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Investigation of the coronal heating through phase relation of solar activity indexes

  • K. J. Li (a1) (a2) (a3), J. C. Xu (a1) (a2) (a3), Z. Q. Yin (a2) (a3), J. L. Xie (a1) (a2) (a3) and W. Feng (a4)...


The coronal heating problem is a long-standing perplexing issue. In this study, 13 solar activity indexes are used to investigate their phase relation with the sunspot number (SSN). Only three of them are found to statistically significantly lag the SSN (large-scale magnetic activity) by about one solar rotation period; the three indexes are total solar irradiance (TSI), the modified coronal index, and the solar wind velocity; the former two indexes may represent the long-term variation of energy quantity of the heated photosphere and corona, respectively. The Mount Wilson Sunspot Index (MWSI) and the Magnetic Plage Strength Index (MPSI), which reflect the large- and small-scale magnetic field activities, respectively, are also utilised to investigate their phase relations with the three indexes. The three indexes are found to be much more intimately related to MPSI than to MWSI, and MWSI statistically significantly leads TSI by about one rotation period. The heated corona is found to pulse perfectly in step with the small-scale magnetic activity rather than the large-scale magnetic activity; furthermore, combined with observations, our statistical evidence should thus attribute coronal heating firmly to small-scale magnetic activity phenomena, such as spicules, micro-flares, nano-flares, and others. The photosphere and the corona are synchronously heated, which should seemingly prefer magnetic reconnection heating to wave heating. In the long term, such a coronal heating way is inferred effective. Statistically, it is also small-scale magnetic activity phenomena that produce TSI enhancement. Coronal heating and solar wind acceleration are found to be synchronous, as standard models require.


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Author for correspondence: W. Feng, E-mail:


