, Bouzit M, Bradley L, Büchel V, Buchlin E, Büchner S, Cabé F, Cadiergues L, Chaigneau M, Chares B, Choque Cortez C, Coker P, Condamin M, Coumar S, Curdt W, Cutler J, Davies D, Davison G, Defise JM, Del Zanna G, Delmotte F, Delouille V, Dolla L, Dumesnil C, Dürig F, Enge R, François S, Fourmond JJ, Gillis JM, Giordanengo B, Gissot S, Green LM, Guerreiro N, Guilbaud A, Gyo M, Haberreiter M, Hafiz A, Hailey M, Halain JP, Hansotte J, Hecquet C, Heerlein K, Hellin ML, Hemsley S, Hermans A, Hervier V, Hochedez JF, Houbrechts Y, Ihsan K, Jacques L, Jérôme A, Jones J, Kahle M, Kennedy T, Klaproth M, Kolleck M, Koller S, Kotsialos E, Kraaijkamp E, Langer P, Lawrenson A, Le Clech' JC, Lenaerts C, Liebecq S, Linder D, Long DM, Mampaey B, Markiewicz-Innes DM, Marquet B, Marsch E, Matthews S, Mazy E, Mazzoli A, Meining S, Meltchakov E, Mercier R, Meyer S, Monecke M, Monfort F, Morinaud G, Moron F, Mountney L, Müller R, Nicula B, Parenti S, Peter H, Pfiffner D, Philippon A, Phillips I, Plesseria JY, Pylyser E, Rabecki F, Ravet-Krill MF, Rebellato J, Renotte E, Rodriguez L, Roosevelt S, Rosin J, Rossi L, Roth P, Rouesnel F, Roullay M, Rousseau A, Ruane K, Scanlan J, Schlatter P, Seaton DB, Silliman K, Smit S, Smith PJ, Solanki SK, Spescha M, Spencer A, Stegen K, Stockman Y, Szwec N, Tamiatto C, Tandy J, Teriaca L, Theobald C, Tychon I, van Driel-Gesztelyi L, Verbeeck C, Vial JC, Werner S, West MJ, Westwood D, Wiegelmann T, Willis G, Winter B, Zerr A, Zhang X, Zhukov AN (2020) The solar orbiter EUI instrument: the extreme ultraviolet imager. Astron Astrophys 642:A8. https://doi.org/10.1051/0004-6361/201936663

Rompolt B (1975) Spectral features to be expected from rotational and expansive motions in fine solar structures. Sol Phys 41(2):329-348. https://doi.org/10.1007/BF00154070

Ruan G, Schmieder B, Mein P, Mein N, Labrosse N, Gunár S, Chen Y (2018) On the dynamic nature of a quiescent prominence observed by IRIS and MSDP spectrographs. Astrophys J 865:123. https://doi.org/10.3847/1538-4357/aada08

Scharmer GB, Bjelksko J, Korhonen TK, Lindberg B, Petterson B (2003) The 1-meter Swedish solar telescope. In: Keil SL, Avakyan SV (eds) Innovative telescopes and instrumentation for solar astrophysics. Society of photo-optical instrumentation engineers (SPIE) conference series, vol 4853, pp 341-350

Scherrer PH, Schou J, Bush RI, Kosovichev AG, Bogart RS, Hoeksema JT, Liu Y, Duvall TL, Zhao J, Title AM, Schrijver CJ, Tarbell TD, Tomczyk S (2012) The Helioseismic and Magnetic Imager (HMI) Investigation for the Solar Dynamics Observatory (SDO). Sol Phys 275(1-2):207-227. https://doi.org/10.1007/s11207-011-9834-2

Schmahl EJ, Orrall FQ (1979) Evidence for continuum absorption above the quiet sun transition region. Astrophys J Lett 231:L41-L44. https://doi.org/10.1086/183001

