employee from 01.01.2015 until now
Sankt-Peterburg, Russian Federation
Institute of Solar-Terrestrial Physics SB RAS
United Kingdom
Saint Petersburg branch of Special Astrophysical Observatory RAS
St. Petersburg, Russian Federation
Irkutsk, Russian Federation
This paper provides an overview of the state-of-the-art studies of oscillatory processes in solar and stellar flares, based on modern observational data from ground-based and space-borne instruments with high temporal, spatial, and spectral resolution in different bands of the electromagnetic spectrum. We examine the mecha-nisms that generate flare emission and its quasi-periodic modulation. We discuss similarities and differences be-tween solar and stellar flares, and address associated problems of superflares on the Sun and space weather. Quasi-periodic pulsations (QPPs) of flare emission are shown to be an effective tool for diagnosing both the flare processes themselves and the parameters of flaring plasmas and accelerated particles. We consider types of QPPs, their statistical properties, and methods of analysis, taking into account the non-stationarity of the QPPs’ parameters. We review the proposed mechanisms of QPPs and summarize open questions.
Sun, solar activity, solar flares, stellar flares, quasi-periodic pulsations
1. Aptekar R.L., Frederiks D.D., Golenetskii S.V., Ilynskii V.N., Mazets E.P., Panov V.N., et al. Konus-W gamma-ray burst experiment for the GGS Wind Spacecraft. Space Sci. Rev. 1995, vol. 71, iss. 1-4, pp. 265-272. DOI:https://doi.org/10.1007/BF00751332.
2. Armstrong D.J., Pugh C.E., Broomhall A.-M., Brown D.J.A., Lund M.N. Osborn H.P., et al. The host stars of Kepler's habitable exoplanets: superflares, rotation and activity. Mon. Not. Roy. Astron. Soc. 2016, vol. 455, pp. 3110-3125. DOI:https://doi.org/10.1093/mnras/stv2419.
3. Artemyev A., Zimovets I. Stability of current sheets in the solar corona. Solar Phys. 2012, vol. 277, iss. 2, pp. 283-298. DOI:https://doi.org/10.1007/s11207-011-9908-1.
4. Aulanier G., Janvier M., Schmieder B. The standard flare model in three dimensions. I. Strong-to-weak shear transition in post-flare loops. Astron. and Astrophys. 2012, vol. 543, id. A110, 14 p. DOI:https://doi.org/10.1051/0004-6361/201219311.
5. Aulanier G., Démoulin P., Schrijver C.J., Janvier M., Pariat E., Schmieder B. The standard flare model in three dimensions. II. Upper limit on solar flare energy. Astron. and Astrophys. 2013, vol. 549, id. A66, 7 p. DOI:https://doi.org/10.1051/0004-6361/201220406.
6. Balona L.A., Broomhall A.-M., Kosovichev A., Nakariakov V.M., Pugh C.E., Van Doorsselaere T. Oscillations in stellar superflares. Mon. Not. Roy. Astron. Soc. 2015, vol. 450, iss. 1, pp. 956-966. DOI:https://doi.org/10.1093/mnras/stv661.
7. Barta M., Buchner J., Karlicky M., Skala J. Spontaneous current-layer fragmentation and cascading reconnection in solar flares. I. Model and analysis. The Astrophys. J. 2011, vol. 737, id. 24. 11 p. DOI:https://doi.org/10.1088/0004-637X/737/1/24.
8. Battaglia M., Motorina G., Kontar E.P. Multithermal representation of the kappa-distribution of solar flare electrons and application to simultaneous X-ray and EUV observations. The Astrophys. J. 2015, vol. 815, id. 73, 8 p. DOI:https://doi.org/10.1088/0004-637X/815/1/73.
9. Benz A.O. Flare observations. Liv. Rev. Solar Phys. 2017, vol. 14, iss. 1, id. 2, 59 p. DOI:https://doi.org/10.1007/s41116-016-0004-3.
10. Benz A.O., Brajša R., Magdalenić J. Are there radio-quiet solar flares? Solar Phys. 2007, vol. 240, iss. 2, pp. 63-270. DOI:https://doi.org/10.1007/s11207-007-0365-9.
11. Bogachev S.A., Somov B.V., Kosugi T., Sakao T. The motions of the hard X-ray sources in solar flares: Images and statistics. The Astrophys. J. 2005, vol. 630, iss. 1, pp. 561-572. DOI:https://doi.org/10.1086/431918.
12. Broomhall A.-M., Davenport J., Hayes L., Inglis A., Kolotkov D., McLaughlin J., et al. A blueprint of state-of-the-art techniques for detecting quasi-periodic pulsations in solar and stellar flares. The Astrophys. J. Suppl. Ser. 2019, vol. 244, iss. 2, id. 44, 37 p. DOI:https://doi.org/10.3847/1538-4365/ab40b3.
13. Carrington R.C. description of a singular appearance seen in the Sun on September 1, 1859. Mon. Not. Roy. Astron. Soc. vol. 20, pp.13-15. DOI:https://doi.org/10.1093/mnras/20.1.13.
14. Caspi A., Lin R.P. RHESSI line and continuum observations of super-hot flare plasma. The Astrophys. J. Lett. 2010, vol. 725, pp. L161-L166. DOI:https://doi.org/10.1088/2041-8205/725/2/L161.
15. Chen P.F., Priest E.R. Transition-region explosive events: Reconnection modulated by p-mode waves. Solar Phys. 2006, vol. 238, iss. 2, pp. 313-327. DOI:https://doi.org/10.1007/s11207-006-0215-1.
