Samara National Research University
Moscow, Russian Federation
Moscow, Russian Federation
We propose a method to measure the energy distribution of low-energy flares (nanoflares) in the energy range below 1023 erg. As an example, we measured the spectrum of nanoflares in the 1021–1026 erg range for two Sun’s frames observed by the SDO/AIA telescope in the 171 Å channel. Nanoflares are shown to have the power law spectrum in the 1022–1026 erg range. The spectral index is approximately constant, i.e. energy-independent. For energies below 1022 erg, the spectrum begins to collapse. For lower energies, below 1021 erg, the method does not give statistically significant results due to major errors. The results of the study indicate that solar nanoflares can be detected up to 1021–1022 erg energies. Results have previously been reported only for 1023 erg and above. The total energy flux of nanoflares in the energy range above 1022 erg, according to our data, is P2104 erg cm–2 s–1, which is about 15 times less than heating losses of the solar corona.
solar activity, nanoflares, coronal heating
1. Aschwanden M.J., Parnell C.E. Time variability of the “Quiet” sun observed with TRACE. II. Physical parameters, temperature evolution, and energetics of extreme-ultraviolet nanoflares. Astrophys. J. 2000, vol. 535, no. 2, p. 1047. DOI:https://doi.org/10.1086/308867.
2. Aschwanden M.J., Parnell C.E. Nanoflare statistics from first principles: fractal geometry and temperature synthesis. Astrophys. J. 2002, vol. 572, no. 2, p. 1048. DOI:https://doi.org/10.1086/340385.
3. Benz A.O., Krucker S. Energy distribution of microevents in the quiet solar corona. Astrophys. J. 2002, vol. 568, no. 1, p. 413. DOI:https://doi.org/10.1086/338807.
4. Berghmans D., Clette F., Moses D. Quiet Sun EUV transient brightenings and turbulence. A panoramic view by EIT on board SOHO. Astronomy and Astrophysics. 1998, vol. 336, pp. 1039-1055.
5. Boerner P., Edwards C., Lemen J., Rausch A., Schrijver C., Shine R., et al. Initial calibration of the atmospheric imaging assembly (AIA) on the solar dynamics observatory (SDO). Solar Phys. 2012, vol. 275, pp. 41-66. DOI:https://doi.org/10.1007/s11207-011-9804-8.
6. Bogachev S.A., Ulyanov A.S., Kirichenko A.S., Loboda I.P., Reva A.A. Microflares and nanoflares in the solar corona. Physics-Uspekhi. 2020, vol. 63, no. 8, p. 783. DOI:https://doi.org/10.3367/UFNe.2019.06.038769.
7. Cho I.H., Moon Y.-J., Cho K.-S., Nakariakov V.M., Lee J-Y, Kim Y-H. A new type of jet in a polar limb of the solar coronal hole. Astrophys. J. Lett. 2019, vol. 884, no. 2, p. L38. DOI:https://doi.org/10.3847/2041-8213/ab4799.
8. Grechnev V.V., Kuzin S.V., Urnov A.M., Zhitnik I.A., Uralov A.M., Bogachev S.A., et al. Long-lived hot coronal structures observed with CORONAS-F/SPIRIT in the Mg XII line. Solar System Res. 2006, vol. 40, no. 4, pp. 286-293.
9. Hudson H.S. Solar flares, microflares, nanoflares, and coronal heating. Solar Phys. 1991, vol. 133, no. 2, pp. 357-369. DOI:https://doi.org/10.1007/BF00149894.
10. Kirichenko A.S., Bogachev S.A. Long-duration plasma heating in solar microflares of X-ray class A1. 0 and lower. Astronomy Letters. 2013, vol. 39, no. 11, pp. 797-807. DOI: 10.1134/ S1063773713110042.
11. Kirichenko A.S., Bogachev S.A. Plasma heating in solar microflares: Statistics and analysis. Astrophys. J. 2017, vol. 840, no. 1, p. 45. DOI:https://doi.org/10.3847/1538-4357/aa6c2b.
12. Lemen J.R., Title A.M., Akin D.J., Boerner P.F., Chou C., Drake J.F., et al. The Atmospheric Imaging Assembly (AIA) on the Solar Dynamics Observatory (SDO). Solar Phys. 2012, vol. 275, pp. 17-40. DOI:https://doi.org/10.1007/s11207-011-9776-8.
13. Li Z., Su Y., Veronig A.M., Kong S., Gan W., Chen W. Detailed thermal and nonthermal processes in an A-class microflare. Astrophys. J. 2022, vol. 930, no. , p. 147. DOI:https://doi.org/10.3847/1538-4357/ac651c.
14. Loboda I.P., Bogachev S.A. Quiescent and eruptive prominences at solar minimum: a statistical study via an automated tracking system. Solar Phys. 2015, vol. 290, no. 7, pp. 1963-1980. DOI:https://doi.org/10.1007/s11207-015-0735-7.