Schmieder B, Raadu MA, Wiik JE (1991) Fine structure of solar filaments. II - Dynamics of threads and footpoints. Astron Astrophys 252:353-365

Schmieder B, Lin Y, Heinzel P, Schwartz P (2004) Multi-wavelength study of a high-latitude EUV filament. Sol Phys 221(2):297-323. https://doi.org/10.1023/B:SOLA.0000035059.50427.68

Schmieder B, Chandra R, Berlicki A, Mein P (2010) Velocity vectors of a quiescent prominence observed by Hinode/SOT and the MSDP (Meudon). Astron Astrophys 514:A68. https://doi.org/10.1051/0004-6361/200913477. arXiv:0911.5091 [astro-ph.SR]

Schmieder B, Kucera TA, Knizhnik K, Luna M, Lopez-Ariste A, Toot D (2013) Propagating waves transverse to the magnetic field in a solar prominence. Astrophys J 777:108. https://doi.org/10.1088/0004-637X/777/2/108. arXiv:1309.1568 [astro-ph.SR]

Schmieder B, Malherbe JM, Wu ST (eds) (2014) Nature of prominences and their role in space weather. IAU symposium, vol 300. Cambridge University Press

Schmieder B, Tian H, Kucera T, López Ariste A, Mein N, Mein P, Dalmasse K, Golub L (2014) Open questions on prominences from coordinated observations by IRIS, Hinode, SDO/AIA, THEMIS, and the Meudon/MSDP. Astron Astrophys 569:A85. https://doi.org/10.1051/0004-6361/201423922. arXiv:1407.3171 [astro-ph.SR]

Schmieder B, Mein P, Mein N, Levens PJ, Labrosse N, Ofman L (2017) Hα Doppler shifts in a tornado in the solar corona. Astron Astrophys 597:A109. https://doi.org/10.1051/0004-6361/201628771. arXiv:1612.02232 [astro-ph.SR]

Schmieder B, Zapiór M, López Ariste A, Levens P, Labrosse N, Gravet R (2017) Reconstruction of a helical prominence in 3D from IRIS spectra and images. Astron Astrophys 606:A30. https://doi.org/10.1051/0004-6361/201730839. arXiv:1706.08078 [astro-ph.SR]

Secchi PA (1877) Le Soleil, vol 2. Paris, Gauthier-Villars

Silva SSA, Fedun V, Verth G, Rempel EL, Shelyag S (2020) Solar vortex tubes: vortex dynamics in the solar atmosphere. Astrophys J 898(2):137. https://doi.org/10.3847/1538-4357/ab99a9. arXiv:2007.04371 [astro-ph.SR]

