Solar Physics

, Volume 245, Issue 2, pp 369–390 | Cite as

Cosmic-Ray Modulation: An Empirical Relation with Solar and Heliospheric Parameters



Long-term variations of galactic cosmic rays were compared with the behavior of various solar activity indices and heliospheric parameters during the current solar cycle. This study continues previous works where the cosmic-ray intensity for the solar cycles 20, 21, and 22 was well simulated from the linear combination of the sunspot number, the number of grouped solar flares, and the geomagnetic index Ap. The application of this model to the current solar cycle characterized by many peculiarities and extreme solar events led us to study more empirical relations between solar-heliospheric variables, such as the interplanetary magnetic field, coronal mass ejections, and the tilt of the heliospheric current sheet, and cosmic-ray modulation. By analyzing monthly cosmic-ray data from the Neutron Monitor Stations of Oulu (cutoff rigidity 0.81 GV) and Moscow (2.42 GV) the contribution of these parameters in the ascending, maximum, and descending phases of the cycle was investigated and it is shown that a combination of these parameters reproduces the majority of the modulation potential variations during this cycle. The approach applied makes it possible to better describe the behavior of cosmic rays in the epochs of the solar maxima, which could not be done before. An extended study of the time profiles, the correlations, and the time lags of the cosmic-ray intensity against these parameters using the method of minimizing RMS over all the considered period 1996 – 2006 determines characteristic properties of this cycle as being an odd cycle. Moreover, the obtained hysteresis curves and a correlative analysis during the positive polarity (qA>0, where q is the particle charge) and during the negative polarity (qA<0) intervals of the cycle result in significantly different behavior between solar and heliospheric parameters. The time lag and the correlation coefficient of the cosmic-ray intensity are higher for the solar indices in comparison to the heliospheric ones. A similar behavior also appears in the case of the intervals with positive and negative polarity of the solar magnetic field.


