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Advances in Space Research 42 (2008) 1288–1292

To the problem on the reliability of solar energetic proton flux models

R.A. Nymmik *

Skobeltsyn Institute of Nuclear Physics, Moscow State University, 119991 Moscow, Russia

Received 10 August 2006; received in revised form 19 December 2007; accepted 19 December 2007

Abstract

This work analyses basic issues of conformity of the most well-known models of solar energetic particles (SEP) fluxes to the exper-imental data. It is shown, that the postulates on neglecting SEP fluxes in quiet Sun years and on invariability SEP fluxes in active Sunyears, underlying some models, contradict the experimental data.� 2008 COSPAR. Published by Elsevier Ltd. All rights reserved.

Keywords: Solar energetic particle fluxes; Models of; Conformity of models to the experimental data

1. Introduction

At present, widely known computation models intendedfor predicting the probability of occurrence of cumulativefluences of SEP event protons during the future space flights.These models are: JPL-91 (Feynman et al., 1993), SPE (Xap-sos et al., 1996, 1998) and the MSU model, the first version ofwhich was published in Nymmik’s paper (1999a). The readercan become familiar with the description of last versions andmake calculations using the MSU model in interactive modeon the Internet (Website Nymmik, 2004).

The first two models were developed under identicalassumptions, that:

� fluxes of SEP particles during the 4-year quiet Sun per-iod can be neglected;� during the 7-year active Sun period the mean rate of

SEP events occurrence is constant.

The MSU model is based on two regularities related toSEP events (Nymmik, 1999b, 2007a,b), namely:

� the mean rate of SEP events is proportional to the levelof solar activity described as a smoothed monthly sun-spot number;

0273-1177/$34.00 � 2008 COSPAR. Published by Elsevier Ltd. All rights rese

doi:10.1016/j.asr.2007.12.011

* Tel.: +7 095 9328861; fax: +7 095 9395034.E-mail address: nymmik@sinp.msu.ru

� the SEP events distribution functions, recorded duringvarious solar activity levels or phases, being divided bythe sums of smoothed monthly mean sunspot numbers(P

W) during the time of observation, are identicalwithin the limits of statistical errors.

The present work is an attempt to demonstrate that sim-plified ideas, underlying first two models, contradict theavailable experimental data.

2. SEP events and fluxes during quiet Sun years

The authors of JPL-91 and SPE models separate thesolar cycle into two parts. The active Sun years are usuallyrepresented by the 7-year period covering 2.5 years before,and 4.5 years after the solar activity maximum. Remainingyears are considered to be the quiet Sun years. These twoperiods are separated by the solar activity (SA) level, whichis determined, to a rather good accuracy, by the sunspot(Wolf’s) number – 40 (Feynman et al., 1990).

Without doubt, during SA minimum years the rate ofSEP events occurrence is lower, than that in years closeto the maximum. Probably, from the viewpoint of quantityof events occurring during active Sun years, the eventsoccurring during quite Sun years can be neglected. How-ever, for the purpose of modeling the space radiation envi-ronment, the question should be stated differently, namely,

rved.

Fig. 2. Differential energy spectra of annual SEP fluences in 1995 and1997 – the dashed and solid line, respectively. Broken lines are the fluencesmeasured by GOES spacecraft instruments, and the smooth lines are therespective energy spectra approximations. The respective annual GCRfluence energy spectra are displayed also.

R.A. Nymmik / Advances in Space Research 42 (2008) 1288–1292 1289

whether is it possible to neglect SEP fluxes in quiet Sunyears as compared to the fluxes of particles of another basiccomponent of radiation environment – the fluxes of parti-cles from galactic cosmic rays (GCR)?

Let us carry out a comparative analysis of SEP andGCR particle fluxes in the quiet Sun years. Fig. 1 showsthe course of solar activity in the last two (22th and 23th)cycles of solar activity in the form of a time dependenceof a smoothed sunspot number (Website NOAA, sun-spots). According to the figure, the quiet Sun periodbetween two SA cycles has covered years of 1994–1997.The quiet Sun period at the end of the 23th cycle beganin October 2004, and in 2005 the smoothed sunspot num-bers decreased from 37.4 in January down to 23.5 inDecember. We shall choose for further analysis the SEPand GCR proton fluences in some of these years.