16. Cho I.-H., Cho K.-S., Nakariakov V.M., Kim S., Kumar P. Comparison of damped oscillations in solar and stellar X-ray flares. Astrophys. J. 2016, vol. 830, iss. 2, id. 110, 12 p. DOI:https://doi.org/10.3847/0004-637X/830/2/110.
17. Davenport J.R.A., Hawley S.L., Hebb L., Wisniewski J.P., Kowalski A.F., Johnson E.C., et al. Kepler flares. II. The temporal morphology of white-light flares on GJ 1243. The Astrophys. J. 2014, vol. 797, iss. 2, id. 122, 11 p. DOI:https://doi.org/10.1088/0004-637X/797/2/122.
18. Dolla L., Marqué C., Seaton D. B., Van Doorsselaere T., Dominique M., Berghmans D., et al. Time delays in quasi-periodic pulsations observed during the X2.2 solar flare on 2011 February 15. The Astrophys. J. Lett. 2012, vol. 749, iss. 1, id. L16, 7 p. DOI:https://doi.org/10.1088/2041-8205/749/1/L16.
19. Dominique M., Zhukov A.N., Dolla L. Inglis A., Lapenta G. Detection of quasi-periodic pulsations in solar EUV time series. Solar Phys. 2018, vol. 293, iss. 4, id. 61, 24 p. DOI:https://doi.org/10.1007/s11207-018-1281-x.
20. Doyle J.G., Shetye J., Antonova A.E., Kolotkov D.Y., Srivastava A.K., Stangalini M., et al. Stellar flare oscillations: evidence for oscillatory reconnection and evolution of MHD modes. Mon. Not. Roy. Astron. Soc. 2018, vol. 475, iss. 2, pp. 2842-2851. DOI: 2018MNRAS.475.2842D.
21. Dubinov A.E., Kolotkov D.Y. Above the weak nonlinearity: super-nonlinear waves in astrophysical and laboratory plasmas. Rev. Mod. Plasma Phys. 2018, vol. 2, id. 2, 46 p. DOI:https://doi.org/10.1007/s41614-018-0014-9.
22. Dudík J., Dzifčáková E., Karlický M., Kulinová A. The bound-bound and free-free radiative losses for the nonthermal distribution in solar and stellar coronae. Astron. and Astrophys. 2011. vol. 529, id. A103, 14 p. DOI:https://doi.org/10.1051/0004-6361/201016329.
23. Dulk G.A., Marsh K.A. Simplified expressions for the gyrosynchrotron radiation from mildly relativistic, nonthermal and thermal electrons. The Astrophys. J. 1982, vol. 259, pp. 350-358. DOI:https://doi.org/10.1086/160171.
24. Edwin P.M., Roberts B. Wave propagation in a magnetic cylinder. Solar Phys. 1983, vol. 88, iss. 1-2, pp. 179-191. DOI:https://doi.org/10.1007/BF00196186.
25. Erkaev N.V., Semenov V.S., Biernat H.K. Magnetic double-gradient instability and flapping waves in a current sheet. Phys. Rev. Lett. 2007, vol. 99, iss. 23, id. 235003. DOI:https://doi.org/10.1103/PhysRevLett.99.235003.
26. Field G.B. Thermal instability. The Astrophys. J. 1965, vol. 142, p. 531. DOI:https://doi.org/10.1086/148317.
27. Fleishman G.D., Kontar E.P. Sub-THz radiation mechanisms in solar flares. The Astrophys. J. Lett. 2010, vol. 709, iss. 2, pp. L127-L132. DOI:https://doi.org/10.1088/2041-8205/709/2/L127.
28. Fleishman G.D., Kontar E.P., Nita G.M., Gary D.E. A cold, tenuous solar flare: Acceleration without heating. The Astrophys. J. Lett. 2011, vol. 731, iss. 1, id. L19, 6 p. DOI:https://doi.org/10.1088/2041-8205/731/1/L19.
29. Frissell N.A., Vega J.S., Markowitz E., Gerrard A.J., Engelke W.D., Erickson P.J., et al. High-frequency communications response to solar activity in September 2017 as observed by amateur radio networks. Space Weather. 2019, vol. 17, pp. 118-132. DOI:https://doi.org/10.1029/2018SW002008.
30. Gershberg R.E. Solar-Type Activity in Main-Sequence Stars. Springer, Berlin, Heidelberg, 2005, 496 p. DOI:https://doi.org/10.1007/3-540-28243-2.
31. Goddard C.R., Nisticò G., Nakariakov V.M., Zimovets I.V. A statistical study of decaying kink oscillations detected using SDO/AIA. Astron. and Astrophys. 2016, vol. 585, id. A137, 9 p. DOI:https://doi.org/10.1051/0004-6361/201527341.
32. Golub L., Deluca E., Austin G., Bookbinder J., Caldwell D., Cheimets P., et al. The X-Ray Telescope (XRT) for the Hinode Mission. Solar Phys. 2007, vol. 243, iss. 1, pp. 63-86. DOI:https://doi.org/10.1007/s11207-007-0182-1.
33. Gryciuk M., Siarkowski M., Sylwester J., Gburek S., Podgorski P., Kepa A., et al. Flare characteristics from X-ray light curves. Solar Phys. 2017, vol. 292, iss. 6, id. 77, 19 p. DOI:https://doi.org/10.1007/s11207-017-1101-8.
