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On the probability of solar cosmic ray fluency during SEP event in dependence of the level of solar activity
Advances in Space Research 39 (2007) 1102–1108 www.elsevier.com/locate/asr
On the probability of solar cosmic ray fluency during SEP event in dependence of the level of solar activity L.I. Dorman a
a,b,* ,
L.A. Pustil’nik
a
Israel Cosmic Ray Space Weather Center and Emilio Segre’ Observatory, Affiliated to Tel Aviv University, Technion and Israel Space Agency, Israel b Cosmic Ray Department of IZMIRAN Russian Academy of Science, 142092, Troitsk, Moscow Region, Russia Received 2 February 2005; received in revised form 27 November 2006; accepted 30 November 2006
Abstract We study the probability of fluency level of solar cosmic ray in different phases of solar activity. Information on fluency distribution is necessary for estimation of radiation hazard both in the space (satellites, interplanetary missions, space stations) and in atmosphere (aircraft level). We estimate probabilities of fluencies on the base of long time observation of proton flux (both direct measurements on the space detectors and on the base of recalculation from ground stations). Restored amplitude spectrum (distribution of events with given interval of amplitudes of the fluency or for fluencies more than given) allows to us estimate probability of dangerous states and extrapolate this distribution to rare events of extremely high amplitudes. Main source of data for this analysis is data from the Catalog of Shea and Smart for 31 year observations’ fluency in space (1990) and for detailed analysis – data from satellites GOES during the last 11 last years (1994–2004). 2007 Published by Elsevier Ltd on behalf of COSPAR. Keywords: Solar cosmic rays; Fluency; GOES; Radiation hazard; Solar activity
1. Introduction In previous works (Dorman et al., 1993; Dorman and Pustil’nik, 1995, 1999) it was found that the frequencies P (in event/year) of events of solar CR fluencies with level of fluency F (particle/cm2) more than given were in dependence on fluency value F. For these works we used fluencies of events, averaged for solar cycle. We performed our analysis of fluency distribution for different levels of solar activity W (sunspot number intervals: 0–40, 40–80, 80–120, 120– 160, 160–200, and more than 200). We used for this analysis a Catalog of Shea and Smart (1990), the unique source of direct satellite data on solar CR fluencies F for particles with energies >10 MeV and >30 MeV. In addition, we used for this aim some indirect data too ((a) restoration of fluencies from the data of ground monitoring by world-wide network of cosmic ray stations, (b) data on Polar Cape *
Corresponding author. Tel.: +972 4 696 4932; fax: +972 4 696 4952. E-mail address: [email protected] (L.I. Dorman).
0273-1177/$30 2007 Published by Elsevier Ltd on behalf of COSPAR. doi:10.1016/j.asr.2006.11.032
Absorption events). Time interval of analysis includes 1955–1986 (three solar cycles 19, 20, and 21). In this work at the beginning, we will summarize our previous results briefly. We will approximate obtained change of probability P(F) from amplitude of fluency F by using analytical fitting (see Section 2). These analytical formulae are convenient for practical estimation of expected probability of the solar energetic particle (SEP) event and level of radiation hazard. This analytical estimation includes dependences from location, from level of solar activity W, generated SEP, and from phase of solar activity (increasing or decreasing) in the moment of observations. In the next step we will analyze statistical properties of the probability of daily fluency realization with the given level of radiation in space. For these aims we use the data on proton fluency from satellites GOES for the period 1994–2004 (GOES-7 for 1994, GOES-8 for 1995–1996 and 1999–2002, GOES-9 for 1997–1998, and GOES-11 for 2003–2004). We conducted this statistical analysis for different energies of CR protons: >1 MeV, >10 MeV, and
L.I. Dorman, L.A. Pustil’nik / Advances in Space Research 39 (2007) 1102–1108
>100 MeV separately. Source of these data: http:// www.sec.noaa.gov/ftpmenu/indices/old_indices.html. We estimate the expected number of ‘‘dangerous days’’ (days with dangerous radiation hazard) in dependence of the level of solar activity. Obtained results we compare with the previous results of Dorman et al. (1993), Dorman and Pustil’nik (1995, 1999) which were derived mainly on the basis of Catalog of Shea and Smart (1990). 2. Summary of our previous results; approximation by analytical formulae As we mentioned in Section 1, all these results were obtained mostly on the basis of Catalog of Shea and Smart (1990). In Fig. 1a are shown dependences of frequency P (events/year) in dependence of the lg (F) in the interval of fluency from about 105 up to about 1012 particle/cm2 for particles with energies >10 MeV and >30 MeV, averaged for full solar cycle. Obtained two curves for particles with energies >10 MeV and >30 MeV can be approximated by the formula h i c c=a P ¼ P c ðF =F c Þ exp a 1 ðF =F c Þ ; ð1Þ where Pc is the maximum value of P and Fc is the corresponding value of fluency. By comparison of Eq. (1) with experimental curves shown in Fig. 1a, we found that for particles with energy >10 MeV 2:05 at F 6 F c c ¼ 1:2; a ¼ ð2Þ 8:0 at F P F c and for particles with energy >30 MeV 1:9 at F 6 F c c ¼ 1:2; a ¼ 12:0 at F P F c
ð3Þ
Let us note that this approximation is in good agreement with the results obtained by McCracken et al. (2001) on the basis of investigation of NO3 events in ice columns