One SEP event was recorded in 1995 – on October, 20,and two SEP events, following one after another, wererecorded in 1997 – on November 4 and 6. The measuredby the GOES-7,8 spacecrafts DOME and TELESCOPEinstruments fluences (Website NOAA, GOES) and corre-sponding energy spectra are presented in Fig. 2. The samefigure presents corresponding annual energy spectra ofGCR fluences according to the model ISO 15390 (2004),also known as the MSU model (Nymmik et al. 1995) whichis used in the GCR – CREME-96 model (Tylka et al. 1996).

It follows from the above data, that in 1995 the SEPfluxes’ energies E < 40 have exceeded GCR fluxes, and in1997 the same phenomenon occurred even at E < 200 MeV.

Consider the situation based on the 1994 and 2005-yeardata (Fig. 3). The SA conditions for these years were thesame (mean annual Wolf number hWi = 30). These quiteSun years for SEP occurrence were completely different.In 1994 there occurred only one SEP event (February20). Year 2005 is known to be distinguished by extremely

Fig. 1. The smoothed sunspot numbers (Website NOAA, sunspots) for1985–2005 years (22nd and 23rd SA cycles). Dashed lines indicate: thelevel of sunspot number W = 40 and corresponding quiet Sun year ranges.

Fig. 3. Differential energy spectra of annual SEP fluences in 1994 and2005 – the dashed and solid line, respectively. Broken lines are thefluences, measured by GOES spacecraft instruments, and the smooth linesare the respective energy spectra approximations. The respective annualGCR fluence energy spectra are displayed also.

great number of recorded SEP events – 13 in all. Fig. 3 pre-sents the cumulative fluences of SEP events for these yearsaccording to the GOES-7 and GOES-11 satellite measure-ment data (Website NOAA, GOES). These data indicatethat in 1994 the SEP proton fluence exceeds the fluenceof GCR particles up to 35 MeV, and in 2005 the one-yearGCR fluence was exceeded even at E �500 MeV. Notice,

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that the average annual value of solar activity for theseyears (hWi = 30) were much lower than the extreme SAlevel for quite Sun years, which is W = 40.

The below (Figs. 6 and 7) we shall demonstrate, that thesituations, occurred in 1994–1998 and 2005, fall within thelimits of estimates of SEP particle fluxes during the quiteSun years, in accordance with the MSU SEP fluxes model(Nymmik, 1999 and Website Nymmik, 2004).

3. SEP events and fluxes in the active Sun years

Let us consider, to what extent a second basic assump-tion of the JPL91 and ESP model, (that during the 7-yearactive Sun period the mean rate of SEP events occurrenceis constant) is true. The implication of this assumption isthat the average annual fluences of SEP events should alsobe identical irrespective of the solar activity level during theseven active Sun years.

Let us see, whether it is a fact? If we separate the activeSun years of the 22-nd and 23-rd cycles into two groupsaccording to the value of average annual Wolf’s numbers100 6W 6 160 (years 1989, 1990, 1991, 2000, 2001 and2002) and 40 6W 6 100 (years 1988, 1992,1993, 1998,1999 and 2003), and use the results of measurements of flu-ences, obtained from the GOES satellites, then it is possibleto calculate the logarithmic averaged annual integral flu-ences energy spectra for these two groups of years. Theresults of calculation are presented in Fig. 4. Note, thatthe energy spectra for the mean fluences of these twogroups of years are not equal (as it follows from the baseproposition of the JPL-91 and ESP models), but differmore than an order of magnitude.

Fig. 4. Average annual integrated energy spectra of SEP events fluencesfor active Sun years (according to measurements on GOES satellites),separated into 2 groups – the events occurred in years with average annualWolf’s numbers of 100 6W 6 160 and 40 6W 6 100. Three upper linesrepresent spectra according to the JPL-91 model for various probabilitiesto annual fluences to exceed the values of the model spectra.

Note that the logarithmically averaged annual fluences,should be close to the annual fluences occurring with prob-ability of 0.5. As seen from the data Fig. 4, the averageannual fluences in both groups of years differ as much asan order of magnitude. Fig. 4 presents also the spectra con-structed based on the data on fluences, whose excess,according to the JPL-91 model, is expected with probabil-ities of 0.5, 0.1 and 0.01. If we ignore discrepancy betweenthe shape of a model spectrum and the shape of a spectrumof measured fluences, then the model spectrum, calculatedbased on the JPL-91 model for the 0.5 probability, will liebetween the experimental data of averaged fluences for twoseparate groups of years.

Nevertheless, it follows from the above analysis, that theJPL-91 model rather roughly describes the experimentaldata on fluences SEP events’ protons, since this modelneglects the dependence of the mean rate of events on thesolar activity level.

