Solar Physics

, 293:141 | Cite as

Long-Term Modulation of Cosmic-Ray Intensity and Correlation Analysis Using Solar and Heliospheric Parameters

  • V. K. MishraEmail author
  • A. P. Mishra


Based on the monthly sunspot numbers (SSNs), the solar-flare index (SFI), grouped solar flares (GSFs), the tilt angle of heliospheric current sheet (HCS), and cosmic-ray intensity (CRI) for Solar Cycles 21 – 24, a detailed correlation study has been performed using the cycle-wise average correlation (with and without time lag) method as well as by the “running cross-correlation” method. It is found that the slope of regression lines between SSN and SFI, as well as between SSN and GSF, is continuously decreasing from Solar Cycle 21 to 24. The length of regression lines has significantly decreased during Cycles 23 and 24 in comparison to Cycles 21 and 22. The cross-correlation coefficient (without time lag) between SSN–CRI, SFI–CRI, and GSF–CRI has been found to be almost the same during Cycles 21 and 22, while during Cycles 23 and 24 it is significantly higher between SSN–CRI and HCS–CRI than for SFI–CRI and GSF–CRI. Considering time lags of 1 to 20 months, the maximum correlation coefficient (negative) amongst all of the sets of solar parameters is observed with almost the same time lags during Cycles 21 – 23, whereas exceptional behaviour of the time lag has been observed during Cycle 24, as the correlation coefficient attains its maximum value with two time lags (four and ten months) in the case of the SSN–CRI relationship. A remarkably large time lag (22 months) between HCS and CRI has been observed during the odd-numbered Cycle 21, whereas during another odd cycle, Cycle 23, the lag is small (nine months) in comparison to that for other solar/flare parameters (13 – 15 months). On the other hand, the time lag between SSN–CRI and HCS–CRI has been found to be almost the same during even-numbered Solar Cycles 22 and 24. A similar analysis has been performed between SFI and CRI, and it is found that the correlation coefficient is maximum at zero time lag during the present solar cycle. The GSFs have shown better maximum correlation with CRI as compared to SFI during Cycles 21 to 23, indicating that GSF could also be used as a significant solar parameter to study the cosmic-ray modulation. Furthermore, the running cross-correlation coefficient between SSN–CRI and HCS–CRI, as well as between solar-flare activity parameters (SFI and GSF) and CRI is observed to be strong during the ascending and descending phases of solar cycles. The level of cosmic-ray modulation during the period of investigation shows the appropriateness of different parameters in different cycles, and even during the different phases of a particular solar cycle. We have also studied the galactic cosmic-ray modulation in relation to combined solar and heliospheric parameters using the empirical model suggested by Paouris et al. (Solar Phys.280, 255, 2012). The proposed model for the calculation of the modulated cosmic-ray intensity obtained from the combination of solar and heliospheric parameter gives a very satisfactory value of standard deviation as well as \(R^{2}\) (the coefficient of determination) for Solar Cycles 21 – 24.


Cosmic rays, galactic Solar cycles, observations Sunspots, statistics 



The authors are thankful to the National Geophysical Data Centre (NGDC) and WDC-SILSO, Royal Observatory of Belgium, Brussels, for providing monthly mean sunspot data. Further, we also acknowledge, with thanks, the staff of the Oulu and Moscow neutron monitors for providing monthly mean cosmic-ray data through their websites. The Wilcox Solar Observatory (WSO) is acknowledged for providing the tilt-angle data of the heliospheric neutral current sheet. The authors are also grateful to the anonymous reviewers for their valuable comments and suggestions to improve the quality of the article.

Disclosure of Potential Conflicts of Interest

The authors declare that they have no conflicts of interest.