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for 1561–1950 (see in details for this method and main results in Chapter 13 of monograph Dorman, 2004). In Fig. 1b are shown the dependencies of frequency P of solar CR event from the solar activity level W (measured as sunspot number) for various values of fluency F for particles with energy >10 MeV. In Fig. 1c we show the same for particles with energy >30 MeV. From Fig. 1b can be seen that P probability of fluency increases with solar activity W only for F = 107–108, 108–109, and 109–1010 particle/ cm2. For low fluency side of distribution F = 107–108 particle/cm2 the frequency P has a maximum at W = 80–120 (high solar activity) and decreases with increase of W after this sunspot maximum. For the biggest observed fluency F = 1010–1011 particle/cm2, these events were observed only in the periods of intermediate solar activity levels W = 40–80 and 80–120. About the same situation can be seen from Fig. 1c for particles with energy >30 MeV. In Fig. 2a the dependencies of frequency P (events/year) of events from the value of logarithm of fluency lg (F) of solar protons with energy >10 MeV for different levels of solar activity are shown. It can be seen from Fig. 2a that at the lowest solar activity W = 0–40 the events’ frequency P is very small: only 0.5 events/year in the fluency range F = 2 · 107–2 · 108 particle/cm2 (but at smaller and bigger fluencies expected P @ 0). Increase of solar activity leads to a correspondent increase of SEP events, but this process takes place in a very inhomogeneous manner for different intervals of fluencies. For example: if for intermediate level of solar activity (W = 30–80) in population of SEP dominate (up to 4 events per year) events with middle level of fluencies (F = 107–108 particle/cm2), but for a higher level of solar activity (80–120, 120–200) input of strong flares with high or very high fluency (F = 108–109.5 particle/ cm2), starts to increase and dominate. This redistribution of events in ‘‘fluency space’’ reflects the fact of relative domination of the strong and giant flares during maximal solar activity. Opposite to low energy protons, behavior of population of more energetic particles (>30 MeV) is another (see
Fig. 1. (a) Histograms of the dependencies of fluency frequency (event/year) from the lg (F) for particles with energies >10 MeV and >30 MeV, averaged for three solar cycles; curves are according to Eq. (1) with parameters c and a according to Eq. (2) for particles with energy >10 MeV, and according to Eq. (3) for particles with energy >30 MeV; (b) Contour map form of 2-D dependence of frequency P of observed events (events/year): abscissa axis – the level of solar activity (yearly sunspot numbers), axis ordinate – logarithm of fluency of solar protons with energy >10 MeV, step in isofrequency levels is 0.2 events/year; (c) the same as in Fig. 1b, but for solar protons with energy >30 MeV.
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Fig. 2. (a) The dependencies of observed frequency P (events/year) of events in given fluence interval as a function from the value of logarithm of fluency lg (F) for solar protons with energy >10 MeV. We present five graphs for different levels of solar activity: W = 0–40, 40–80, 80–120, 120–160, 160–200; (b) the same, but for more energetic particles with energy >30 MeV.
Fig. 2b): distribution in fluency increases in amplitude with solar activity (from P @ 0,5 for minimal W up to P @ 4 for the maximal one). However redistribution of events in ‘‘fluency space’’ does not take place – distribution of events with fluency increases self-likely on its own conservation form and position of maximum. Only for intermediate level activity (W = 80–120) some disturbance of this law takes place – input of high fluency events increases and forms flat maximum, covering range of fluencies 2 · 107–2 · 109 particle/cm2. This disturbance reflects well-known fact of increase of probability for high amplitude solar flares in the transition states of solar activity from minimum to maximum and back. 3. Statistical properties of the radiation hazard frequencies derived from GOES 7–11 for 19942004 data on daily fluencies 3.1. Using data We analyzed 11-year data on daily fluencies (number of particles with energy more than 1 MeV, 10 MeV, and 100 MeV, accumulated by 1 cm2 from 1 steradian during one day) from satellites GOES (GOES-7 for 1994, GOES-8 for 1995–1996 and 1999–2002, GOES-9 for
10
>10 Mev >100 Mev >1 Mev
1997–1998, and GOES-11 for 2003–2004), available from Internet (http://www.sec.noaa.gov/ftpmenu/indices/ old_indices.html) as Daily Particle Indices (see Fig. 3). As it may be seen from Fig. 3, daily fluencies include 2 components: background and SEP – Solar Energetic Particles. Backgrounds for different energies change from a daily fluency of about 103.5 particle cm2 for energies >100 MeV, about 104 particle cm2 for energies >10 MeV and from 105 up to 106.5 particle cm2 for energy >1 MeV. Variations of the low energy background were caused probably by the Earth’s radiation belt’s input. 3.2. Integrated solar proton fluencies for energies >1 MeV, >10 MeV, >100 MeV, accumulated during a total 11-year period 1994–2004 Integrated solar proton fluencies for energies more than 1 MeV, 10 MeV, and 100 MeV, accumulated during a total 11-year period 1994–2004 for each different interval of fluencies, are shown in Fig. 4. From Fig. 4, it can be seen that integrated input to accumulated proton fluency during total 1994–2004 period from rare but strong events (lg (daily fluency) > 9 or daily fluency > 109 particle/(cm2 ster)) is much more than the input from numerous weak events (noise like) with daily fluencies 104.5–107 particle/(cm2 ster).
Daily Fluency 1994-2004
lg(daily fluency)
9 8 7 6 5 4 3 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 Fig. 3. Daily fluency (in particle/(cm2 ster)) dynamics during 1994–2004 years for particle energies >1, >10, >100 MeV.
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Fig. 4. Distribution of total particle number during 1994–2004 years for particle energies E > 1, >10, and >100 MeV (left ordinate axis) in intervals of fluencies for proton energies E > 1 MeV (abscissa axis) and distribution of days number with given fluency interval integrated in total interval 1994–2004 (right ordinate axis).