34. Guo M.-Z., Chen S.-X., Li B., Xia L.-D., Yu H. Inferring flare loop parameters with measurements of standing sausage modes. Solar Phys. 2016, vol. 291, iss. 3, pp. 877-896. DOI:https://doi.org/10.1007/s11207-016-0868-3.
35. Gurevich S.I. Once more about effect of geomagnetic storms on the relay protection. Releinaya zashchita I avtomatizatsiya [Relay protection and automation]. 2016, no. 2 (23), pp. 19-21. (In Russian).
36. Hayes L.A., Gallagher P.T., Dennis B.R., Ireland J., Inglis A.R., Ryan D.F. Quasi-periodic pulsations during the impulsive and decay phases of an X-class flare. The Astrophys. J. Lett. 2016, vol. 827, iss. 2, id. L30, 6 p. DOI:https://doi.org/10.3847/2041-8205/827/2/L30.
37. Hayes L.A., Gallagher P.T., McCauley J., Dennis B.R., Ireland J., Inglis A. Pulsations in the Earth's lower ionosphere synchronized with solar flare emission. J. Geophys. Res.: Space Phys. 2017, vol. 122, iss. 10, pp. 9841-9847. DOI:https://doi.org/10.1002/2017JA024647.
38. Hayes L.A., Gallagher P.T., Dennis B.R., Ireland J., Inglis A., Morosan D.E. Persistent quasi-periodic pulsations during a large X-class solar flare. The Astrophys. J. 2019, vol. 875, iss. 1, id. 33, 11 p. DOI:https://doi.org/10.3847/1538-4357/ab0ca3.
39. Heinzel P., Avrett E.H. Optical-to-radio continua in solar flares. Solar Phys. 2012, vol. 277, iss. 1, pp. 31-44. DOI:https://doi.org/10.1007/s11207-011-9823-5.
40. Heinzel P., Kleint L. Hydrogen Balmer continuum in solar flares detected by the Interface Region Imaging Spectrograph (IRIS). The Astrophys. J. Lett. 2014, vol. 794, iss. 2, id. L23, 6 p. DOI:https://doi.org/10.1088/2041-8205/794/2/L23.
41. Heinzel P., Shibata K. Can flare loops contribute to the white-light emission of stellar superflares? The Astrophys. J. 2018, vol. 859, iss. 2, id. 143, 7 p. DOI:https://doi.org/10.3847/1538-4357/aabe78.
42. Hnat B., Kolotkov D.Y., O'Connell D., Nakariakov V.M., Rowlands G. Nonlinear waves in the terrestrial quasiparallel foreshock. Phys. Rev. Lett. 2016, vol. 117, id. 235102. DOI:https://doi.org/10.1103/PhysRevLett.117.235102.
43. Holman G.D., Sui L., Schwartz R.A., Emslie A.G. Electron bremsstrahlung hard X-ray spectra, electron distributions, and energetics. The Astrophys. J. 2003, vol. 595, iss. 2, pp. L97-L101. DOI:https://doi.org/10.1086/378488.
44. Huang N.E., Wu Z. A review on Hilbert-Huang transform: Method and its applications to geophysical studies. Rev. Geophys. 2008, vol. 46, iss. 2, Id. RG2006. DOI:https://doi.org/10.1029/2007RG000228.
45. Huang N.E., Shen Z., Long S.R., Wu M.C., Shih H.H., Zheng Q., et al. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Royal Soc. London Proc. Ser. A. 1998, vol. 454, iss. 1971, pp. 903-998. DOI:https://doi.org/10.1098/rspa.1998.0193.
46. Hudson H.S. Chasing white-light flares. Solar Phys. 2016, vol. 291, iss. 5, pp. 1273-1322. DOI:https://doi.org/10.1007/s11207-016-0904-3.
47. Hudson H.S., Canfield R.C., Kane S.R. Indirect estimation of energy deposition by non-thermal electrons in solar flares. Solar Phys. 1978, vol. 60, p. 137-142. DOI:https://doi.org/10.1007/BF00152338.
48. Inglis A.R., Nakariakov V.M. A multi-periodic oscillatory event in a solar flare. Astron. and Astrophys. 2009, vol. 493, iss. 1, pp. 259-266. DOI:https://doi.org/10.1051/0004-6361:200810473.
49. Inglis A.R., van Doorsselaere T., Brady C.S., Nakaria-kov V.M. Characteristics of magnetoacoustic sausage modes. Astron. and Astrophys. 2009, vol. 503, iss. 2, pp. 569-575. DOI:https://doi.org/10.1051/0004-6361/200912088.
50. Inglis A.R., Ireland J., Dennis B.R., Hayes L., Gallagher P. A large-scale search for evidence of quasi-periodic pulsations in solar flares. The Astrophys. J. 2016, vol. 833, iss. 2, id. 284, 16 p. DOI:https://doi.org/10.3847/1538-4357/833/2/284.
51. Jakimiec J., Tomczak M. Investigation of quasi-periodic variations in hard X-rays of solar flares. II. Further investigation of oscillating magnetic traps. Solar Phys. 2012, vol. 278, pp. 393-410. DOI:https://doi.org/10.1007/s11207-012-9934-7.
52. Jelínek P., Karlický M., Van Doorsselaere T., Bárta M. Oscillations excited by plasmoids formed during magnetic reconnection in a vertical gravitationally stratified current sheet. The Astrophys. J. 2017, vol. 847, iss. 2, id. 98, 15 p. DOI:https://doi.org/10.3847/1538-4357/aa88a6.