Silva SSA, Verth G, Rempel EL, Shelyag S, Schiavo LACA, Fedun V (2021) Solar vortex tubes. II. On the origin of magnetic vortices. Astrophys J 915(1):24. https://doi.org/10.3847/1538-4357/abfec2
Rochus P, Auchère F, Berghmans D, Harra L, Schmutz W, Schühle U, Addison P, Appourchaux T, Aznar Cuadrado R, Baker D, Barbay J, Bates D, BenMoussa A, Bergmann M, Beurthe C, Borgo B, Bonte K, Bouzit M, Bradley L, Büchel V, Buchlin E, Büchner S, Cabé F, Cadiergues L, Chaigneau M, Chares B, Choque Cortez C, Coker P, Condamin M, Coumar S, Curdt W, Cutler J, Davies D, Davison G, Defise JM, Del Zanna G, Delmotte F, Delouille V, Dolla L, Dumesnil C, Dürig F, Enge R, François S, Fourmond JJ, Gillis JM, Giordanengo B, Gissot S, Green LM, Guerreiro N, Guilbaud A, Gyo M, Haberreiter M, Hafiz A, Hailey M, Halain JP, Hansotte J, Hecquet C, Heerlein K, Hellin ML, Hemsley S, Hermans A, Hervier V, Hochedez JF, Houbrechts Y, Ihsan K, Jacques L, Jérôme A, Jones J, Kahle M, Kennedy T, Klaproth M, Kolleck M, Koller S, Kotsialos E, Kraaijkamp E, Langer P, Lawrenson A, Le Clech' JC, Lenaerts C, Liebecq S, Linder D, Long DM, Mampaey B, Markiewicz-Innes DM, Marquet B, Marsch E, Matthews S, Mazy E, Mazzoli A, Meining S, Meltchakov E, Mercier R, Meyer S, Monecke M, Monfort F, Morinaud G, Moron F, Mountney L, Müller R, Nicula B, Parenti S, Peter H, Pfiffner D, Philippon A, Phillips I, Plesseria JY, Pylyser E, Rabecki F, Ravet-Krill MF, Rebellato J, Renotte E, Rodriguez L, Roosevelt S, Rosin J, Rossi L, Roth P, Rouesnel F, Roulliy M, Rousseau A, Ruane K, Scanlan J, Schlatter P, Seaton DB, Silliman K, Smit S, Smith PJ, Solanki SK, Spescha M, Spencer A, Stegen K, Stockman Y, Szwec N, Tamiatto C, Tandy J, Teriaca L, Theobald C, Tychon I, van Driel-Gesztelyi L, Verbeeck C, Vial JC, Werner S, West MJ, Westwood D, Wiegelmann T, Willis G, Winter B, Zerr A, Zhang X, Zhukov AN (2020) The solar orbiter EUI instrument: the extreme ultraviolet imager. Astron Astrophys 642:A8. https://doi.org/10.1051/0004-6361/201936663

Rompolt B (1975) Spectral features to be expected from rotational and expansive motions in fine solar structures. Sol Phys 41(2):329-348. https://doi.org/10.1007/BF00154070

Ruan G, Schmieder B, Mein P, Mein N, Labrosse N, Gunár S, Chen Y (2018) On the dynamic nature of a quiescent prominence observed by IRIS and MSDP spectrographs. Astrophys J 865:123. https://doi.org/10.3847/1538-4357/aada08

Scharmer GB, Bjelksko J, Korhonen TK, Lindberg B, Petterson B (2003) The 1-meter Swedish solar telescope. In: Keil SL, Avakyan SV (eds) Innovative telescopes and instrumentation for solar astrophysics. Society of photo-optical instrumentation engineers (SPIE) conference series, vol 4853, pp 341-350

Scherrer PH, Schou J, Bush RI, Kosovichev AG, Bogart RS, Hoeksema JT, Liu Y, Duvall TL, Zhao J, Title AM, Schrijver CJ, Tarbell TD, Tomczyk S (2012) The Helioseismic and Magnetic Imager (HMI) Investigation for the Solar Dynamics Observatory (SDO). Sol Phys 275(1-2):207-227. https://doi.org/10.1007/s11207-011-9834-2

Schmahl EJ, Orrall FQ (1979) Evidence for continuum absorption above the quiet sun transition region. Astrophys J Lett 231:L41-L44. https://doi.org/10.1086/183001

Schmieder B, Raadu MA, Wiik JE (1991) Fine structure of solar filaments. II - Dynamics of threads and footpoints. Astron Astrophys 252:353-365

Schmieder B, Lin Y, Heinzel P, Schwartz P (2004) Multi-wavelength study of a high-latitude EUV filament. Sol Phys 221(2):297-323. https://doi.org/10.1023/B:SOLA.0000035059.50427.68

Schmieder B, Chandra R, Berlicki A, Mein P (2010) Velocity vectors of a quiescent prominence observed by Hinode/SOT and the MSDP (Meudon). Astron Astrophys 514:A68. https://doi.org/10.1051/0004-6361/200913477. arXiv:0911.5091 [astro-ph.SR]