It is correct both for fluencies, which included low energy particles (E > 1 MeV) and for fluencies of high energy particles with energies >10 MeV and >100 MeV. Another conclusion from Fig. 4 can be made about the frequency–fluency spectrum: dependence of frequency – number of days N(F) with given daily fluency F has power character k
N ðF Þ ¼ N 0 ðF =F 0 Þ :
ð4Þ
The exponent value k changed from k = 0.6 for particles with energy >1 MeV, k = 0.4 for particles with energy >10 MeV and k = 0.2 for particles with energy >100 MeV. 3.3. On the variation of daily fluencies for particles with energies more than 1 MeV, 10 MeV, and 100 MeV with solar activity In Fig. 5a are shown variations of sunspot number and number of days N with daily fluencies F(E > 100 MeV) > 104 particle/(cm2 ster) during 1994–2004. From Fig. 5a, it can be seen that number of days with high fluency events is in general in some correlation with the level of sunspot activity. However, this connection is not so strong (correlation coefficient only 0.55); it includes big variances from proportional law. For example, let us consider 1999 year (1 year
before maximum of solar activity) when strong SEP fluencies almost were absent. Other examples – anomaly low levels of SEP fluencies in the year of maximum of sunspot number (2000 year) with levels compared with 1998 year (2 years after minimum of sunspot cycle) and 2003 (phase of the fall down of sunspot activity). It means that sunspot number parameter does not adequate for control and forecasting of great SEP fluency levels: there is quite large probability to obtain high fluency event near minimum phase of sunspot number, and correspondingly, very low fluency input near maximum state of solar activity. For comparison in Fig. 5b are shown variations of sunspot number W and number of days N with daily fluencies F(E > 10 MeV) > 104.5 particle/(cm2 ster) during 1994– 2004 (obtained correlation coefficient 0.86), in Fig. 5c – for daily fluencies F(E > 1 MeV) > 106.5 particle/(cm2 ster) with correlation coefficient 0.58, and in Fig. 5d – for daily fluencies F(E > 1 MeV) > 107 particle/(cm2 ster) with correlation coefficient 0.73. For the case of F(E > 1 MeV) the increase of low limit from 106.5 particle/(cm2 ster) to 107 particle/(cm2 ster) leads to sufficient increase of correlation coefficient from 0.58 to 0.73 (see Fig. 5c and d). From our opinion it is caused by decrease of the background fluencies’ influence, not connected with solar flares in the case described by Fig. 5d in comparison with Fig. 5c.
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Fig. 5. (a) Variations of sunspot number W (right Y-axis) and number of days per year N (left Y-axis) with given fluency interval for different energy channels during 1994–2004: for events with daily fluencies F(E > 100 MeV) > 104 particle/(cm2 ster) – correlation coefficient 0.55; (b) the same for events with daily fluencies F(E > 10 MeV) > 104.5 particle/(cm2 ster) – correlation coefficient 0.86; (c) the same for events with daily fluencies F(E > 1 MeV) > 106.5 particle/(cm2 ster) correlation coefficient 0.58; (d) the same for events with daily fluencies F(E > 1 MeV) > 107 particle/(cm2 ster) – correlation coefficient 0.73.
3.4. On the asymmetry of SEP statistical properties in minimum and maximum solar activity
that this asymmetry exists in reality but its level decreases with decrease of the level of fluency: for F(E > 100 MeV) > 107 particle/(cm2 ster) we see only 2 events in 2000 and 1 in 2003 (near maximum of solar activity), and nothing near minimum of solar activity; for F(E > 100 MeV) > 106 particle/(cm2 ster) we see 3 events
In Fig. 6a we show the asymmetry of high fluency SEP for high energy particles (E > 100 MeV) relative to the maximum and minimum states of solar activity. We see
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Fig. 6. (a) Number of events per year (left scale) with fluency F(E > 100 MeV) > 107 particle/(cm2 ster) and F(E > 100 MeV) > 106 particle/(cm2 ster), and the level of solar activity (yearly sunspot numbers W, right scale) in dependence of time in interval 1994–2004; (b) the asymmetry in the frequency–fluency distributions for minimum and maximum solar activity. Ordinate axis – lg (number of days with fluency F(E > 1 MeV)), abscissa axis – lg (fluency F(E > 1 MeV)) in interval of fluencies 104.5–09 particle/(cm2 ster).
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Fig. 7. (a) Diagram of scattering of fluencies of high (E > 100 MeV) and medium energy particles (E > 10 MeV) on fluencies of low energy particles (E > 1 MeV). Ellipses select different populations of fluencies. (b) Diagram of scattering of fluencies of high energy particles (E > 100 MeV) on fluencies of medium energy particles (E > 10 MeV). Ellipses select different populations of fluencies.
