1. Long-term prediction of solar extreme events basing on the general regularities of energetic particle generation by the Sun by Rikho Nymmik Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University SEE-2005 Nor Amberd, Armenia 28 September 2005 S E ? ?

2. The SEP generation by the Sun and the SEP event occurrences in the Earth orbit are of probabilistic nature. But certain regularities inherent to SEP fluxes and events can well be inferred from the present-day experimental data. These regularities may be used in predicting the probability for SEP events (the solar extreme events, in particular) to occur. Rikho Nymmik Nor Amberd, September 2005

3. There exist some myths about the extreme SEP event occurrences These myths were formulated by: J. King (1974) J. Goswami et al. (1988) J. Feynman et al. (1990) Rikho Nymmik Nor Amberd, September 2005

4. J. King (1974) (in King, J.H. Solar Proton Fluences for 1977-1983 Space Missions, Journal of Spacecraft and Rockets, v.11, No.6, pp.401-409, 1974.) states that Rikho Nymmik Nor Amberd, September 2005 “anomalously large events are somewhat more likely to occur early or late in the active phase of solar cycle”.

5. J. Goswami et al. (1988) in (Goswami J.N.,.McGuire R.E,.Reedy R.C,.Lal D, and Jha R., Solar flare protons and alpha particles during the last three solar cycles, JGR, V.93, No.A7, pp.7195-7205, 1988.) claim that „it is the fact that major flare events are relative rare near the sunspot maximum and occur mostly in the ascending and declining phases of sunspot occurrence“. Rikho Nymmik Nor Amberd, September 2005

6. J. Feynman et al. (1990) in (Feynman J., T.P.Armstrong, L.Dao-Gibner, and S.Silverman, Solar proton events during solar cycles 19, 20, and 21. Solar Physics 126, 385-401, 1990b.) say Rikho Nymmik Nor Amberd, September 2005 “there may be a tendency for the largest events to occur during the 2nd to 4th year after SA maximum”

7. All these declarations are of illusory but not physical nature, because they have never been supported by any mathematical or statistical argument Rikho Nymmik Nor Amberd, September 2005

8. We set forth quite a different concept of the extreme SEP event occurrences, basing on the statistical and mathematical methods of analyzing the SEP experimental data. We presented our concept first at the ICRC-25 in 1999. (Nymmik R.A., Relationships among solar activity, SEP occurrence frequency, and solar energetic particle distribution function, in: Proceedings of the 26-th ICRC V. 8, 3197-3200, 1999.) Rikho Nymmik Nor Amberd, September 2005

9. The concept of this work was essentially as follows: The SEP event proton distribution functions for different solar activity periods can be described to be power-law functions that have the same spectral form (i.e., the same spectral indices and depending on particle energy turnoff fluxes). The large (extreme) SEP events occur to within quite a definite probability at any SA, even during solar minima. Rikho Nymmik Nor Amberd, September 2005

10. It is now indisputable that the extremely solar events are part of the total set of SEP events. Therefore, our detailed analysis is made in terms of investigating the set of SEP events. The SEP event set is primarily characterized by the event distribution functions. Therefore, the detailed examination of the SEP event distribution functions and their properties underlies our analysis. Rikho Nymmik Nor Amberd, September 2005

11. Compared with our earlier works, we shall study in more detail the dependence of SEP event distribution on solar activity. In our analysis, we only used the experimental data, of which we are quite confident that: the SEP events are selected as physical, but not technical phenomenon, they have been checked on carefully, and they do not suffer systematical errors. Rikho Nymmik Nor Amberd, September 2005

12. Therefore, we used and analyzed the experimental data on the ≥30 MeV SEP events, proton fluences and peak fluxes measured by the CPME instrument on IMP-8 from July 1974 to September 1986 and by the TELESCOPE and DOME instruments on GOES-7,8,10,11 (so called uncorrected data) from October 1986 to September 2005. Rikho Nymmik Nor Amberd, September 2005

13. If we neglect the threshold effect, then the experimental data will lead to the distribution function form generalizations that are far from reality (Kurt and Nymmik, 1997). Examples of that kind the function forms are: the lognormal distribution function (J.Feynman, et al., 1991), or the power-law functions with a knee (Smart and Shea,1997, S.Gabriel and J.Feynman, 1996, et al.). In our opinion, if we bear in mind the threshold effect, the real distribution is a power law with exponential turnoff in the range of high SEP fluences and peak fluxes. Rikho Nymmik Nor Amberd, September 2005

14. SEP data base Rikho Nymmik Nor Amberd, September 2005 The SEP event distribution function of ≥30 MeV proton fluences.  =0.32 and Ф o =8.9  10 9.

15. SEP data base Rikho Nymmik Nor Amberd, September 2005 Distribution function SEP events by E≥30 MeV proton peak fluxes.  =0.32 and Ф o =9.1  10 3.

16. The properties of the distribution functions The main problem is: are the distribution functions independent of solar activity, or they are different at different SA levels? We grouped all the events into 1. - the events that occurred during SA W≥80, 2. – during W<80, and 3. – during W<40 (“quiet" time period) and calculated their distribution functions separately for each group. Rikho Nymmik Nor Amberd, September 2005

17. Functions for separate groups Rikho Nymmik Nor Amberd, September 2005 The data from top to bottom are: for the total set of events, for events at W>80, for events at W<80, for events at W<40.