Schmieder B, Kucera TA, Knizhnik K, Luna M, Lopez-Ariste A, Toot D (2013) Propagating waves transverse to the magnetic field in a solar prominence. Astrophys J 777:108. https://doi.org/10.1088/0004-637X/777/2/108. arXiv:1309.1568 [astro-ph.SR]

Schmieder B, Malherbe JM, Wu ST (eds) (2014) Nature of prominences and their role in space weather. IAU symposium, vol 300. Cambridge University Press

Schmieder B, Tian H, Kucera T, López Ariste A, Mein N, Mein P, Dalmasse K, Golub L (2014) Open questions on prominences from coordinated observations by IRIS, Hinode, SDO/AIA, THEMIS, and the Meudon/MSDP. Astron Astrophys 569:A85. https://doi.org/10.1051/0004-6361/201423922. arXiv:1407.3171 [astro-ph.SR]

Schmieder B, Mein P, Mein N, Levens PJ, Labrosse N, Ofman L (2017) Hα Doppler shifts in a tornado in the solar corona. Astron Astrophys 597:A109. https://doi.org/10.1051/0004-6361/201628771. arXiv:1612.02232 [astro-ph.SR]

Schmieder B, Zapiór M, López Ariste A, Levens P, Labrosse N, Gravet R (2017) Reconstruction of a helical prominence in 3D from IRIS spectra and images. Astron Astrophys 606:A30. https://doi.org/10.1051/0004-6361/201730839. arXiv:1706.08078 [astro-ph.SR]

Secchi PA (1877) Le Soleil, vol 2. Paris, Gauthier-Villars

Silva SSA, Fedun V, Verth G, Rempel EL, Shelyag S (2020) Solar vortex tubes: vortex dynamics in the solar atmosphere. Astrophys J 898(2):137. https://doi.org/10.3847/1538-4357/ab99a9. arXiv:2007.04371 [astro-ph.SR]

Silva SSA, Verth G, Rempel EL, Shelyag S, Schiavo LACA, Fedun V (2021) Solar vortex tubes. II. On the origin of magnetic vortices. Astrophys J 915(1):24. https://doi.org/10.3847/1538-4357/abfec2
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Suematsu Y, Tsuneta S, Ichimoto K, Shimizu T, Otsubo M, Katsukawa Y, Nakagiri M, Noguchi M, Tamura T, Kato Y, Hara H, Kubo M, Mikami I, Saito H, Matsushita T, Kawaguchi N, Nakaoji T, Nagae K, Shimada S, Takeyama N, Yamamuro T (2008) The Solar Optical Telescope of Solar-B (Hinode): the optical telescope assembly. Sol Phys 249:197-220. https://doi.org/10.1007/s11207-008-9129-4

Tei A, Gunár S, Heinzel P, Okamoto TJ, Štěpán J, Ječič S, Shibata K (2020) IRIS Mg II observations and non-LTE modeling of off-limb spicules in a solar polar coronal hole. Astrophys J 888(1):42. https://doi.org/10.3847/1538-4357/ab5db1. arXiv:1911.12243 [astro-ph.SR]

Tripathi D, Isobe H, Jain R (2009) Large amplitude oscillations in prominences. Space Sci Rev 149:283-298. https://doi.org/10.1007/s11214-009-9583-9. arXiv:0910.4059 [astro-ph.SR]

Tsuneta S, Ichimoto K, Katsukawa Y, Nagata S, Otsubo M, Shimizu T, Suematsu Y, Nakagiri M, Noguchi M, Tarbell T, Title A, Shine R, Rosenberg W, Hoffmann C, Jurcevich B, Kushner G, Levay M, Lites B, Elmore D, Matsushita T, Kawaguchi N, Saito H, Mikami I, Hill LD, Owens JK (2008) The solar optical telescope for the hinode mission: an overview. Sol Phys 249:167-196. https://doi.org/10.1007/s11207-008-9174-z. arXiv:0711.1715