in 2000–2001 (near maximum of solar activity), 2 events in 2002–2003 (the fall of solar activity), but also 1 event in 1997 (near minimum of solar activity). With decrease of the level of F(E > 100 MeV) to >105 particle/(cm2 ster) and >104 particle/(cm2 ster) the asymmetry decreases essentially. Another manifestation of this asymmetry we see in Fig. 6b which shows the difference in frequency–fluency distributions of SEP for minimal and maximal states of solar activity. As it can be seen from Fig. 6b this asymmetry in the low energy range is not trivial: for low fluencies days near the background level from lg (F(E > 1 MeV)) = 5 up to value 7.5 different between maximum state of the solar activity and the minimum one is negligible or even opposite to that expected from standard approach. Namely, fluency days with lg (F(E > 1 MeV)) for fluency levels with 5 < lg (F(E > 1 MeV)) < 7 is in minimal state of solar activity even more than in the maximum one. Only for high fluency events with lg (F(E > 1 MeV)) > 7 we observe evident dominance of SEP events in maximal solar activity state. Possible reason for the absence or opposite attraction of low fluency events to solar maximum may be caused by input to low fluency state on the low energies of Earth radiation belts, which are in some anticorrelation with sunspot activity. 3.5. On connection between SEP fluencies for different channels of particle energy; two different populations of particle fluencies Next question is the possible connection between FEP Fluencies for different channels of particle energy. In other words – does fluency of high energy particles (>100 MeV) depend on the level of fluency in low (>1 MeV) or medium (>10 MeV) energy channels? For this aim we constructed two diagrams: (i) lg F(>10 MeV, >100 MeV) from lg F(>1 MeV) – Fig. 7a,
(ii) lg F(>100 MeV) from lg F(>10 MeV) – Fig. 7b. From Fig. 7a and b we see that input in the observed fluencies is caused by two different populations of events with different sources of particles for them: First group provides input to low energy particles with a wide interval of fluency (lg (F(>1 MeV) = 4.5–8.5)), which does not give any input to medium- and high-energy fluencies. Possible sources of these particles are small solar flare events, CME, and interplanetary shock waves without high energy particle generation. Second group of the SEP is the source of higher amplitude SEP fluencies, which shows evident correlation between fluencies in different energetic channels: between high energy and medium energy, and between high energy and low energy.
4. Conclusions
1. We summarized the results on the dependency of frequency of events P (events/year) with different fluencies F for particles with energies >10 MeV and >30 MeV in dependence from the level of solar activity. This analysis was based mainly on the Catalog of Shea and Smart (1990), in which direct satellite data on solar CR are presented, and indirect data (based on ground CR monitoring by world-wide network and data on Polar Cape Absorption events) for 1955–1986 (three solar cycles 19, 20, and 21). Obtained distribution of probabilities was fitted by analytical formula and may be used for forecasting in future. 2. On the basis of 11-year observations on GOES 7–11 for 1994–2004 of daily fluencies for particles with energies E > 1, >10, and >100 MeV it was shown that main input to the integral fluency during 1994–2004 was caused by
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few rare events with the highest fluencies. Several rare giant events gave a bigger input to integral fluency for 11-year cycle than thousands of lower fluency events. 3. Fluencies for different energy channels demonstrate different asymmetry relative to minimum and maximum states of solar activity. In spite of general correlation of frequency of high fluency SEP events with sunspot number (correlation coefficients from 0.55 to 0.86), there are strong deviations between variation of sunspot numbers and frequencies of fluency (in agreement with Shea and Smart (1990)). 4. Energy spectrum of particles appears in observed fluencies and its distribution in 2-D diagrams (Fluency(low energies)–Fluency(high energies)). It shows existence of two different populations of events: first population consists of events in low energy particles without any reaction in high energy particle fluencies; second population consists of events with simultaneous proportional reaction in all energetic channels from >1 to >100 MeV (regression coefficients about 0.9 and correlation coefficients 0.7–0.8). We suppose that the origin of the second population is SEP generation in great solar flares with wide energy spectrum; the origin of the first low energy population may be caused by weak solar flares, CME and interplanetary shock waves without high energy particle generation. 5. Our preliminary estimation of the radiation doses in space from the greatest SEP events with fluencies F(E > 1 MeV) > 109 particle/(cm2 ster) shows that this group of events is the source of real radiation hazard (tens–hundreds rem during event).
Acknowledgements Our thanks to the GOES team which presented the observational data for 1994–2004 to open access. Our thanks also to Prof. Yuval Ne’eman, Dr. Abraham Sternlieb, Prof. Isaac Ben Israel, Dr. Zvi Kaplan, and Dr. Gideon Bella for useful discussions and permanent support. This research is in the frame of INTAS 810 and Project COST 724. References Dorman, L.I. Cosmic Rays in the Earth’s Atmosphere and Underground. Kluwer Ac. Publ., Dordrecht/Boston/London, 2004. Dorman, I.V., Dorman, L.I., Venkatesan, D. Solar cosmic ray event frequency distribution in dependence of fluence and of solar activity level, in: Proceedings of the 23rd International Cosmic Ray Conference, Calgary, vol. 3, pp. 79–82, 1993. Dorman, L.I., Pustil’nik, L.A. Solar cosmic ray events: statistical characteristics for the diagnostic of acceleration, escaping and propagation processes, in: Proceedings of the 24th International Cosmic Ray Conference, Rome, vol. 4, pp. 86–89, 1995. Dorman, L.I., Pustil’nik, L.A. Statistical characteristics of FEP events and their connection with acceleration, escaping and propagation mechanisms, in: Proceedings of the 26th International Cosmic Ray Conference, Salt Lake City, vol. 6, pp. 407–410, 1999. McCracken, K.G., Smart, D.F., Shea, M.A., Dreschhoff, G.A.M. 400 years of large fluence solar proton events, in; Proceedings of the 27th International Cosmic Ray Conference, Hamburg, vol. 8, pp. 3209– 3212, 2001. Shea, M.A., Smart, D.F. A summary of major solar proton events. Solar Physics 127, 297–320, 1990.