Cosmic rays Solar cycle Neutron monitors 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Akasofu, S.I.: 1981, Solar Phys. 71, 175. CrossRefADSGoogle Scholar
  2. Alanko-Huotari, K., Mursula, K., Usoskin, I.G., Kovaltsov, G.A.: 2006, Solar Phys. 238, 391. CrossRefADSGoogle Scholar
  3. Badhwar, G.D., O’Neil, P.M.: 1993, Proc. 23rd ICRC 3, 535. Google Scholar
  4. Bai, T.: 2006, Solar Phys. 234, 409. CrossRefADSGoogle Scholar
  5. Belov, A.: 2000, Space Sci. Rev. 93, 79. CrossRefADSGoogle Scholar
  6. Belov, A.V., Gushchina, R.T., Yanke, V.G.: 1997, Proc. 25th ICRC 2, 61. Google Scholar
  7. Belov, A., Shelding, B.D., Gushchina, R.T., Obridko, V.N., Kharshiladze, A.F., Yanke, V.G.: 2001, J. Atmos. Solar-Terr. Phys 63, 1923. CrossRefADSGoogle Scholar
  8. Belov, A., Baisultanova, L., Eroshenko, E., Mavromichalaki, H., Yanke, V., Pchelkin, V., Plainaki, C., Mariatos, G.: 2005, J. Geophys. Res. 110, 9. CrossRefGoogle Scholar
  9. Burlaga, L.F., McDonald, F.B., Ness, N.F.: 1993, J. Geophys. Res. 98, 1. ADSGoogle Scholar
  10. Cane, H.V.: 1993, J. Geophys. Res. 98, 3509. ADSGoogle Scholar
  11. Cane, H.V.: 1998, Proc. 25th ICRC 8, 135. Google Scholar
  12. Cane, H.V.: 2000, Space Sci. Rev. 93, 55. CrossRefADSGoogle Scholar
  13. Cane, H.V., Richardson, I.G., von Rosenvinge, T.T.: 1996, J. Geophys. Res. 101, 21561. CrossRefADSGoogle Scholar
  14. Cane, H.V., Richardson, I.G., Wibberenz, G.: 1994, J. Geophys. Res. 99, 21429. CrossRefADSGoogle Scholar
  15. Cane, H.V., Wibberenz, G., Richardson, I.G., von Rosenvinge, T.T.: 1999, Geophys. Res. Let. 26, 565. CrossRefADSGoogle Scholar
  16. Chirkov, N.P., Kuzmin, A.I.: 1979, Proc. 16th ICRC 4, 360. Google Scholar
  17. Cliver, E.W., Ling, A.G.: 2001, Astrophys. J. 556, 432. CrossRefADSGoogle Scholar
  18. Eroshenko, E., Belov, A., Mavromichalaki, H., Mariatos, G., Oleneva, V., Plainaki, C., Yanke, V.: 2004, Solar Phys. 224, 345. CrossRefADSGoogle Scholar
  19. Exarhos, G., Moussas, X.: 1999, Solar Phys. 187, 157. CrossRefADSGoogle Scholar
  20. Forbush, S.E.: 1958, J. Geophys. Res. 63, 651. ADSGoogle Scholar
  21. Gnevyshev, M.N.: 1967, Solar Phys. 51, 175. ADSGoogle Scholar
  22. Gonzalez, W.D., Joselyn, J.A., Kamide, Y., Kroehl, H.W., Rostoker, G., Tsurutani, B.T., Vasyliunas, V.M.: 1994, J. Geophys. Res. 99, 5771. CrossRefADSGoogle Scholar
  23. Gosling, J.T., McComas, D.J., Phillips, J.L., Bame, S.J.: 1991, J. Geophys. Res. 96, 7831. ADSCrossRefGoogle Scholar
  24. Gosling, J.T., McComas, D.J., Phillips, J.L., Weiss, L.A., Pizzo, V.J., Goldstein, B.E., Forsyth, R.J.: 1993, Geophys. Res. Let. 21, 2271. CrossRefADSGoogle Scholar
  25. Gupta, M., Mishra, V.K., Mishra, A.P.: 2006, J. Astrophys. Astron. 27, 455. CrossRefADSGoogle Scholar
  26. Hatton, G.J.: 1980, Solar Phys. 66, 159. CrossRefADSGoogle Scholar
  27. Jokipii, J.R., Thomas, B.: 1981, Astrophys. J. 243, 1115. CrossRefADSGoogle Scholar
  28. Kahler, S.: 1987, Rev. Geophys. 25, 663. ADSGoogle Scholar
  29. Kane, R.P.: 2006, Solar Phys. 233, 107. CrossRefADSGoogle Scholar
  30. Kota, J., Jokipii, J.R.: 1991, Geophys. Res. Lett. 8, 1979. Google Scholar
  31. Kudela, K., Storini, M., Hofer, M.Y., Belov, A.: 2000, Space Sci. Rev. 93, 153. CrossRefADSGoogle Scholar
  32. Lantos, P.: 2005, Solar Phys. 229, 373. CrossRefADSGoogle Scholar
  33. Lockwood, J.A.: 1971, Space Sci. Rev. 12, 658. CrossRefADSGoogle Scholar
  34. Lockwood, J.A., Webber, W.R., Hoeksema, J.T.: 1988, J. Geophys. Res. 93, 7521. ADSGoogle Scholar
  35. Mavromichalaki, H., Petropoulos, B.: 1984, Astrophys. Space Sci. 106, 61. CrossRefADSGoogle Scholar
  36. Mavromichalaki, H., Petropoulos, B.: 1987, Earth Moon Planets 37, 79. CrossRefADSGoogle Scholar
  37. Mavromichalaki, H., Belehaki, A., Rafios, X.: 1998, Astron. Astrophys. 330, 764. ADSGoogle Scholar
  38. Mavromichalaki, H., Marmatsouri, E., Vassilaki, A.: 1988, Earth Moon Planets 42, 233. CrossRefADSGoogle Scholar
  39. Mavromichalaki, H., Marmatsouri, E., Vassilaki, A.: 1990, Solar Phys. 125, 409. CrossRefADSGoogle Scholar
  40. Mavromichalaki, H., Paouris, E., Karalidi, T.: 2006, AIP Conf. Ser. 48, 184. CrossRefADSGoogle Scholar
  41. Mavromichalaki, H., Belehaki, A., Rafios, X., Tsagouri, I.: 1997, Astrophys. Space Sci. 246, 7. CrossRefADSGoogle Scholar
  42. McDonald, F.B.: 1998, Space Sci. Rev. 83, 33. CrossRefADSGoogle Scholar
  43. Moraal, H.: 1976, Space Sci. Rev. 19, 845. CrossRefADSGoogle Scholar
  44. Morishita, I., Sakakibara, S.: 1999, Proc. 28th ICRC 7, 87. Google Scholar
  45. Nagashima, K., Morishita, I.: 1980a, Planet. Space Sci. 28, 117. CrossRefGoogle Scholar
  46. Nagashima, K., Morishita, I.: 1980b, Planet. Space Sci. 28, 177. CrossRefADSGoogle Scholar
  47. Newirk, G. Jr., Hundhausen, A.J., Pizzo, V.: 1981, J. Geophys. Res. 86, 5387. ADSGoogle Scholar
  48. Otaola, J., Perez-Enriquez, R., Valdes-Galicia, J.F.: 1985, In: Proc. 19th ICRC (La Jolla) 4, 93. Google Scholar
  49. Perko, J.S., Fisk, L.A.: 1983, J. Geophys. Res. 12, 343. Google Scholar
  50. Pomerantz, M.A., Dugal, S.R.: 1974, Rev. Geophys. Space Phys. 12, 343. ADSGoogle Scholar
  51. Potgieter, M.S.: 1998, Space Sci. Rev. 83, 147. CrossRefADSGoogle Scholar
  52. Usoskin, I., Kananen, H., Mursula, K., Tanskanen, P., Kovaltsov, G.A.: 1998, J. Geophys. Res. 103, 9567. CrossRefADSGoogle Scholar
  53. Usoskin, I., Mursula, K., Solanki, S., Shuessler, M., Kovaltsov, G.: 2002, J. Geophys. Res. 107, DOI: 10.1029/2002JA009343.
  54. Wibberenz, G., Cane, H.V.: 2000, J. Geophys. Res. 105, 18315. CrossRefADSGoogle Scholar
  55. Xanthakis, J., Mavromichalaki, H., Petropoulos, B.: 1981, Astrophys. Space Sci. 74, 303. CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Physics DepartmentNational and Kapodistrian University of AthensAthensGreece
  2. 2.Department of Physics and AstrophysicsUniversity of UtrechtUtrechtThe Netherlands

Personalised recommendations