53. Jenkins A. Self-oscillation. Phys. Rep. 2013, vol. 525, pp. 167-222. DOI:https://doi.org/10.1016/j.physrep.2012.10.007.
54. Kane S.R., Kai K., Kosugi T., Enome S., Landecker P.B., McKenzie D.L. Acceleration and confinement of energetic particles in the 1980 June 7 solar flare. The Astrophys. J. 1983, vol. 271, pp. 376-387. DOI:https://doi.org/10.1086/161203.
55. Kashapova L.K., Tokhchukova S.K., Rudenko G.V., Bogod V.M., Muratov A.A. On the possible mechanisms of energy release in a C-class flare. Cen. Europ. Astrophys. Bull. 2013, vol. 37, pp. 573-583.
56. Katsova M.M., Kitchatinov L.L., Livshits M.A., Moss D.L., Sokoloff D.D., Usoskin I.G. Can superflares occur on the Sun? A view from dynamo theory. Astron. Rep. 2018, vol. 62, iss. 1, pp. 72-80. DOI:https://doi.org/10.1134/S106377291801002X.
57. Kaufmann P., Correia E., Costa J.E.R., Zodi Vaz A.M. A synchrotron/inverse Compton interpretation of a solar burst producing fast pulses at lambda less than 3-mm and hard X-rays. Astron. and Astrophys. 1986, vol. 157, pp. 11-18.
58. Khaikin S.E., Kaidanovsky N.L., Pariisky Yu.N., Esepkina N.A. Radio telescope RATAN-600. Izvestiya Glavnoi astronomicheskoi observatorii v Pulkove [Bulletin of the Main Astronomical Observatory at Pulkovo]. 1972, vol. 188, pp. 3-12. (In Russian).
59. Kim S., Nakariakov V.M., Shibasaki K. Slow magnetoacoustic oscillations in the microwave emission of solar flares. The Astrophys. J. Lett. 2012, vol. 756, iss. 2, id. L36, 5 p. DOI:https://doi.org/10.1088/2041-8205/756/2/L36.
60. Kislyakov A.G., Zaitsev V.V., Stepanov A.V., Urpo S. On the possible connection between photospheric 5-min oscillation and solar flare microwave emission. Solar Phys. 2006, vol. 233, pp. 89-106. DOI:https://doi.org/10.1007/s11207-006-2850-y.
61. Kitchatinov L.L., Olemskoy S.V. Dynamo model for grand maxima of solar activity: can superflares occur on the Sun? Mon. Not. Roy. Astron. Soc. 2016, vol. 459, iss. 4, pp. 4353-4359. DOI:https://doi.org/10.1093/mnras/stw875.
62. Kliem B., Karlický M., Benz A.O. Solar flare radio pulsations as a signature of dynamic magnetic reconnection. Astron. and Astrophys. 2000, vol. 360, pp. 715-728
63. Kolotkov D.Y., Nakariakov V.M., Kupriyanova E.G., Ratcliffe H., Shibasaki K. Multi-mode quasi-periodic pulsations in a solar flare. Astron. and Astrophys. 2015, vol. 574, id. A53, 6 p. DOI:https://doi.org/10.1051/0004-6361/201424988.
64. Kolotkov D.Y., Anfinogentov S.A., Nakariakov V.M. Empirical mode decomposition analysis of random processes in the solar atmosphere. Astron. and Astrophys. 2016a, vol. 592, id. A153, 9 p. DOI:https://doi.org/10.1051/0004-6361/201628306.
65. Kolotkov D.Y., Nakariakov V.M., Rowlands G. Nonlinear oscillations of coalescing magnetic flux ropes. Phys. Rev. E. 2016b, vol. 93, iss. 5, id. 053205. DOI:https://doi.org/10.1103/PhysRevE. 93.053205.
66. Kolotkov D.Y., Pugh C.E., Broomhall A.-M., Nakariakov V.M. Quasi-periodic pulsations in the most powerful solar flare of cycle 24. The Astrophys. J. Lett. 2018, vol. 858, iss. 1, id. L3, 8 p. DOI:https://doi.org/10.3847/2041-8213/aabde9.
67. Kontar E.P., Motorina G.G., Jeffrey N.L.S., Tsap Y.T., Fleishman G.D., Stepanov A.V. Observation-driven model of the frequency rising sub-THz emission component in solar flares. Astron. and Astrophys. 2018, vol. 620, id. A95, 6 p. DOI:https://doi.org/10.1051/0004-6361/201834124.
68. Kopylova Yu.G., Stepanov A.V., Tsap Yu.T. Radial oscillations of coronal loops and microwave radiation from solar flares. Astron. Lett. 2002, vol. 28, iss. 11, pp. 783-791.
69. Kopylova Yu.G., Melnikov A.V., Stepanov A.V., Tsap Yu.T., Goldvarg T.B. Oscillations of coronal loops and second pulsations of solar radio emission. Astron. Lett. 2007, vol. 33, iss. 10, pp. 706-713. DOI:https://doi.org/10.1134/S1063773707100088.
70. Kotrč P., Procházka O., Heinzel P. New observations of Balmer continuum flux in solar flares. Instrument description and first results. Solar Phys. 2016, vol. 291, iss. 3, pp. 779-789. DOI:https://doi.org/10.1007/s11207-016-0860-y.