On the probability of solar cosmic ray fluency during SEP event in dependence of the level of solar activity L.I. Dorman a
a,b,* ,
L.A. Pustil’nik
a
Israel Cosmic Ray Space Weather Center and Emilio Segre’ Observatory, Affiliated to Tel Aviv University, Technion and Israel Space Agency, Israel b Cosmic Ray Department of IZMIRAN Russian Academy of Science, 142092, Troitsk, Moscow Region, Russia Received 2 February 2005; received in revised form 27 November 2006; accepted 30 November 2006
Abstract We study the probability of fluency level of solar cosmic ray in different phases of solar activity. Information on fluency distribution is necessary for estimation of radiation hazard both in the space (satellites, interplanetary missions, space stations) and in atmosphere (aircraft level). We estimate probabilities of fluencies on the base of long time observation of proton flux (both direct measurements on the space detectors and on the base of recalculation from ground stations). Restored amplitude spectrum (distribution of events with given interval of amplitudes of the fluency or for fluencies more than given) allows to us estimate probability of dangerous states and extrapolate this distribution to rare events of extremely high amplitudes. Main source of data for this analysis is data from the Catalog of Shea and Smart for 31 year observations’ fluency in space (1990) and for detailed analysis – data from satellites GOES during the last 11 last years (1994–2004). 2007 Published by Elsevier Ltd on behalf of COSPAR. Keywords: Solar cosmic rays; Fluency; GOES; Radiation hazard; Solar activity
1. Introduction In previous works (Dorman et al., 1993; Dorman and Pustil’nik, 1995, 1999) it was found that the frequencies P (in event/year) of events of solar CR fluencies with level of fluency F (particle/cm2) more than given were in dependence on fluency value F. For these works we used fluencies of events, averaged for solar cycle. We performed our analysis of fluency distribution for different levels of solar activity W (sunspot number intervals: 0–40, 40–80, 80–120, 120– 160, 160–200, and more than 200). We used for this analysis a Catalog of Shea and Smart (1990), the unique source of direct satellite data on solar CR fluencies F for particles with energies >10 MeV and >30 MeV. In addition, we used for this aim some indirect data too ((a) restoration of fluencies from the data of ground monitoring by world-wide network of cosmic ray stations, (b) data on Polar Cape *
Corresponding author. Tel.: +972 4 696 4932; fax: +972 4 696 4952. E-mail address: [email protected] (L.I. Dorman).
0273-1177/$30 2007 Published by Elsevier Ltd on behalf of COSPAR. doi:10.1016/j.asr.2006.11.032
Absorption events). Time interval of analysis includes 1955–1986 (three solar cycles 19, 20, and 21). In this work at the beginning, we will summarize our previous results briefly. We will approximate obtained change of probability P(F) from amplitude of fluency F by using analytical fitting (see Section 2). These analytical formulae are convenient for practical estimation of expected probability of the solar energetic particle (SEP) event and level of radiation hazard. This analytical estimation includes dependences from location, from level of solar activity W, generated SEP, and from phase of solar activity (increasing or decreasing) in the moment of observations. In the next step we will analyze statistical properties of the probability of daily fluency realization with the given level of radiation in space. For these aims we use the data on proton fluency from satellites GOES for the period 1994–2004 (GOES-7 for 1994, GOES-8 for 1995–1996 and 1999–2002, GOES-9 for 1997–1998, and GOES-11 for 2003–2004). We conducted this statistical analysis for different energies of CR protons: >1 MeV, >10 MeV, and
L.I. Dorman, L.A. Pustil’nik / Advances in Space Research 39 (2007) 1102–1108
>100 MeV separately. Source of these data: http:// www.sec.noaa.gov/ftpmenu/indices/old_indices.html. We estimate the expected number of ‘‘dangerous days’’ (days with dangerous radiation hazard) in dependence of the level of solar activity. Obtained results we compare with the previous results of Dorman et al. (1993), Dorman and Pustil’nik (1995, 1999) which were derived mainly on the basis of Catalog of Shea and Smart (1990). 2. Summary of our previous results; approximation by analytical formulae As we mentioned in Section 1, all these results were obtained mostly on the basis of Catalog of Shea and Smart (1990). In Fig. 1a are shown dependences of frequency P (events/year) in dependence of the lg (F) in the interval of fluency from about 105 up to about 1012 particle/cm2 for particles with energies >10 MeV and >30 MeV, averaged for full solar cycle. Obtained two curves for particles with energies >10 MeV and >30 MeV can be approximated by the formula h i c c=a P ¼ P c ðF =F c Þ exp a 1 ðF =F c Þ ; ð1Þ where Pc is the maximum value of P and Fc is the corresponding value of fluency. By comparison of Eq. (1) with experimental curves shown in Fig. 1a, we found that for particles with energy >10 MeV 2:05 at F 6 F c c ¼ 1:2; a ¼ ð2Þ 8:0 at F P F c and for particles with energy >30 MeV 1:9 at F 6 F c c ¼ 1:2; a ¼ 12:0 at F P F c
ð3Þ
Let us note that this approximation is in good agreement with the results obtained by McCracken et al. (2001) on the basis of investigation of NO3 events in ice columns