Tziotziou K, Tsiropoula G, Kontogiannis I, Scullion E, Doyle JG (2018) A persistent quiet-sun small-scale tornado. I. Characteristics and dynamics. Astron Astrophys 618:A51. https://doi.org/10.1051/0004-6361/201833101

Tziotziou K, Scullion E, Shelyag S, Steiner O, Khomenko E, Tsiropoula G, Canivete Cuissa JR, Wedemeyer S, Kontogiannis I, Yadav N, Kitiashvili IN, Skirvin SJ, Dakanalis I, Kosovichev AG, Fedun V (2023) Vortex motions in the solar atmosphere. Space Sci Rev 219(1):1. https://doi.org/10.1007/s11214-022-00946-8

Vial JC, Engvold O (eds) (2015) Solar prominences. Astrophysics and space science library, vol 415. Springer, Cham. https://doi.org/10.1007/978-3-319-10416-4

Wang W, Liu R, Wang Y (2017) January. Tornado-like evolution of a kink-unstable solar prominence. Astrophys J 834(1):38. https://doi.org/10.3847/1538-4357/834/1/38. arXiv:1611.04667 [astro-ph.SR]

Warren HP, Brooks DH, Ugarte-Urra I, Reep JW, Crump NA, Doschek GA (2018) Spectroscopic observations of current sheet formation and evolution. Astrophys J 854:122. https://doi.org/10.3847/1538-4357/aaa9b8. arXiv:1711.10826 [astro-ph.SR]

Wedemeyer S, Steiner O (2014) On the plasma flow inside magnetic tornadoes on the Sun. Publ Astron Soc Jpn 66:S10. https://doi.org/10.1093/pasj/psu086. arXiv:1406.7270 [astro-ph.SR]

Wedemeyer S, Scullion E, Rouppe van der Voort L, Bosnjak A, Antolin P (2013) Are giant tornadoes the legs of solar prominences? Astrophys J 774:123. https://doi.org/10.1088/0004-637X/774/2/123

Wedemeyer S, Scullion E, Steiner O, de la Cruz Rodriguez J, Rouppe van der Voort LHM (2013) Magnetic tornadoes and chromospheric swirls - definition and classification. J Phys Conf Ser 440(1):012005. https://doi.org/10.1088/1742-6596/440/1/012005. arXiv:1303.0179 [astro-ph.SR]

Wedemeyer-Böhm S, Scullion E, Steiner O, Rouppe van der Voort L, de La Cruz Rodriguez J, Fedun V, Erdélyi R (2012) Magnetic tornadoes as energy channels into the solar corona. Nature 486:505-508. https://doi.org/10.1038/nature11202

Yadav N, Cameron RH, Solanki SK (2020) Simulations show that vortex flows could heat the chromosphere in solar plage. Astrophys J Lett 894(2):L17. https://doi.org/10.3847/2041-8213/ab8dc5. arXiv:2004.13996 [astro-ph.SR]

Yadav N, Cameron RH, Solanki SK (2021) Vortex flow properties in simulations of solar plage region: evidence for their role in chromospheric heating. Astron Astrophys 645:A3. https://doi.org/10.1051/0004-6361/202038965. arXiv:2010.14971 [astro-ph.SR]

Yang Z, Tian H, Peter H, Su Y, Samanta T, Zhang J, Chen Y (2018) Two solar tornadoes observed with the interface region imaging spectrograph. Astrophys J 852:79. https://doi.org/10.3847/1538-4357/aa9e04. arXiv:1711.08968 [astro-ph.SR]

Young PR, O'Dwyer B, Mason HE (2012) Velocity measurements for a solar active region fan loop from Hinde/EIS Observations. Astrophys J 744:14. https://doi.org/10.1088/0004-637X/744/1/14. arXiv:1107.2362 [astro-ph.SR]

Zapiór M, Martínez-Gómez D (2016) Direct detection of the helical magnetic field geometry from 3D reconstruction of prominence knot trajectories. Astrophys J 817:123. https://doi.org/10.3847/0004-637X/817/2/123