71. Kretzschmar M. The Sun as a star: observations of white-light flares. Astron. and Astrophys. 2011, vol. 530, id. A84, 7 p. DOI:https://doi.org/10.1051/0004-6361/201015930.
72. Kupriyanova E.G., Ratcliffe H. Minute pulsations in microwaves and X-rays during the flare on May 6, 2005. Adv. Space Res. 2016, vol. 57, iss. 7, pp. 1456-1467. DOI:https://doi.org/10.1016/j.asr.2016.01.012.
73. Kupriyanova E.G., Melnikov V.F., Nakariakov V.M., Shibasaki K. Types of microwave quasi-periodic pulsations in single flaring loops. Solar Phys. 2010, vol. 267, pp. 329-342. DOI:https://doi.org/10.1007/s11207-010-9642-0.
74. Kupriyanova E.G., Kashapova L.K., Reid H.A.S., Myagkova I.N. Relationship of type III radio bursts with quasi-periodic pulsations in a solar flare. Solar Phys. 2016, vol. 291, iss. 11, pp. 3427-3438. DOI:https://doi.org/10.1007/s11207-016-0958-2.
75. Kuznetsov S.N., Kudela K., Ryumin S.P., Gotselyuk Y.V. CORONAS-F satellite: Tasks for study of particle acceleration. Adv. Space Res. 2002, vol. 30, i. 7, pp. 1857-1863, DOI:https://doi.org/10.1016/S0273-1177(02)00462-3.
76. Kuznetsov S.A., Zimovets I.V., Morgachev A.S., Struminsky A.B. Spatio-temporal dynamics of sources of hard X-ray pulsations in solar flares. Solar Phys. 2016, vol. 291, iss. 11, pp. 3385-3426, DOI:https://doi.org/10.1007/s11207-016-0981-3.
77. Lesovoi S., Altyntsev A., Kochanov A., Grechnev V., Gubin A., Zhdanov D., et al. Siberian Radioheliograph: first results. Solar-Terr. Phys. 2017, vol. 3, iss. 1, pp. 3-18. DOI:https://doi.org/10.12737/article_58f96ec60fec52.86165286.
78. Lin R.P., Hudson H.S. Non-thermal processes in large solar flares. Solar Phys. 1976, vol. 50, pp. 153-178. DOI:https://doi.org/10.1007/BF00206199.
79. Lin R.P., Dennis B.R., Hurford G.J., Smith D.M., Zehnder A., Harvey P.R., et al. The Reuven Ramaty High-Energy Solar Spectroscopic Imager (RHESSI). Solar Phys. 2002, vol. 210, iss. 1, pp. 3-32. DOI:https://doi.org/10.1023/A:1022428818870.
80. Loukitcheva M., Solanki S.K., Carlsson M., Stein R.F. Millimeter observations and chromospheric dynamics. Astron. and Astrophys. 2004, vol. 419, pp. 747-756. DOI: 10.1051/ 0004-6361:20034159.
81. Lysenko A.L., Altyntsev A.T., Meshalkina N.S., Zhdanov D., Fleishman G.D. Statistics of “cold” early impulsive solar flares in X-ray and microwave domains. The Astrophys. J. 2018, vol. 856, iss. 2, id. 111, 29 p. DOI:https://doi.org/10.3847/1538-4357/aab271.
82. Maehara H., Shibayama T., Notsu S., Notsu Y., Nagao T., Kusaba S., et al. Superflares on solar-type stars. Nature. 2012, vol. 485, iss. 7399, pp. 478-481. DOI:https://doi.org/10.1038/nature11063.
83. Maehara H., Shibayama T., Notsu Y., Notsu S., Honda S., Nogami D., et al. Statistical properties of superflares on solar-type stars based on 1-min cadence data. Earth, Planets and Space. 2015, vol. 67, id. 59, 10 p. DOI:https://doi.org/10.1186/s40623-015-0217-z.
84. Masuda S., Shimojo M., Kawate T., Ishikawa S., Ohno M. Extremely microwave-rich solar flare observed with Nobeyama Radioheliograph. Publ. Astron. Soc. Japan. 2013, vol. 65, iss. SP1, id. S1, 6 p. DOI:https://doi.org/10.1093/pasj/65.sp1.S1.
85. McLaughlin J.A., Hood A.W., de Moortel I. Review article: MHD wave propagation near coronal null points of magnetic fields. Space Sci. Rev. 2011, vol. 158, iss. 2-4, pp. 205-236. DOI:https://doi.org/10.1007/s11214-010-9654-y.
86. McLaughlin J.A., Nakariakov V.M., Dominique M., Jelínek P., Takasao S. Modelling quasi-periodic pulsations in solar and stellar flares. Space Sci. Rev. 2018, vol. 214, id. 45, 54 p. DOI:https://doi.org/10.1007/s11214-018-0478-5.
87. Mészárosová H., Karlický M., Rybák J., Jiřička K. Tadpoles in wavelet spectra of a solar decimetric radio burst. The Astrophys. J. Lett. 2009, vol. 697, iss. 2, pp. L108-L110. DOI:https://doi.org/10.1088/0004-637X/697/2/L108.
88. Murray M. J., van Driel-Gesztelyi L., Baker D. Simulations of emerging flux in a coronal hole: oscillatory reconnection. Astron. and Astrophys. 2009, vol. 494, iss. 1. pp. 329-337, DOI:https://doi.org/10.1051/0004-6361:200810406.
89. Nagovitsyn Yu.A. A nonlinear mathematical model for the solar cyclicity and prospects for reconstructing the solar activity in the past. The Astron. Lett. 1997, vol. 23, iss. 6, pp. 742-748.