15. Loboda I.P., Bogachev S.A. Plasma dynamics in solar macrospicules from high-cadence extreme-UV observations. Astronomy and Astrophysics. 2017, vol. 597, p. A78. DOI:https://doi.org/10.1051/0004-6361/201527559.
16. Loboda I.P., Bogachev S.A. What is a macrospicule? Astrophys. J. 2019, vol. 871, no. 2, p. 230. DOI:https://doi.org/10.3847/1538-4357/aafa7a.
17. Madjarska M.S. Coronal bright points. Living Reviews in Solar Physics. 2019, vol. 16, no. 1, pp. 1-79. DOI:https://doi.org/10.1007/s41116-019-0018-8.
18. Mitra-Kraev U., Del Zanna G. Solar microflares: a case study on temperatures and the Fe XVIII emission. Astronomy and Astrophysics. 2019, vol. 628, p. A134. DOI:https://doi.org/10.1051/0004-6361/201834856.
19. Murphy N.A., Raymond J.C., Korreck K.E. Plasma heating during a coronal mass ejection observed by the solar and heliospheric observatory. Astrophys. J. 2011, vol. 735, no. 1, p. 17. DOI:https://doi.org/10.1088/0004-637X/735/1/17.
20. Parker E.N. Magnetic neutral sheets in evolving fields. I-General theory. Astrophys. J. 1983, vol. pp. 635-647. DOI:https://doi.org/10.1086/160636.
21. Parker E.N. Nanoflares and the solar X-ray corona. Astrophys. J. 1988, vol. 330, pp. 474-479. DOI:https://doi.org/10.1086/166485.
22. Parnell C.E., Jupp P.E. Statistical analysis of the energy distribution of nanoflares in the quiet Sun. Astrophys. J. 2000, vol. 529, no. 1, p. 554. DOI:https://doi.org/10.1086/308271.
23. Purkhart S., Veronig A.M. Nanoflare distributions over solar cycle 24 based on SDO/AIA differential emission measure observations. Astronomy and Astrophysics. 2022, vol. 661, p. A149. DOI:https://doi.org/10.1051/0004-6361/202243234.
24. Reva A., Shestov S., Bogachev S., Kuzin S. Investigation of hot X-ray points (HXPs) using spectroheliograph Mg XII experiment data from CORONAS-F/SPIRIT. Solar Phys. 2012, vol. 276, no. 1, pp. 97-112. DOI:https://doi.org/10.1007/s11207-011-9883-6.
25. Reva A., Ulyanov A., Kirichenko A., Bogachev S., Kuzin S. Estimate of the upper limit on hot plasma differential emission measure (DEM) in non-flaring active regions and nanoflare frequency based on the Mg xii spectroheliograph data from CORONAS-F/SPIRIT. Solar Phys. 2018, vol. 293, no. 10, pp. 1-15. DOI:https://doi.org/10.1007/s11207-018-1363-9.
26. Reva A.A., Bogachev S.A., Loboda I.P., Ulyanov A.S., Kirichenko A.S. Observations of current sheet heating in X-ray during a solar flare. Astrophys. J. 2022, vol. 931,no. 2, p. 93. DOI:https://doi.org/10.3847/1538-4357/ac6b3d.
27. Shimojo M., Kawate T., Okamoto T.J., Yokoyama T., Narukage N., Sakao T., et al. Estimating the temperature and density of a spicule from 100 GHz data obtained with ALMA. Astrophys. J. Lett. 2020, vol. 888, no. 2, p. L28. DOI:https://doi.org/10.3847/2041-8213/ab62a5.
28. Ulyanov A.S., Bogachev S.A., Kuzin S.V. Bright points and ejections observed on the sun by the KORONAS-FOTON instrument TESIS. Astronomy Rep. 2010, vol. 54, no. 10, pp. 948-957. DOI:https://doi.org/10.1134/S1063772910100082.
29. Ulyanov A.S., Bogachev S.A., Reva A.A., Kirichenko A.S., Loboda I.P. The energy distribution of nanoflares at the minimum and rising phase of solar cycle 24. Astronomy Lett. 2019, vol. 45, no. 4, pp. 248-257. DOI:https://doi.org/10.1134/S1063 773719040078.
30. Withbroe G.L., Noyes R.W. Mass and energy flow in the solar chromosphere and corona. Ann. Rev. Astron. Astrophys. 1977, vol. 15, pp. 363-387. DOI:https://doi.org/10.1146/annurev.aa.15.090177. 002051.
31. Zavershinsky D.I., Bogachev S.A., Belov S.A., Ledentsov L.S. Method for searching nanoflares and their spatial distribution in the solar corona. Astronomy Lett. 2022, vol. 48, no. 9. (In print).