Zapiór M, Rudawy P (2012) Estimation of solar prominence magnetic fields based on the reconstructed 3D trajectories of prominence knots. Sol Phys 280:445-456. https://doi.org/10.1007/s11207-012-0072-z. arXiv:1207.2005 [astro-ph.SR]
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Su Y, Gömöry P, Veronig A, Temmer M, Wang T, Vanninathan K, Gan W, Li Y (2014) Solar magnetized tornadoes: rotational motion in a tornado-like prominence. Astrophys J Lett 785:L2. https://doi.org/10.1088/2041-8205/785/1/L2. arXiv:1312.5226 [astro-ph.SR]

Suematsu Y, Tsuneta S, Ichimoto K, Shimizu T, Otsubo M, Katsukawa Y, Nakagiri M, Noguchi M, Tamura T, Kato Y, Hara H, Kubo M, Mikami I, Saito H, Matsushita T, Kawaguchi N, Nakaoji T, Nagae K, Shimada S, Takeyama N, Yamamuro T (2008) The Solar Optical Telescope of Solar-B (Hinode): the optical telescope assembly. Sol Phys 249:197-220. https://doi.org/10.1007/s11207-008-9129-4

Tei A, Gunár S, Heinzel P, Okamoto TJ, Štěpán J, Ječič S, Shibata K (2020) IRIS Mg II observations and non-LTE modeling of off-limb spicules in a solar polar coronal hole. Astrophys J 888(1):42. https://doi.org/10.3847/1538-4357/ab5db1. arXiv:1911.12243 [astro-ph.SR]

Tripathi D, Isobe H, Jain R (2009) Large amplitude oscillations in prominences. Space Sci Rev 149:283-298. https://doi.org/10.1007/s11214-009-9583-9. arXiv:0910.4059 [astro-ph.SR]

Tsuneta S, Ichimoto K, Katsukawa Y, Nagata S, Otsubo M, Shimizu T, Suematsu Y, Nakagiri M, Noguchi M, Tarbell T, Title A, Shine R, Rosenberg W, Hoffmann C, Jurcevich B, Kushner G, Levay M, Lites B, Elmore D, Matsushita T, Kawaguchi N, Saito H, Mikami I, Hill LD, Owens JK (2008) The solar optical telescope for the hinode mission: an overview. Sol Phys 249:167-196. https://doi.org/10.1007/s11207-008-9174-z. arXiv:0711.1715

Tziotziou K, Tsiropoula G, Kontogiannis I, Scullion E, Doyle JG (2018) A persistent quiet-sun small-scale tornado. I. Characteristics and dynamics. Astron Astrophys 618:A51. https://doi.org/10.1051/0004-6361/201833101

Tziotziou K, Scullion E, Shelyag S, Steiner O, Khomenko E, Tsiropoula G, Canivete Cuissa JR, Wedemeyer S, Kontogiannis I, Yadav N, Kitiashvili IN, Skirvin SJ, Dakanalis I, Kosovichev AG, Fedun V (2023) Vortex motions in the solar atmosphere. Space Sci Rev 219(1):1. https://doi.org/10.1007/s11214-022-00946-8

Vial JC, Engvold O (eds) (2015) Solar prominences. Astrophysics and space science library, vol 415. Springer, Cham. https://doi.org/10.1007/978-3-319-10416-4

Wang W, Liu R, Wang Y (2017) January. Tornado-like evolution of a kink-unstable solar prominence. Astrophys J 834(1):38. https://doi.org/10.3847/1538-4357/834/1/38. arXiv:1611.04667 [astro-ph.SR]

Warren HP, Brooks DH, Ugarte-Urra I, Reep JW, Crump NA, Doschek GA (2018) Spectroscopic observations of current sheet formation and evolution. Astrophys J 854:122. https://doi.org/10.3847/1538-4357/aaa9b8. arXiv:1711.10826 [astro-ph.SR]