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Alfven, H. 1947, MNRAS, 107, 211. doi: 10.1093/mnras/107.2.211
Arregui, I. 2015, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 373, 20140261. doi: 10.1098/rsta.2014.0261
Atac, T., 1987 Astrophysics Space Science, 135, 201. doi: 10.1007/BF00644477
Cranmer, S. R. 2009, Living Reviews in Solar Physics, 6, 1. doi: 10.12942/lrsp-2009-3
Cranmer, S. R. 2012, Space Sci. Rev., 172, 145. doi: 10.1007/s11214-010-9674-7
Das, T. K., Chatterjee, T. N., & Sen, A. K. 1993, SoPh, 148, 61. doi: 10.1007/BF00675535
De Moortel, I., & Browning, P. 2015, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 373, 20140269. doi: 10.1098/rsta.2014.0269
Fisher, R. A. 1915, Biometrika, 10, 507. doi: 10.1093/biomet/10.4.507
Frohlich, C. 2006, Space Sci. Rev., 125, 53. doi: 10.1007/s11214-006-9046-5
Golub, L., Krieger, A. S., Silk, J. K., Timothy, A. F., & Vaiana, G. S. 1974, ApJ, 189, L93.
Hassler, D. M., Dammasch, I. E., Lemaire, P., et al. 1999, Science 283, 810. doi: 10.1126/science.283.5403.810
Heath, D. F., & Schlesinger, B. M. 1986, JGR, 91, 8672. doi: 10.1029/JD091iD08p08672
Hempelmann, A., & Weber, W. 2012, SoPh, 277, 417. doi: 10.1007/s11207-011-9905-4
Howard, R. 1980, Quarterly Bulletin on Solar Activity, 203, 275.
Ji, H. S., Cao, W. D., & Goode, P. R. 2012, ApJ, 750, L25. doi: 10.1088/2041-8205/750/1/L25
Li, K. J., Feng, W., Liang, H. F., Zhan, L. S., & Gao, P. X. 2011, Annales Geophysicae, 29, 341. doi: 10.5194/angeo-29-341-2011
Li, K. J., Feng, W., Xu, J. C., et al. 2012, ApJ, 747, 135. doi: 10.1088/0004-637X/747/2/135
Li, K. J., Irie, M., Wang, J. X., et al. 2002, Publ. Astron. Soc. Japan, 54, 787. doi: 10.1093/pasj/54.5.787
Li, K. J., Kong, D. F., Liang, H. F., Feng, W. 2014, Astron. Nachr., 335, 371. doi: doi:10.1002/asna.201312016
Li, K. J., Zhanng, J., & Feng, W. 2016, AJ, 151, 128. doi: 10.3847/0004-6256/151/5/128
Li, K. J., Xu, J. C., & Feng, W. 2018, ApJSS, 237, 7. doi: 10.3847/1538-4365/aac7c8
Lukac, B., & Rybansky, M. 2010, SoPh, 263, 43. doi: 10.1007/s11207-010-9545-0
Martin, S. F. 1988, SoPh, 117, 243. doi: 10.1007/BF00147246
Minarovjech, M., Rusin, V., & Saniga, M. 2011, Contrib. Astron. Obs. Skalnate Pleso, 41, 137.
Parker, E. N. 1972, ApJ, 174, 499. doi: 10.1086/151512
Parker, E. N. 1988, ApJ, 330, 474. doi: doi:10.1086/166485
Parker, E. N. 1991, ApJ, 372, 719. doi: doi:10.1086/170015
Porter, J. G., Moore, R. L., Reichmann, E. J., Engvold, O., & Harvey, K. L. 1987, ApJ, 323, 380. doi: 10.1086/165835
Shibata, K., Nakamura, T., Matsumoto, T., et al. 2007, Science, 318, 1591. doi: 10.1126/science.1146708
Solanki, S. K., Krivova, N. A., & Haigh, J. D. 2013, Ann. Rev. of Astron. and Astrophys., 51, 311. doi: 10.1146/annurev-astro-082812-141007
Spruit, H. C., & Zwaan, C. 1981, SoPh, 70, 207. doi: 10.1007/BF00151329
Storini, M., Hofer, M. Y., & Sykora, J. 2006, Advances in Space Research, 38, 912. doi:
Tavabi, E., Koutchmy, S., & Golub, L. 2015, SoPh, 290, 2871. doi: 10.1007/s11207-015-0771-3
Tavabi, E. 2018, MNRAS, 476, 868. doi: 10.1093/mnras/sty020
Tu, C. Y., Zhou, C., Marsch, E., et al. 2005, Science 308, 519. doi: 10.1126/science.1109447
Waldmeier, M. 1981, SoPh, 70, 251. doi: 10.1007/BF00151332
Wang, Y. M. 2012, Space Sci. Rev., 172, 123. doi: 10.1007/s11214-010-9733-0
Wilhelm, K., Dammasch, I. E., Marsch, E., & Hassler, D. M. 2000, A&A, 353, 749.
Wilmot-Smith, A. L. 2015, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 373, 20140265. doi: 10.1098/rsta.2014.0265
Viereck, R. A., & Puga, L. C. 1999, JGR, 104, 9995. doi: 10.1029/1998JA900163
Xiang, N. B., Qu, Z. N., & Zhai, Q. 2014, AJ, 148, 12. doi: 10.1088/0004-6256/148/1/12
Xiang, N. B., & Qu, Z. N. 2016, AJ, 151, 3. doi: 10.3847/0004-6256/151/3/76
Yang, K. E, Longcope, D. W., Ding, M. D., & Guo, Y. 2018, NatCo, 9, 692. doi: 10.1038/s41467-018-03056-8
Zhang, J., & Liu, Y. 2011, ApJL, 741, L7. doi: 10.1088/2041-8205/741/1/L7


Investigation of the coronal heating through phase relation of solar activity indexes

  • K. J. Li (a1) (a2) (a3), J. C. Xu (a1) (a2) (a3), Z. Q. Yin (a2) (a3), J. L. Xie (a1) (a2) (a3) and W. Feng (a4)...


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