90. Nakajima H., Sekiguchi H., Aiba S., Shiomi Y., Kuwabara T., Sawa M., et al. A new 17-GHz solar radio interferometer at Nobeyama. Publ. Astron. Soc. Japan. 1980, vol. 32, pp. 639-650.
91. Nakajima H., Kosugi T., Kai K., Enome S. Successive electron and ion accelerations in impulsive solar flares on 7 and 21 June 1980. Nature. 1983, vol. 305, pp. 292-294, DOI:https://doi.org/10.1038/305292a0.
92. Nakajima H., Sekiguchi H., Sawa M., Kai K., Kawashima S. The radiometer and polarimeters at 80, 35, and 17 GHz for solar observations at Nobeyama. Publ. Astron. Soc. Japan. 1985, vol. 37, pp. 163-170.
93. Nakariakov V.M., Melnikov V.F. Quasi-periodic pulsations in solar flares. Space Sci. Rev. 2009, vol. 149, iss. 1-4, pp. 119-151. DOI:https://doi.org/10.1007/s11214-009-9536-3.
94. Nakariakov V.M., Zimovets I.V. Slow magnetoacoustic waves in two-ribbon flares. The Astrophys. J. Lett. 2011, vol. 730, iss. 2, id. L27, 4 p. DOI:https://doi.org/10.1088/2041-8205/730/2/L27.
95. Nakariakov V.M., Foullon C., Verwichte E., Young N.P. Quasi-periodic modulation of solar and stellar flaring emission by magnetohydrodynamic oscillations in a nearby loop. Astron. and Astrophys. 2006, vol. 452, iss. 1, pp. 343-346. DOI:https://doi.org/10.1051/0004-6361:20054608.
96. Nakariakov V.M., Foullon C., Myagkova I.N., Inglis A.R. Quasi-periodic pulsations in the gamma-ray emission of a solar flare. The Astrophys. J. Lett. 2010a, vol. 708, L47-L51. DOI:https://doi.org/10.1088/2041-8205/708/1/L47.
97. Nakariakov V.M., Inglis A.R., Zimovets I.V., Foullon C., Verwichte E., Sych R., et al. Oscillatory processes in solar flares. Plasma Phys. and Controlled Fusion. 2010b, vol. 52, iss. 12, id. 124009. DOI:https://doi.org/10.1088/0741-3335/52/12/124009.
98. Nakariakov V.M., Hornsey C., Melnikov V.F. Sausage oscillations of coronal plasma structures. The Astrophys. J. 2012, vol. 761, iss. 2, id. 134, 6 p. DOI:https://doi.org/10.1088/0004-637X/761/2/134.
99. Nakariakov V.M., Pilipenko V., Heilig B., Jelínek P., Karlický M., Klimushkin D.Y., et al. Magnetohydrodynamic oscillations in the solar corona and Earth's magnetosphere: Towards consolidated understanding. Space Sci. Rev. 2016, vol. 200, pp. 75-203. DOI:https://doi.org/10.1007/s11214-015-0233-0.
100. Nakariakov V.M., Kolotkov D.Y., Kupriyanova E.G., Mehta T., Pugh C.E., Lee D.-H., et al. Non-stationary quasi-periodic pulsations in solar and stellar flares. Plasma Phys. and Controlled Fusion 2019, vol. 61, id. 014024. DOI:https://doi.org/10.1088/1361-6587/aad97c.
101. Neupert W.M. Comparison of solar X-ray line emission with microwave emission during flares. The Astrophys. J. 1968, vol. 153, p. L59. DOI:https://doi.org/10.1086/180220.
102. Pascoe D.J., Russell A.J.B., Anfinogentov S.A., Simões P.J.A., Goddard C.R., Nakariakov V.M., et al. Seismology of contracting and expanding coronal loops using damping of kink oscillations by mode coupling. Astron. and Astrophys. 2017, vol. 607, id. A8, 9 p. DOI:https://doi.org/10.1051/0004-6361/201730915.
103. Penn M., Krucker S., Hudson H., Jhabvala M., Jennings D., Lunsford A., et al. Spectral and imaging observations of a white-light solar flare in the mid-infrared. The Astrophys. J. Lett. 2016, vol. 819, iss. 2, id. L30, 5 p. DOI:https://doi.org/10.3847/2041-8205/819/2/L30.
104. Pugh C.E., Nakariakov V.M., Broomhall A.-M. A multi-period oscillation in a stellar superflare. The Astrophys. J. Lett. 2015, vol. 813, iss. 1, id. L5, 5 p. DOI:https://doi.org/10.1088/2041-8205/813/1/L5.
105. Pugh C.E., Broomhall A.-M., Nakariakov V.M. Significance testing for quasi-periodic pulsations in solar and stellar flares. Astron. and Astrophys. 2017a, vol. 602, id. A47, 8 p., DOI:https://doi.org/10.1051/0004-6361/201730595.
106. Pugh C.E., Nakariakov V.M., Broomhall A.-M., Bogomolov A.V., Myagkova I.N. Properties of quasi-periodic pulsations in solar flares from a single active region. Astron. and Astrophys. 2017b, vol. 608, id. A101, 23 p. DOI:https://doi.org/10.1051/0004-6361/201731636.