  1. Ahluwalia, H.S.: 1979, In: Miyake, S. (ed.) Proc. 16th ICRC 5, Inst. Cosmic Ray Research, Univ. of Tokyo, Tokyo, 182. Google Scholar
  2. Belov, A.: 2000, Space Sci. Rev. 93, 79. ADSCrossRefGoogle Scholar
  3. Belov, A., Gushchina, R.T., Sirotina, I.V.: 1995, In: Iucci, N., Lamanna, E. (eds.) Proc. 24th ICRC 4, Int. Union Pure Appl. Phys., Rome, 542. Google Scholar
  4. Chattopadhyay, R., Midya, S.K., De, U.K.: 2003, Indian J. Radio Space Phys. 32, 135. Google Scholar
  5. Dorman, I.V., Dorman, L.I.: 1967, J. Geophys. Res. 72, 1513. ADSCrossRefGoogle Scholar
  6. Forbush, S.E.: 1958, J. Geophys. Res. 63, 651. ADSCrossRefGoogle Scholar
  7. Gupta, M., Mishra, V.K., Mishra, A.P.: 2006a, Indian J. Radio Space Phys. 35, 167. Google Scholar
  8. Gupta, M., Mishra, V.K., Mishra, A.P.: 2006b, Indian J. Phys. 80, 697. Google Scholar
  9. Gupta, M., Mishra, V.K., Mishra, A.P.: 2006c, J. Astrophys. Astron. 27, 455. ADSCrossRefGoogle Scholar
  10. Gupta, M., Mishra, V.K., Mishra, A.P.: 2007, J. Geophys. Res. 112, A05105. DOI. ADSCrossRefGoogle Scholar
  11. Gupta, M., Narang, S.R., Mishra, V.K., Mishra, A.P.: 2014, Int. J. Eng. Tech. Manag. Appl. Sci. 2, 104. Google Scholar
  12. Hathaway, D.H., Wilson, R.M., Reichmann, E.J.: 2002, Solar Phys. 211, 357. DOI. ADS. ADSCrossRefGoogle Scholar
  13. Iskara, K., Wybraniec, B.: 2001, In: Droege, N.W., Kunow, H., Scholer, M. (eds.) 27th Int. Cosmic Ray Conf. 9, Copernicus, Hamburg, 3807. Google Scholar
  14. Jokipii, J.R., Levy, E.H., Hubbard, W.B.: 1977, Astrophys. J. 213, 861. ADSCrossRefGoogle Scholar
  15. Jokipii, J.R., Thomas, B.T.: 1981, Astrophys. J. 243, 1115. ADSCrossRefGoogle Scholar
  16. Kleczek, J.: 1952, Pub. Inst. Centr. Astron. 22, Prague. Google Scholar
  17. Kota, J., Jokipii, J.R.: 1991, Geophys. Res. Lett. 8, 1979. Google Scholar
  18. Mavromichalaki, H.: 2012, In: Maris, G., Demetrescu, C. (eds.) Adv. Solar SolarTerr. Phys. 135. Google Scholar
  19. Mavromichalaki, H., Belehaki, A., Rafios, X.: 1998, Astron. Astrophys. 330, 764. ADSGoogle Scholar
  20. Mavromichalaki, H., Marmatsouri, E., Vassilaki, A.: 1990, Solar Phys. 125, 409. DOI. ADS. ADSCrossRefGoogle Scholar
  21. Mavromichalaki, H., Paouris, E.: 2012, Adv. Astron. 2012, 607172. DOI. ADSCrossRefGoogle Scholar
  22. Mavromichalaki, H., Paouris, E., Karalidi, T.: 2007, Solar Phys. 245, 369. DOI. ADS. ADSCrossRefGoogle Scholar
  23. Mishra, A.P., Gupta, M., Mishra, V.K.: 2006, Solar Phys. 239, 475. DOI. ADS. ADSCrossRefGoogle Scholar
  24. Mishra, V.K., Mishra, A.P.: 2016a, Indian J. Phys. 90, 1333. ADSCrossRefGoogle Scholar
  25. Mishra, V.K., Mishra, A.P.: 2016b, Int. J. Sci. Eng. Tech. Res. 5, 390. CrossRefGoogle Scholar
  26. Mishra, V.K., Tiwari, D.P.: 2003, Indian J. Radio Space Phys. 32, 65. Google Scholar
  27. Mishra, V.K., Tiwari, D.P., Tiwari, C.M., Agrawal, S.P.: 2005, Indian J. Radio Space Phys. 34, 13. Google Scholar
  28. Mishra, V.K., Gupta, M., Mishra, B.N., Nigam, S.K., Mishra, A.P.: 2008, J. Astrophys. Astron. 29, 257. ADSCrossRefGoogle Scholar
  29. Nagashima, K., Morishita, I.: 1980a, Planet. Space Sci. 28, 117. Google Scholar
  30. Nagashima, K., Morishita, I.: 1980b, Planet. Space Sci. 28, 177. ADSCrossRefGoogle Scholar
  31. Pacini, A.A., Usoskin, I.G.: 2015, Solar Phys. 290, 943. DOI. ADS. ADSCrossRefGoogle Scholar
  32. Paouris, E., Mavromichalaki, H., Belov, A., Gushchina, R., Yanke, V.: 2012, Solar Phys. 280, 255. DOI. ADS. ADSCrossRefGoogle Scholar
  33. Pomerantz, M.A., Duggal, S.P.: 1971, Space Sci. Rev. 12, 75. ADSCrossRefGoogle Scholar
  34. Potgieter, M.S.: 1998, Space Sci. Rev. 83, 147. ADSCrossRefGoogle Scholar
  35. Potgieter, M.S.: 2013, Living Rev. Solar Phys. 10, 3. ADSCrossRefGoogle Scholar
  36. Rao, U.R.: 1972, Space Sci. Rev. 12, 719. ADSCrossRefGoogle Scholar
  37. Sabbah, I., Kudela, K., Al Jasar, H.K., Rybansky, M.: 2003, Geophys. Res. Abstr. 5, 08367. Google Scholar
  38. Smart, M.A., Shea, D.F.: 1981, Adv. Space Res. 1, 147. ADSCrossRefGoogle Scholar
  39. Smith, E.J.: 1990, J. Geophys. Res. 95, 731. Google Scholar
  40. Thomas, S.R., Owens, M.J., Lockwood, M.: 2014, Solar Phys. 289, 407. DOI. ADS. ADSCrossRefGoogle Scholar
  41. Usoskin, I.G., Kananen, H., Mursula, K., Tankanen, P., Kavaltsov, G.A.: 1998, J. Geophys. Res. 103(A5), 9567. ADSCrossRefGoogle Scholar
  42. Valdes-Galicia, J.F., Caballero-Lopez, R.A.: 2003, In: Kajita, T., Asaoka, Y., Kawachi, A., Sasaki, M., Matsubara, U. (eds.) Proc. 28th ICRC SH 3.4, Universal Academy Press, Tuskuba, 4107. Google Scholar
  43. Webber, W.R., Lockwood, J.A.: 1988, J. Geophys. Res. 93, 8735. ADSCrossRefGoogle Scholar

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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of PhysicsA.P.S. UniversityRewaIndia

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