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for 1561–1950 (see in details for this method and main results in Chapter 13 of monograph Dorman, 2004). In Fig. 1b are shown the dependencies of frequency P of solar CR event from the solar activity level W (measured as sunspot number) for various values of fluency F for particles with energy >10 MeV. In Fig. 1c we show the same for particles with energy >30 MeV. From Fig. 1b can be seen that P probability of fluency increases with solar activity W only for F = 107–108, 108–109, and 109–1010 particle/ cm2. For low fluency side of distribution F = 107–108 particle/cm2 the frequency P has a maximum at W = 80–120 (high solar activity) and decreases with increase of W after this sunspot maximum. For the biggest observed fluency F = 1010–1011 particle/cm2, these events were observed only in the periods of intermediate solar activity levels W = 40–80 and 80–120. About the same situation can be seen from Fig. 1c for particles with energy >30 MeV. In Fig. 2a the dependencies of frequency P (events/year) of events from the value of logarithm of fluency lg (F) of solar protons with energy >10 MeV for different levels of solar activity are shown. It can be seen from Fig. 2a that at the lowest solar activity W = 0–40 the events’ frequency P is very small: only 0.5 events/year in the fluency range F = 2 · 107–2 · 108 particle/cm2 (but at smaller and bigger fluencies expected P @ 0). Increase of solar activity leads to a correspondent increase of SEP events, but this process takes place in a very inhomogeneous manner for different intervals of fluencies. For example: if for intermediate level of solar activity (W = 30–80) in population of SEP dominate (up to 4 events per year) events with middle level of fluencies (F = 107–108 particle/cm2), but for a higher level of solar activity (80–120, 120–200) input of strong flares with high or very high fluency (F = 108–109.5 particle/ cm2), starts to increase and dominate. This redistribution of events in ‘‘fluency space’’ reflects the fact of relative domination of the strong and giant flares during maximal solar activity. Opposite to low energy protons, behavior of population of more energetic particles (>30 MeV) is another (see
Fig. 1. (a) Histograms of the dependencies of fluency frequency (event/year) from the lg (F) for particles with energies >10 MeV and >30 MeV, averaged for three solar cycles; curves are according to Eq. (1) with parameters c and a according to Eq. (2) for particles with energy >10 MeV, and according to Eq. (3) for particles with energy >30 MeV; (b) Contour map form of 2-D dependence of frequency P of observed events (events/year): abscissa axis – the level of solar activity (yearly sunspot numbers), axis ordinate – logarithm of fluency of solar protons with energy >10 MeV, step in isofrequency levels is 0.2 events/year; (c) the same as in Fig. 1b, but for solar protons with energy >30 MeV.
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4.5 W=0-40 W=40-80 W=80-120 W=120-160 W=160-200
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Fig. 2. (a) The dependencies of observed frequency P (events/year) of events in given fluence interval as a function from the value of logarithm of fluency lg (F) for solar protons with energy >10 MeV. We present five graphs for different levels of solar activity: W = 0–40, 40–80, 80–120, 120–160, 160–200; (b) the same, but for more energetic particles with energy >30 MeV.
Fig. 2b): distribution in fluency increases in amplitude with solar activity (from P @ 0,5 for minimal W up to P @ 4 for the maximal one). However redistribution of events in ‘‘fluency space’’ does not take place – distribution of events with fluency increases self-likely on its own conservation form and position of maximum. Only for intermediate level activity (W = 80–120) some disturbance of this law takes place – input of high fluency events increases and forms flat maximum, covering range of fluencies 2 · 107–2 · 109 particle/cm2. This disturbance reflects well-known fact of increase of probability for high amplitude solar flares in the transition states of solar activity from minimum to maximum and back. 3. Statistical properties of the radiation hazard frequencies derived from GOES 7–11 for 19942004 data on daily fluencies 3.1. Using data We analyzed 11-year data on daily fluencies (number of particles with energy more than 1 MeV, 10 MeV, and 100 MeV, accumulated by 1 cm2 from 1 steradian during one day) from satellites GOES (GOES-7 for 1994, GOES-8 for 1995–1996 and 1999–2002, GOES-9 for
10
>10 Mev >100 Mev >1 Mev
1997–1998, and GOES-11 for 2003–2004), available from Internet (http://www.sec.noaa.gov/ftpmenu/indices/ old_indices.html) as Daily Particle Indices (see Fig. 3). As it may be seen from Fig. 3, daily fluencies include 2 components: background and SEP – Solar Energetic Particles. Backgrounds for different energies change from a daily fluency of about 103.5 particle cm2 for energies >100 MeV, about 104 particle cm2 for energies >10 MeV and from 105 up to 106.5 particle cm2 for energy >1 MeV. Variations of the low energy background were caused probably by the Earth’s radiation belt’s input. 3.2. Integrated solar proton fluencies for energies >1 MeV, >10 MeV, >100 MeV, accumulated during a total 11-year period 1994–2004 Integrated solar proton fluencies for energies more than 1 MeV, 10 MeV, and 100 MeV, accumulated during a total 11-year period 1994–2004 for each different interval of fluencies, are shown in Fig. 4. From Fig. 4, it can be seen that integrated input to accumulated proton fluency during total 1994–2004 period from rare but strong events (lg (daily fluency) > 9 or daily fluency > 109 particle/(cm2 ster)) is much more than the input from numerous weak events (noise like) with daily fluencies 104.5–107 particle/(cm2 ster).
Daily Fluency 1994-2004
lg(daily fluency)
9 8 7 6 5 4 3 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 Fig. 3. Daily fluency (in particle/(cm2 ster)) dynamics during 1994–2004 years for particle energies >1, >10, >100 MeV.
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9.5 > lg(F) >9.0
9.0 > lg(F) >8.5
8.5 > lg(F )>8.0
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7.5 > lg(F) >7
7.0 > lg(F) >6.5
6.5 > lg(F) >6.0
6.0 > lg(F) >5.5
5.5 > lg(F) >5.0
0 5.0 > lg(F) >4.5
0
Fig. 4. Distribution of total particle number during 1994–2004 years for particle energies E > 1, >10, and >100 MeV (left ordinate axis) in intervals of fluencies for proton energies E > 1 MeV (abscissa axis) and distribution of days number with given fluency interval integrated in total interval 1994–2004 (right ordinate axis).