107. Reva A., Shestov S., Zimovets I., Bogachev S., Kuzin S. Wave-like formation of hot loop arcades. Solar Phys. 2015, vol. 290, iss. 10, pp. 2909-2921. DOI:https://doi.org/10.1007/s11207-015-0769-x.
108. Reznikova V.E., Shibasaki K. Flare quasi-periodic pulsations with growing periodicity // Astron. Astrophys. 2011, vol. 525, id. A112, 7 p. DOI:https://doi.org/10.1051/0004-6361/201015600
109. Reznikova V.E., Nakariakov V.M., Melnikov V.F., Shibasaki K. Diagnostics of MHD-oscillation modes of a flaring loop using microwave observations with high spatial resolution. Proceedings of the 11th European Solar Physics Meeting "The Dynamic Sun: Challenges for Theory and Observations" (ESA SP-600). 11-16 September 2005, Leuven, Belgium. 2005. id. 140.1, 4 p.
110. Ryutov D.A., Ryutova M.P. Sound oscillations in a plasma with "magnetic filaments". J. Exper. and Theor. Phys. 1976, vol. 43, p. 491-497.
111. Saint-Hilaire P., Benz A.O., Monstein C. Short-duration radio bursts with apparent extragalactic dispersion. The Astrophys. J. 2014, vol. 795, iss. 1, id. 19, 6 p. DOI:https://doi.org/10.1088/0004-637X/795/1/19.
112. Sakai J.I., Nagasugi Y., Saito S., Kaufmann P. Simulating the emission of electromagnetic waves in the terahertz range by relativistic electron beams. Astron. and Astrophys. 2006, vol. 457, pp. 313-318. DOI:https://doi.org/10.1051/0004-6361:20065368.
113. Scherrer P.H., Schou J., Bush R.I., Kosovichev A.G., Bogart R.S., Hoeksema J.T., et al. The Helioseismic and Magnetic Imager (HMI) investigation for the Solar Dynamics Observatory (SDO). Solar Phys. 2012, vol. 275, iss. 1-2, pp. 207-227. DOI:https://doi.org/10.1007/s11207-011-9834-2.
114. Shibasaki K. High-Beta disruption in the solar atmosphere. The Astrophys. J. 2001, vol. 557, pp. 326-331. DOI:https://doi.org/10.1086/321651.
115. Shibayama T., Maehara H., Notsu S., Notsu Y., Nagao T., Honda S., et al. Superflares on solar-type stars observed with Kepler. I. Statistical properties of superflares. The Astrophys. J. Suppl. 2013, vol. 209, iss. 1, id. 5, 13 p. DOI:https://doi.org/10.1088/0067-0049/209/1/5.
116. Silva A.V.R., Share G.H., Murphy R.J., Costa J.E.R., de Castro C.G.G., Raulin J.-P., et al. Evidence that synchrotron emission from nonthermal electrons produces the increasing submillimeter spectral component in solar flares. Solar Phys. 2007, vol. 245, pp. 311-326. DOI:https://doi.org/10.1007/s11207-007-9044-0.
117. Simões P.J.A., Hudson H.S., Fletcher L. Soft X-ray pulsations in solar flares. Solar Phys. 2015, vol. 290, iss. 12, pp. 3625-3639. DOI:https://doi.org/10.1007/s11207-015-0691-2.
118. Somov B. V. Magnetic reconnection in solar flares. Uspekhi fizicheskikh nauk [Advances in Physical Sciences. Physics-Uspekhi]. 2010, vol. 180, pp. 997-1000. (In Russian).
119. Stepanov A.V., Kopylova Yu.G., Tsap Yu.T., Kupriyanova E.G. Oscillations of optical emission from flare stars and coronal loop diagnostics. Astron. Lett. 2005, vol. 31, iss. 9, pp. 612-619, DOI:https://doi.org/10.1134/1.2039972.
120. Su J.T., Shen Y.D., Liu Y. Extreme-ultraviolet multi-wavelength observations of quasi-periodic pulsations in a solar post-flare cusp-shape loop with SDO/AIA. The Astrophys. J. 2012, vol. 754, iss. 1, id. 43, 8 p., DOI:https://doi.org/10.1088/0004-637X/754/1/43.
121. Švestka Z. Optical observations of solar flares. Space Sci. Rev. 1966, vol. 5, iss. 3, pp. 388-418. DOI:https://doi.org/10.1007/BF02653250.
122. Tajima T., Sakai J., Nakajima H., Kosugi T., Brunel F., Kundu M.R. Current loop coalescence model of solar flares. The Astrophys. J. 1987, vol. 321, pp. 1031-1048. DOI:https://doi.org/10.1086/165694.
123. Takasao S, Shibata K. Above-the-loop-top oscillation and quasi-periodic coronal wave generation in solar flares. The Astrophys. J. 2016, vol. 823, iss. 2, id. 150, 11 p. DOI:https://doi.org/10.3847/0004-637X/823/2/150.
124. Tan B., Yu Z., Huang J., Tan C., Zhang Y. Very long-period pulsations before the onset of solar flares. The Astrophys. J. 2016, vol. 833, iss. 2, id. 206, 6 p. DOI:https://doi.org/10.3847/1538-4357/833/2/206.
125. Tapping K.F. A torsional wave model for solar radio pulsations. Solar Phys. 1983, vol. 87, iss. 1, pp.177-186. DOI:https://doi.org/10.1007/BF00151168.
126. Thurgood J.O., Pontin D.I., McLaughlin J.A. On the periodicity of linear and nonlinear oscillatory reconnection. Astron. and Astrophys. 2019, vol. 621, id. A106, 12 p. DOI:https://doi.org/10.1051/0004-6361/201834369.
