see-2005 nor amberd, armenia 28 september 2005

Long-term prediction of solar extreme events

basing on the general regularities of energetic particle generation by the Sun

by Rikho NymmikSkobeltsyn Institute of Nuclear Physics,

Lomonosov Moscow State University

SEE-2005 Nor Amberd, Armenia 28 September 2005

S

E

? ?

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 NymmikNor Amberd, September 2005

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)


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


“anomalously large events are somewhat more likely

to occur early or late in the active phase of solar cycle”.

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“.


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


“there may be a tendency for the largest events

to occur during the 2nd to 4th year after SA maximum”

All these declarations are of illusory but not physical

nature, because they have never been

supported by any mathematical or statistical

argument


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.)


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.


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.


• 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.


Therefore,we used and analyzed the experimental data on the ≥30 MeV

SEP events, proton

fluences andpeak 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.


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.


SEP data base


The SEP event distribution function of ≥30 MeV proton fluences.

o

exp

)(

=0.32 and Фo=8.9109.

SEP data base


Distributionfunction SEP events by E≥30 MeV proton peak fluxes.

o

exp

)(

=0.32 and Фo=9.1103.

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.


Functions for separate groups


The data from topto bottom are:• for the total set of events,• for events at W>80,• for events at W<80,• for events at W<40.

Normalized distribution functions


∑Wall=27819,

∑W≥80=20189,

∑W<80=7630

∑W≤40=3018.

SEP events and fluences


1 SA All W≥80 W<80 W<40

2 Months 279 162 217 140

3 ∑W 27819 20189 7630 3018

4 n(F30≥106) 194 133 61 30

5 n(F30≥106)/ ∑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

6 n(F30≥4·108) 18 13 5 2

7 n(F30≥4·108)/ ∑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 ∑F30 [prot/cm2] 3.1·1010 2.4·1010 7.1·109 1.6·109

9 ∑F30/ ∑W 1.12·106 1.2·106 9.4·105 5.4·105

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.



The distribution functions

for the ascending

and declining phases

The normalized distribution functions

•


The normalized functions of the

ascending and declining

phases are close to one

another because the ascending phase

is shorter andcontains a

smaller total sum of sunspots

compared withthe declining

phase

SEP events and fluences


1 SA phase Ascending Declining Maximum

2 Duration (years) 9.4 18.6 3

3 ∑W 9394 13080 5020

4 n(F30≥106) 60 90 43

5 n(F30≥106)/ ∑W (6.4±0.6)∙10-3 (6.9±0.6)∙10-3 (8.5±1.3)∙10-3

6 n(F30≥4·108)/(∑W) 4 (4.2±2.1)-4 7 (5.4±2.0)-4 7 (1.4±0.5)-3

7 n(F30≥4·109) 1 0 1

8 ∑F30 [prot/cm2] 9.7∙109 9.1∙109 1.3∙109

9 ∑F30/ ∑W 1.0∙106 7.0∙105 2.5∙106

Quiet Sun and SEP events


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 caseof the radiation hazard

calculations!In this Fig. we

see the situation after August 2004.

Quiet Sun and SEP fluences


This Fig. shows the SEP cumulative

fluence differentialenergy spectra

for SA minimum of 1994-1997

and for the SA minimum

months after Aug. 2004

together with GCR spectra

W=390W=990

Quiet Sun of 2004-2005 and SEP fluences


The Quiet Sun period

began in Aug. 2004Since Sept. 2005,

18 significant SEP events

occurred,including two

largest events.The event of 20.

January 2005 havethe hardest energy

spectrum

W=390

Quiet Sun of 2004- 2005, SEP fluences, and the MSU model


Actually, this situation

is not surprising.According to the

MSU SEPfluence model,

such large fluencesshould occur with

probability p=0.1 for

SA ∑W=390 and p=0.01

for E>400 MeV.

Quiet Sun of 1994-1997, SEP fluences, and the MSU model


For this period (∑W=990),

the situation with the SEP

and GCRfluences was quite

ordinary.According to the MSU SEP

model,the SEP fluence

occurrence probability

was close to 0.5.

CONCLUSION


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.

CONCLUSIONS


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).

CONCLUSIONS


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.

see-2005 nor amberd, armenia 28 september 2005

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