It is correct both for fluencies, which included low energy particles (E > 1 MeV) and for fluencies of high energy particles with energies >10 MeV and >100 MeV. Another conclusion from Fig. 4 can be made about the frequency–fluency spectrum: dependence of frequency – number of days N(F) with given daily fluency F has power character k
N ðF Þ ¼ N 0 ðF =F 0 Þ :
ð4Þ
The exponent value k changed from k = 0.6 for particles with energy >1 MeV, k = 0.4 for particles with energy >10 MeV and k = 0.2 for particles with energy >100 MeV. 3.3. On the variation of daily fluencies for particles with energies more than 1 MeV, 10 MeV, and 100 MeV with solar activity In Fig. 5a are shown variations of sunspot number and number of days N with daily fluencies F(E > 100 MeV) > 104 particle/(cm2 ster) during 1994–2004. From Fig. 5a, it can be seen that number of days with high fluency events is in general in some correlation with the level of sunspot activity. However, this connection is not so strong (correlation coefficient only 0.55); it includes big variances from proportional law. For example, let us consider 1999 year (1 year
before maximum of solar activity) when strong SEP fluencies almost were absent. Other examples – anomaly low levels of SEP fluencies in the year of maximum of sunspot number (2000 year) with levels compared with 1998 year (2 years after minimum of sunspot cycle) and 2003 (phase of the fall down of sunspot activity). It means that sunspot number parameter does not adequate for control and forecasting of great SEP fluency levels: there is quite large probability to obtain high fluency event near minimum phase of sunspot number, and correspondingly, very low fluency input near maximum state of solar activity. For comparison in Fig. 5b are shown variations of sunspot number W and number of days N with daily fluencies F(E > 10 MeV) > 104.5 particle/(cm2 ster) during 1994– 2004 (obtained correlation coefficient 0.86), in Fig. 5c – for daily fluencies F(E > 1 MeV) > 106.5 particle/(cm2 ster) with correlation coefficient 0.58, and in Fig. 5d – for daily fluencies F(E > 1 MeV) > 107 particle/(cm2 ster) with correlation coefficient 0.73. For the case of F(E > 1 MeV) the increase of low limit from 106.5 particle/(cm2 ster) to 107 particle/(cm2 ster) leads to sufficient increase of correlation coefficient from 0.58 to 0.73 (see Fig. 5c and d). From our opinion it is caused by decrease of the background fluencies’ influence, not connected with solar flares in the case described by Fig. 5d in comparison with Fig. 5c.
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a
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Fig. 5. (a) Variations of sunspot number W (right Y-axis) and number of days per year N (left Y-axis) with given fluency interval for different energy channels during 1994–2004: for events with daily fluencies F(E > 100 MeV) > 104 particle/(cm2 ster) – correlation coefficient 0.55; (b) the same for events with daily fluencies F(E > 10 MeV) > 104.5 particle/(cm2 ster) – correlation coefficient 0.86; (c) the same for events with daily fluencies F(E > 1 MeV) > 106.5 particle/(cm2 ster) correlation coefficient 0.58; (d) the same for events with daily fluencies F(E > 1 MeV) > 107 particle/(cm2 ster) – correlation coefficient 0.73.
3.4. On the asymmetry of SEP statistical properties in minimum and maximum solar activity
that this asymmetry exists in reality but its level decreases with decrease of the level of fluency: for F(E > 100 MeV) > 107 particle/(cm2 ster) we see only 2 events in 2000 and 1 in 2003 (near maximum of solar activity), and nothing near minimum of solar activity; for F(E > 100 MeV) > 106 particle/(cm2 ster) we see 3 events
In Fig. 6a we show the asymmetry of high fluency SEP for high energy particles (E > 100 MeV) relative to the maximum and minimum states of solar activity. We see
4
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30
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0 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004
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0
5.5 >lgF >5.0
0.0
5.0 >lgF >4.5
Number of days per year
N(lgF(>100Mev)>6)
Fig. 6. (a) Number of events per year (left scale) with fluency F(E > 100 MeV) > 107 particle/(cm2 ster) and F(E > 100 MeV) > 106 particle/(cm2 ster), and the level of solar activity (yearly sunspot numbers W, right scale) in dependence of time in interval 1994–2004; (b) the asymmetry in the frequency–fluency distributions for minimum and maximum solar activity. Ordinate axis – lg (number of days with fluency F(E > 1 MeV)), abscissa axis – lg (fluency F(E > 1 MeV)) in interval of fluencies 104.5–09 particle/(cm2 ster).
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Fig. 7. (a) Diagram of scattering of fluencies of high (E > 100 MeV) and medium energy particles (E > 10 MeV) on fluencies of low energy particles (E > 1 MeV). Ellipses select different populations of fluencies. (b) Diagram of scattering of fluencies of high energy particles (E > 100 MeV) on fluencies of medium energy particles (E > 10 MeV). Ellipses select different populations of fluencies.
