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An empirical statistical model of the radiation characteristics of solar proton events in near-Earth space
Radiation Measurements, Vol. 26, No. 3, pp. 451-454, 1996 Copyright © 1996ElsevierScienceLtd Printed in Great Britain.All rights reserved PII: S13,~-4457(96)00043-1 1350-4487/96$15.00+ 0.00
Pergamon
AN EMPIRICAL STATISTICAL MODEL OF THE RADIATION CHARACTERISTICS OF SOLAR PROTON EVENTS IN NEAR-EARTH SPACE N. K. PEREYASLOVA, M. N. NAZAROVA and I. E. PETRENKO Institute of Applied Geophysics, Rostokinskaya 9, Moscow 129226, Russia Abstract---Characteristics of solar proton events (SPE) with a maximum flux of 1 cm-~ s - ' sr(Ep > 10 MeV) in the Earth's orbit over the last three I 1-year solar cycles are studied using satellite observations. The number of SPEs responsible for strong disturbances in the 22nd cycle has increased considerably. Based on the set of radiation and heliogeophysical parameters, statistical and empirical radiation situation (RS) models are described. The models have been developed from the data on the variations of radiation parameters of solar proton events for the 20th, 21st and 22nd cycles of solar activity. RS models are presented as combined distributions of SPE radiation parameters (statistical model), and as the flare heliolongitude dependencies of temporal and spectral characteristics for two classes of SPE (empirical model). Copyright © 1996 Elsevier Science Ltd
1. INTRODUCTION
I = J J d t = integral proton flux over the whole events;
The state of the radiation situation in near-Earth space (NES) is mainly determined by temporal, spatial and spectral characteristics of the SCR (solar cosmic ray) proton component within the energy range 5-200 MeV, which are caused by solar flares generating protons which penetrate space. The occurrence and intensity of solar proton flares varies considerably with the phase of the I l-year solar activity (s.a.) cycle. The term "near-Earth space" stands for the part of space free from the Earth's radiation belts embracing the area of the open force lines of the geomagnetic field stretching to the magnetotail and reconnecting with IMP (interplanetary magnetic field) force lines, often referred to as "polar caps" or "high-latitude zones of the Earth's magnetosphere". The radiation situation (RS) forecast in the NES is a baseline for predicting radiation conditions on any spacecraft orbit. When developing RS models, statistical methods for investigating solar proton events (SPE) including solar activity cyclicity were used. On the basis of investigations of SPE radiation characteristics and their variations in 1965-1989 a statistical model as an SPE number distribution according to radiation characteristics and an empirical model in the form of SPE radiation characteristic dependencies on the heliolongitude of the flareproton source for two classes of events were developed (Avdyushin et al., 1990). The system of "Meteor" satellites provides regular recording of the SPE protons. For the period from 1990 to December 1992, 80 SPEs were recorded. Their flux and spectral characteristics were evaluated:
Jm = proton flux at the SPE maximum; y, = spectral index at the SPE maximum in power representation of the integral proton spectrum J( > E) = A E - "~.The proton sources have been identified and temporal characteristics of events have been determined: to = time from the beginning of H~ flare observations till the proton arrival in the Earth's orbit; tm= time from flare onset till the SPE maximum; Atm = time from SPE onset till its maximum; T = SPE duration. 2. A STATISTICAL MODEL OF RS IN THE NES A statistical model taking into account events recorded in 1990 is given in Fig, 1. As is seen from the histogram the values of J~ and I did not exceed 105 cm -~ s -~ sr -m and 2 x 10 "cm -2, respectively. The spectral index varied within 0.5--7, the most probable value being 1 < Ym< 3. SPE distributions over Jm and I are satisfactorily described by log-normal functions. For temporal characteristics the approximate analytical equations are obtained (Table 1). 3. EMPIRICAL MODEL OF SPE RADIATION PARAMETERS
451
Investigations, described in Mikirova and Pereyaslova (1977), Pereyaslova et al. (1983); Pereyaslova et al., (1986) and Smart and Shea (1979) of the relations of radiation characteristics with flare heliolongitude, the structure of the coronal magnetic