18. Normalized distribution functions Rikho Nymmik Nor Amberd, September 2005 ∑W all =27819, ∑W≥80=20189, ∑W<80=7630 ∑W≤40=3018.

19. SEP events and fluences Rikho Nymmik Nor Amberd, September 2005 1SA AllW≥80W<80W<40 2Months279162217140 3∑W∑W278192018976303018 4n(F 30 ≥10 6 )1941336130 5n(F 30 ≥10 6 )/ ∑W (7.0±0.5) 10 -3 (6.6±0.6) 10 -3 (8.0±1.0) 10 -3 (9.9±1.8) 10 -3 6n(F 30 ≥4·10 8 )181352 7n(F 30 ≥4·10 8 )/ ∑W (6.5±1.5) 10 -4 (6.5±1.8) 10 -4 (6.7±1.5) 10 -4 (6.9±4.9) 10 -4 8∑F 30 [prot/cm 2 ] 3.1·10 10 2.4·10 10 7.1·10 9 1.6·10 9 9∑F 30 / ∑W 1.12·10 6 1.2·10 6 9.4·10 5 5.4·10 5

20. About the ascending and declining SA phases First of all let us define the ascending and the declining SA phases and the SA maximum period. A SA maximum can be defined to be a one-year period around the adopted months of the Sun’s field sign reversal. Such periods are proposed to be : 1979.96÷1980.96 - for Cycle 21, 1989.46÷1990.46 - for Cycle 22, and 2001.12÷2002.12 - for Cycle 23. The ascending period is defined to last from solar minimum to the left side of solar maximum, and the declining period from the right side of solar maximum to solar minimum. Rikho Nymmik Nor Amberd, September 2005

21. Rikho Nymmik Nor Amberd, September 2005 The distribution functions for the ascending and declining phases

22. The normalized distribution functions Rikho Nymmik Nor Amberd, September 2005 The normalized functions of the ascending and declining phases are close to one another because the ascending phase is shorter and contains a smaller total sum of sunspots compared with the declining phase

23. SEP events and fluences Rikho Nymmik Nor Amberd, September 2005 1SA phaseAscendingDecliningMaximum 2Duration (years)9.418.63 3∑W∑W9394130805020 4n(F 30 ≥10 6 )609043 5n(F 30 ≥10 6 )/ ∑W (6.4±0.6)∙10 -3 (6.9±0.6)∙10 -3 (8.5±1.3)∙10 -3 6n(F 30 ≥4·10 8 )/(∑W) 4 (4.2±2.1) -4 7 (5.4±2.0) -4 7 (1.4±0.5) -3 7n(F 30 ≥4·10 9 )101 8∑F 30 [prot/cm 2 ]9.7∙10 9 9.1∙10 9 1.3∙10 9 9∑F 30 / ∑W1.0∙10 6 7.0∙10 5 2.5∙10 6

24. Quiet Sun and SEP events Rikho Nymmik Nor Amberd, September 2005 According to the NASA SEP models JPL-91 and ESP, the high-energy solar particles that occur during Quiet Sun period (W<40) can be neglected in case of the radiation hazard calculations! In this Fig. we see the situation after August 2004.

25. Quiet Sun and SEP fluences Rikho Nymmik Nor Amberd, September 2005 This Fig. shows the SEP cumulative fluence differential energy spectra for SA minimum of 1994-1997 and for the SA minimum months after Aug. 2004 together with GCR spectra W=390 W=990

26. Quiet Sun of 2004-2005 and SEP fluences Rikho Nymmik Nor Amberd, September 2005 The Quiet Sun period began in Aug. 2004 Since Sept. 2005, 18 significant SEP events occurred, including two largest events. The event of 20. January 2005 have the hardest energy spectrum W=390

27. Quiet Sun of 2004- 2005, SEP fluences, and the MSU model Rikho Nymmik Nor Amberd, September 2005 Actually, this situation is not surprising. According to the MSU SEP fluence model, such large fluences should occur with probability p=0.1 for SA ∑W=390 and p=0.01 for E>400 MeV.

28. Quiet Sun of 1994-1997, SEP fluences, and the MSU model Rikho Nymmik Nor Amberd, September 2005 For this period (∑W=990), the situation with the SEP and GCR fluences was quite ordinary. According to the MSU SEP model, the SEP fluence occurrence probability was close to 0.5.

29. CONCLUSION Rikho Nymmik Nor Amberd, September 2005 The extremely large SEP events can occur during any solar activity phase. The probability for them to occur is the same in the periods of identical sums of smoothed mean-monthly sunspot numbers.

30. CONCLUSIONS Rikho Nymmik Nor Amberd, September 2005 The results obtained disprove quite a number of widespread fallacies, first of all the claimed negligible SEP fluxes during quiet Sun that underlie the JPL-91 (Feynman et al. 1993) and ESP (Xapsos et al. 1998,1999) SEP flux and fluence models (NASA).

31. CONCLUSIONS Rikho Nymmik Nor Amberd, September 2005 From the invariance of the normalized distribution function, it follows that the extremely large SEP events can well occur during any solar activity phase, including even the quite Sun period.