127. Torrence C., Compo G.P. A practical guide to wavelet analysis. Bull. Amer. Meteor. Soc. 1998, vol. 79, pp. 61-78. DOI:https://doi.org/10.1175/1520-0477(1998)079<0061:APGTWA>2.0.CO;2.
128. Trottet G., Raulin J.-P., MacKinnon A., Giménez de Castro G., Simões P.J.A., Cabezas D., et al. Origin of the 30 THz emission detected during the solar flare on 2012 March 13 at 17:20 UT. Solar Phys. 2015, vol. 290, iss. 10, pp. 2809-2826. DOI:https://doi.org/10.1007/s11207-015-0782-0.
129. Tsap Yu. T., Stepanov A.V., Kopylova Yu.G., Zhilyaev B.E. Diagnostics of a flare on EQ Peg B from optical pulsations. Astron. Lett. 2011, vol. 37, iss. 1, pp. 49-54. DOI:https://doi.org/10.1134/S1063773710101032.
130. Tsap Y.T., Smirnova V.V., Motorina G.G., Morgachev A.S., Kuznetsov S.A., Nagnibeda V.G., et al. Millimeter and X-ray emission from the 5 July 2012 solar flare. Solar Phys. 2018, vol. 293, 15 p. DOI:https://doi.org/10.1007/s11207-018-1269-6.
131. Van Doorsselaere T., Nakariakov V.M., Verwichte E. Detection of waves in the solar corona: kink or Alfvén? The Astrophys. J. Lett. 2008, vol. 676, pp. L73-L75. DOI:https://doi.org/10.1086/587029.
132. Van Doorsselaere T., De Groof A., Zender J., Berghmans D., Goossens M. LYRA observations of two oscillation modes in a single flare. The Astrophys. J. 2011, vol. 740, id. 90, 8 p. DOI:https://doi.org/10.1088/0004-637X/740/2/90.
133. Van Doorsselaere T., Kupriyanova E.G., Yuan D. Quasi-periodic pulsations in solar and stellar flares: an overview of recent results (Invited Review). Solar Phys. 2016, vol. 291, iss. 11, pp. 3143-3164. DOI:https://doi.org/10.1007/s11207-016-0977-z.
134. Vaughan S. A simple test for periodic signals in red noise. Astron. and Astrophys. 2005, vol. 431, pp. 391-403. DOI:https://doi.org/10.1051/0004-6361:20041453.
135. Wang T., Innes D.E., Qiu J. Determination of the coronal magnetic field from hot-loop oscillations observed by SUMER and SXT. Astrophys. J. 2007, vol. 656, iss. 1, pp. 598-609. DOI:https://doi.org/10.1086/510424.
136. Wedemeyer S., Bastian T., Brajša R., Hudson H., Fleishman G., Loukitcheva M., et al. Solar science with the Atacama Large Millimeter/Submillimeter Array - a new view of our Sun. Space Sci. Rev. 2016, vol. 200, iss. 1-4, pp. 1-73. DOI:https://doi.org/10.1007/s11214-015-0229-9.
137. Xu Y., Cao W., Liu C., Yang G., Qiu J., Jing J., et al. Near-infrared observations at 1.56 microns of the 2003 October 29 X10 white-light flare. The Astrophys. J. 2004, vol. 607, iss. 2, pp. L131-L134. DOI:https://doi.org/10.1086/422099.
138. Zaitsev V.V., Stepanov A.V. To the nature of the pulsations of the solar type IV radio bursts. Issledovaniya po geomagnetizmu, aeronomii i fizike Solntsa [Research on geomagnetism, aeronomy and solar physics]. 1975, no. 37, p. 3. (In Russian).
139. Zaitsev V.V., Stepanov A.V. On the origin of solar hard X-ray pulsations. Soviet Astronomy Letters. 1982, vol. 8, p. 132.
140. Zaitsev V.V., Stepanov A.V. Coronal magnetic loops. Uspekhi fizicheskikh nauk [Advances in Physical Sciences. Physics-Uspekhi]. 2008, vol. 51, no. 11, pp. 1123-1160. DOI:https://doi.org/10.1070/PU2008v051n11ABEH006657. (In Russian).
141. Zaitsev V.V., Stepanov A.V., Kaufmann P. On the origin of pulsations of sub-THz emission from solar flares. Solar Phys. 2014, vol. 289, pp. 3017-3032. DOI:https://doi.org/10.1007/s11207-014-0515-9.
142. Zaitsev V.V., Kronshtadtov P.V., Stepanov A.V. Rayleigh-Taylor instability and excitation of super-Dreicer electric fields in the solar chromosphere. Solar Phys. 2016, vol. 291, pp. 3451-3459. DOI:https://doi.org/10.1007/s11207-016-0983-1.
143. Zhdanov D.A., Zandanov V.G. Observations of microwave fine structures by the Badary Broadband Microwave Spectropolarimeter and the Siberian Solar Radio Telescope. Solar Phys. 2015, vol. 290, iss. 1, pp. 287-294. DOI:https://doi.org/10.1007/s11207-014-0553-3.
144. URL: https://legacy.helioviewer.org/ (accessed November 11, 2019).
145. URL: http://sdc.uio.no/sdc/ (accessed November 11, 2019).
146. URL: http://solar.nro.nao.ac.jp/norh/doc/manuale.pdf (accessed November 11, 2019).