The MSU model, with parameters which depend on thesolar activity level better describe the above experimentaldata. In case of higher SA (hWi = 130), the experimentaldata correspond to the model probability of p = 0.5, forlower activity (hWi = 79) the experimental data correspondto the probability p = 0.7 to exceed the values determinedby these model spectra (Fig. 5).

4. The occurrence probabilities of SEP fluences in quiet Sun

years

The MSU model predicts the occurrence the SEP events,the peak fluxes and fluences for all SA levels, the quiet Sunperiod included.

Fig. 5. The same measured by GOES energy spectra, as on the Fig. 4. Thethree lines are for energy spectra calculated using the MSU model formean annual sunspot numbers hWi = 79 and hWi = 130, respectively, andvarious probabilities that annual fluences will exceed the values deter-mined by model spectra (see explanations in the inset).

Fig. 7. The same measured annual differential energy spectra as on theFig. 3 for years 1994 and 2005 (dashed and solid lines accordingly). Thethree curves are calculated energy spectra for mean annual sunspotnumbers hWi = 30 using the MSU model for various probabilities that theannual fluences will exceed the values determined by the model spectra (seeexplanations in the inset).

Fig. 6. The same measured annual differential energy spectra as on theFig. 2 for years 1995 and 1997 (solid and dashed lines, respectively). Fourcurves are energy spectra for mean annual sunspot numbers hWi = 17 andhWi = 22 from the MSU model calculated for various probabilities thatthe annual fluences will exceed the values determined by the model spectra(see explanations in the inset).

R.A. Nymmik / Advances in Space Research 42 (2008) 1288–1292 1291

On the Fig. 6 are displayed the data of years 1995 and1997. For the 1995 (hWi = 17) the probability to exceedthe fluences really observed is 0.7. For the 1997(hWi = 22) the probability to exceed the fluences reallyobserved is 0.25 � 0.3. Both cases are quit ordinary.

No SEP events were observed in 1996. The averageannual sunspot numbers in this year was hWi = 9; thatis, we have dealt with the year of deep SA minimum. TheMSU model allows one to calculate characteristic SEPparameters for this period. It states, that the probabilityto occur for SEP events with the fluence of theE P 30 MeV protons P105 protons/cm2 is equal to 0.57.

The comparison of experimental data with model calcu-lation (Fig. 7) has shown that the situation with annual flu-ences of 2005 year’s SEP events corresponds exactly to theprobability of 0.1 to exceed the values observed. Thismeans that the observed fluences in the 2005, a year withan annual SA level of hWi = 30, is expected to be occuronce per 10 years. The SEP energetic spectra of the 20 Feb-ruary 1994 was very soft. Therefore the fluence values atsmall energies correspond to the occurrence probabilities0.3–0.5 and at high energies 0.5–0.9.

5. Discussion

As follows from the presented data, the basic postulates,used in developing the JPL91 and ESP models, result inconsiderable errors in description of fluxes of energetic par-ticles (the radiation environment) in the space.

This is, first of all, a consequence of the mistaken assump-tion, that the role of SEP can be neglected in the quiet Sunyears. As seen from Figs. 2 and 3, the fluences of solar pro-tons exceed the GCR fluences up to the energy of 100 and,sometimes (as in 2005), up to 500 MeV.

In this case, the average annual fluences of solar protonsat 30 MeV energies exceed the fluences of GCR protons bythree, four or even five orders of magnitude (for the years1995, 1997 and 2005, respectively).

Naturally, as an exception, at the deep SA minimum (in1996, for example) significant SEP events can be absent.But, taking into account radiation conditions duringplanned space flights, it would be risky to plan on theabsence of SEP events even in those years. Most likely, dur-ing the quiet Sun period one could expect, to a considerableprobability of large (or even extreme) SEP events (Nym-mik, 2007b).

It is also obvious, that the values of expected averageannual fluences during the 7-year active Sun period dependon the real SA level. This is seen even for the rough sepa-ration of active Sun years into two groups, for which theaverage Wolf numbers do not differ so much (hWi � 79and hWi � 130).

Naturally, such distinctions are revealed for rather shortspace flights. For flight durations lasting a complete SAcycle or several SA cycles, the use of aforementioned pos-tulates in the JPL91 and ESP models do not result in signif-icant errors. In this case the other factors, which can distortthe modeling results, become of primary importance. Thisis, for example, the degree of reliability of experimentaldata used in developing the models, or the adequacy ofthe functional form for the distribution of events to repre-sent the experimental data.

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Acknowledgement

This work was supported by the Russian Foundationfor Basic Research, project no. 06-02-16268.

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