Wedemeyer S, Steiner O (2014) On the plasma flow inside magnetic tornadoes on the Sun. Publ Astron Soc Jpn 66:S10. https://doi.org/10.1093/pasj/psu086. arXiv:1406.7270 [astro-ph.SR]

Wedemeyer S, Scullion E, Rouppe van der Voort L, Bosnjak A, Antolin P (2013) Are giant tornadoes the legs of solar prominences? Astrophys J 774:123. https://doi.org/10.1088/0004-637X/774/2/123

Wedemeyer S, Scullion E, Steiner O, de la Cruz Rodriguez J, Rouppe van der Voort LHM (2013) Magnetic tornadoes and chromospheric swirls - definition and classification. J Phys Conf Ser 440(1):012005. https://doi.org/10.1088/1742-6596/440/1/012005. arXiv:1303.0179 [astro-ph.SR]

Wedemeyer-Böhm S, Scullion E, Steiner O, Rouppe van der Voort L, de La Cruz Rodriguez J, Fedun V, Erdélyi R (2012) Magnetic tornadoes as energy channels into the solar corona. Nature 486:505-508. https://doi.org/10.1038/nature11202

Yadav N, Cameron RH, Solanki SK (2020) Simulations show that vortex flows could heat the chromosphere in solar plage. Astrophys J Lett 894(2):L17. https://doi.org/10.3847/2041-8213/ab8dc5. arXiv:2004.13996 [astro-ph.SR]

Yadav N, Cameron RH, Solanki SK (2021) Vortex flow properties in simulations of solar plage region: evidence for their role in chromospheric heating. Astron Astrophys 645:A3. https://doi.org/10.1051/0004-6361/202038965. arXiv:2010.14971 [astro-ph.SR]

Yang Z, Tian H, Peter H, Su Y, Samanta T, Zhang J, Chen Y (2018) Two solar tornadoes observed with the interface region imaging spectrograph. Astrophys J 852:79. https://doi.org/10.3847/1538-4357/aa9e04. arXiv:1711.08968 [astro-ph.SR]

Young PR, O'Dwyer B, Mason HE (2012) Velocity measurements for a solar active region fan loop from Hinde/EIS Observations. Astrophys J 744:14. https://doi.org/10.1088/0004-637X/744/1/14. arXiv:1107.2362 [astro-ph.SR]

Zapiór M, Martínez-Gómez D (2016) Direct detection of the helical magnetic field geometry from 3D reconstruction of prominence knot trajectories. Astrophys J 817:123. https://doi.org/10.3847/0004-637X/817/2/123

Zapiór M, Rudawy P (2012) Estimation of solar prominence magnetic fields based on the reconstructed 3D trajectories of prominence knots. Sol Phys 280:445-456. https://doi.org/10.1007/s11207-012-0072-z. arXiv:1207.2005 [astro-ph.SR]
Zapiór M, Kotrč P, Rudawy P, Oliver R (2015) Simultaneous observations of solar prominence oscillations using two remote telescopes. Sol Phys 290:1647–1659. https://doi.org/10.1007/s11207-015-0696-x

Zhang QM, Chen PF, Xia C, Keppens R, Ji HS (2013) Parametric survey of longitudinal prominence oscillation simulations. Astron Astrophys 554:124

Zhong S, Li K (1994) Observation and study of the tornado-like prominence on August 29, 1990. In: Publications of the Yunnan observatory, vol 4, pp 1–6

Zhou YH, Xia C, Keppens R, Fang C, Chen PF (2018) Three-dimensional MHD simulations of solar prominence oscillations in a magnetic flux rope. Astrophys J 856(2):179. https://doi.org/10.3847/1538-4357/aab614

Zirker JB, Engvold O, Martin SF (1998) Counter-streaming gas flows in solar prominences as evidence for vertical magnetic fields. Nature 396(6710):440–441. https://doi.org/10.1038/24798