in 2000–2001 (near maximum of solar activity), 2 events in 2002–2003 (the fall of solar activity), but also 1 event in 1997 (near minimum of solar activity). With decrease of the level of F(E > 100 MeV) to >105 particle/(cm2 ster) and >104 particle/(cm2 ster) the asymmetry decreases essentially. Another manifestation of this asymmetry we see in Fig. 6b which shows the difference in frequency–fluency distributions of SEP for minimal and maximal states of solar activity. As it can be seen from Fig. 6b this asymmetry in the low energy range is not trivial: for low fluencies days near the background level from lg (F(E > 1 MeV)) = 5 up to value 7.5 different between maximum state of the solar activity and the minimum one is negligible or even opposite to that expected from standard approach. Namely, fluency days with lg (F(E > 1 MeV)) for fluency levels with 5 < lg (F(E > 1 MeV)) < 7 is in minimal state of solar activity even more than in the maximum one. Only for high fluency events with lg (F(E > 1 MeV)) > 7 we observe evident dominance of SEP events in maximal solar activity state. Possible reason for the absence or opposite attraction of low fluency events to solar maximum may be caused by input to low fluency state on the low energies of Earth radiation belts, which are in some anticorrelation with sunspot activity. 3.5. On connection between SEP fluencies for different channels of particle energy; two different populations of particle fluencies Next question is the possible connection between FEP Fluencies for different channels of particle energy. In other words – does fluency of high energy particles (>100 MeV) depend on the level of fluency in low (>1 MeV) or medium (>10 MeV) energy channels? For this aim we constructed two diagrams: (i) lg F(>10 MeV, >100 MeV) from lg F(>1 MeV) – Fig. 7a,
(ii) lg F(>100 MeV) from lg F(>10 MeV) – Fig. 7b. From Fig. 7a and b we see that input in the observed fluencies is caused by two different populations of events with different sources of particles for them: First group provides input to low energy particles with a wide interval of fluency (lg (F(>1 MeV) = 4.5–8.5)), which does not give any input to medium- and high-energy fluencies. Possible sources of these particles are small solar flare events, CME, and interplanetary shock waves without high energy particle generation. Second group of the SEP is the source of higher amplitude SEP fluencies, which shows evident correlation between fluencies in different energetic channels: between high energy and medium energy, and between high energy and low energy.
4. Conclusions
1. We summarized the results on the dependency of frequency of events P (events/year) with different fluencies F for particles with energies >10 MeV and >30 MeV in dependence from the level of solar activity. This analysis was based mainly on the Catalog of Shea and Smart (1990), in which direct satellite data on solar CR are presented, and indirect data (based on ground CR monitoring by world-wide network and data on Polar Cape Absorption events) for 1955–1986 (three solar cycles 19, 20, and 21). Obtained distribution of probabilities was fitted by analytical formula and may be used for forecasting in future. 2. On the basis of 11-year observations on GOES 7–11 for 1994–2004 of daily fluencies for particles with energies E > 1, >10, and >100 MeV it was shown that main input to the integral fluency during 1994–2004 was caused by
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few rare events with the highest fluencies. Several rare giant events gave a bigger input to integral fluency for 11-year cycle than thousands of lower fluency events. 3. Fluencies for different energy channels demonstrate different asymmetry relative to minimum and maximum states of solar activity. In spite of general correlation of frequency of high fluency SEP events with sunspot number (correlation coefficients from 0.55 to 0.86), there are strong deviations between variation of sunspot numbers and frequencies of fluency (in agreement with Shea and Smart (1990)). 4. Energy spectrum of particles appears in observed fluencies and its distribution in 2-D diagrams (Fluency(low energies)–Fluency(high energies)). It shows existence of two different populations of events: first population consists of events in low energy particles without any reaction in high energy particle fluencies; second population consists of events with simultaneous proportional reaction in all energetic channels from >1 to >100 MeV (regression coefficients about 0.9 and correlation coefficients 0.7–0.8). We suppose that the origin of the second population is SEP generation in great solar flares with wide energy spectrum; the origin of the first low energy population may be caused by weak solar flares, CME and interplanetary shock waves without high energy particle generation. 5. Our preliminary estimation of the radiation doses in space from the greatest SEP events with fluencies F(E > 1 MeV) > 109 particle/(cm2 ster) shows that this group of events is the source of real radiation hazard (tens–hundreds rem during event).
Acknowledgements Our thanks to the GOES team which presented the observational data for 1994–2004 to open access. Our thanks also to Prof. Yuval Ne’eman, Dr. Abraham Sternlieb, Prof. Isaac Ben Israel, Dr. Zvi Kaplan, and Dr. Gideon Bella for useful discussions and permanent support. This research is in the frame of INTAS 810 and Project COST 724. References Dorman, L.I. Cosmic Rays in the Earth’s Atmosphere and Underground. Kluwer Ac. Publ., Dordrecht/Boston/London, 2004. Dorman, I.V., Dorman, L.I., Venkatesan, D. Solar cosmic ray event frequency distribution in dependence of fluence and of solar activity level, in: Proceedings of the 23rd International Cosmic Ray Conference, Calgary, vol. 3, pp. 79–82, 1993. Dorman, L.I., Pustil’nik, L.A. Solar cosmic ray events: statistical characteristics for the diagnostic of acceleration, escaping and propagation processes, in: Proceedings of the 24th International Cosmic Ray Conference, Rome, vol. 4, pp. 86–89, 1995. Dorman, L.I., Pustil’nik, L.A. Statistical characteristics of FEP events and their connection with acceleration, escaping and propagation mechanisms, in: Proceedings of the 26th International Cosmic Ray Conference, Salt Lake City, vol. 6, pp. 407–410, 1999. McCracken, K.G., Smart, D.F., Shea, M.A., Dreschhoff, G.A.M. 400 years of large fluence solar proton events, in; Proceedings of the 27th International Cosmic Ray Conference, Hamburg, vol. 8, pp. 3209– 3212, 2001. Shea, M.A., Smart, D.F. A summary of major solar proton events. Solar Physics 127, 297–320, 1990.