**Publisher's Note** Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Authors and Affiliations

Stanislav Gunár¹ ID • Nicolas Labrosse² ID • Manuel Luna³ ID • Brigitte Schmieder⁴,⁵,²

Petr Heinzel¹,⁶ ID • Therese A. Kucera⁷ ID • Peter J. Levens² • Arturo López Ariste⁸

Duncan H. Mackay⁹ • Maciej Zapiór¹ ID

<figure><img src="image_19.png" /></figure>

S. Gunár
gunar@asu.cas.cz

¹ Astronomical Institute, The Czech Academy of Sciences, 251 65 Ondřejov, Czech Republic

² SUPA, School of Physics & Astronomy, University of Glasgow, Glasgow, United Kingdom

³ Departament de Física, Universitat de les Illes Balears, 07122 Palma de Mallorca, Spain

⁴ LESIA, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Université de Paris, 5 place Janssen, 92290 Meudon Principal Cedex, France

⁵ Centre for mathematical Plasma Astrophysics, Dept. of Mathematics, KU Leuven, 3001 Leuven, Belgium

⁶ Centre of Scientific Excellence — Solar and Stellar Activity, University of Wroclaw, Wroclaw, Poland

⁷ Heliophysics Science Division, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA

⁸ IRAP, Université de Toulouse, CNRS, CNES, UPS. 14, Av. E. Belin, 31400 Toulouse, France

⁹ School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS, UK
Zapiór M, Kotrč P, Rudawy P, Oliver R (2015) Simultaneous observations of solar prominence oscillations using two remote telescopes. Sol Phys 290:1647–1659. https://doi.org/10.1007/s11207-015-0696-x

Zhang QM, Chen PF, Xia C, Keppens R, Ji HS (2013) Parametric survey of longitudinal prominence oscillation simulations. Astron Astrophys 554:124

Zhong S, Li K (1994) Observation and study of the tornado-like prominence on August 29, 1990. In: Publications of the Yunnan observatory, vol 4, pp 1–6

Zhou YH, Xia C, Keppens R, Fang C, Chen PF (2018) Three-dimensional MHD simulations of solar prominence oscillations in a magnetic flux rope. Astrophys J 856(2):179. https://doi.org/10.3847/1538-4357/aab614

Zirker JB, Engvold O, Martin SF (1998) Counter-streaming gas flows in solar prominences as evidence for vertical magnetic fields. Nature 396(6710):440–441. https://doi.org/10.1038/24798

**Publisher's Note** Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Authors and Affiliations

Stanislav Gunár¹ ID • Nicolas Labrosse² ID • Manuel Luna³ ID • Brigitte Schmieder⁴,⁵,²

Petr Heinzel¹,⁶ ID • Therese A. Kucera⁷ ID • Peter J. Levens² • Arturo López Ariste⁸

Duncan H. Mackay⁹ • Maciej Zapiór¹ ID

<figure><img src="image_19.png" /></figure>

S. Gunár
gunar@asu.cas.cz

¹ Astronomical Institute, The Czech Academy of Sciences, 251 65 Ondřejov, Czech Republic

² SUPA, School of Physics & Astronomy, University of Glasgow, Glasgow, United Kingdom

³ Departament de Física, Universitat de les Illes Balears, 07122 Palma de Mallorca, Spain

⁴ LESIA, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Université de Paris, 5 place Janssen, 92290 Meudon Principal Cedex, France

⁵ Centre for mathematical Plasma Astrophysics, Dept. of Mathematics, KU Leuven, 3001 Leuven, Belgium

⁶ Centre of Scientific Excellence — Solar and Stellar Activity, University of Wroclaw, Wroclaw, Poland

⁷ Heliophysics Science Division, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA

⁸ IRAP, Université de Toulouse, CNRS, CNES, UPS. 14, Av. E. Belin, 31400 Toulouse, France

⁹ School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS, UK

<figure><img src="image_20.png" /></figure>