N. K. PEREYASLOVA et al.
452 250
50 -
50 200
50 - -
Jm
150
30
I
"Ym
30
100 50
10
c~
10
-
[
105
107
o
e~
o
100
102
104 crn-2s-lsr-1
10 9
I0 II cm -2
0
L
i 1--,--,
2
4
6
70
250 70
e~ 200
z
5o
150
50
100
.~ N 3o
50
50 At m
50
tm
3o
30
I0
10
30
8 I0
~
10
I 0 30 60 90 h 0 30 60 90 h 0 30 60 90 h 0 8 16 20 day Fig. 1. Proton event distributions over radiation parameters during the 1965-1990 period. field and the intcrlocation of the source and the proton detector were used when developing an empirical model of SPE temporal and spectral characteristics. This model, together with flux parameters, determines the radiation situation in the NES. In accordance with the obtained dependencies (Mikirova and Pereyaslova, 1977; Pereyaslova et al., 1983), all SPEs with proton flux in the maximum being Jm --> 1 crn -2 s - l sr -~ for protons with E~ > 10 MeV were divided into two classes. The first class includes events for which the flare and the base of the Earth-Sun force line are located in a single unipolar solar region, the second class of events includes the location of the flare and the base of the Earth-Sun force line in different unipolar regions. Taking into account circumsolar propagation and hcliolongitudinal dependencies for radiation characteristics---t0, t~, Arm at T--two classes of SPEs were obtained. Figure 2 illustrates the SPE radiation parameters for protons with Ep > 10 McV as a function of the flare heliolongitude using the data for the 20th, 21st and 22nd (1990 inclusive) s.a. cycles. The data are averaged within a 30° heliolongitude interval. Standard deviation from the mean value is shown in each heliolongitude interval. The dependencies were Table 1. Analytical equations for the approximation of SPE distribution over radiation characteristics Radiation parameter
Approxnnate equations
to, h
N = 327e-o.:s,o+ 56c-o.~,o
Arm, h
N = 227e-°'°~- + 16c -°'°sA'N = 351e-°°~'N = 569e-°"2r + 77e -°'~°r
t®, h T, day
,~= ~ ~ ~ : ~ "~ .~ E"
10
2 class
1 class
~5,_. 9= ., .~ 30 ~ ,,~ ~ < 20 lO o
I
2 class
I
;
lcl"s
40
~ 30
2 class
20 [" E
10
~
3
I
.I.
1 class
t
v~~' ~ .~ .
2 r 1 E 90 °
2 class
[ - ~ l c l a s s 60
30
0
30
60
90 ° W
Fig. 2. Heliolongitudinal dependence of radiation parameters for two SPE classes in the 20-22 solar cycles.
SOLAR PROTON
EVENTS IN NEAR-EARTH
SPACE
453
Table 2. Regression equation between SPE radiation characteristics and flare heliolongitude from the 1965-1990 data Parameter
SPE class
to, h
Approximate equations
1 2 1 2 1 2 1 2
Arm, h tin, h ~
2.36 11.2 5.32 19.1 7.67 26.2 2.08 2.90 --
SPE number taken into account
0.0332 + 0.00043. 2 0.0453. + 0.000622 0.0182 + 0.000122 0.1603. + 0.002422 0.048,~ + 0.00043.2 0.1743. + 0.00153. 2 0.0053. + 0.000053. 2 0.0023. + 0.000033. 2
183 118 186 110 179 158 189 170
(a)
4
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--J.
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1 • Q
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X-ray intensity IogF x (mlerg cm-2s -]) Fig. 3. Correlations between the proton flux during the event maximum and maximum X-ray burst intensities (a) for class 1 of SPE and (b) for class 2.
454
N . K . PEREYASLOVA et al.
approximated with second-order parabolas; calculations were carried out using the least squares method. Regression equations are presented in Table 2. Similar distributions were obtained for the protons with Ep > 30, 60 MeV. A relation is established between the maximum proton flux with Ep > 10 MeV and the maximum X-ray burst intensity within 1-8 A, accompanying the flare--the source of proton injection (Mikirova and Pereyaslova, 1983). To forecast the maximum proton flux, functions of the predicting variables for two classes of events were obtained. Figure 3 shows the correlation dependence between Jm values and Fx--the maximum value of X-ray burst intensity. Regression equations for two classes of SPEs: log Jm = 0.75(Iog Fx)2 -- 1.71 log Fx + 1.88 class 1 log Jm = 0.82 log F~ -- 0.09 class 2 For SPE of class 1, J~ dependence on Fx is satisfactorily described by the second-order equation (parabola); for SPE of the second class, linear dependence with a correlation coefficient o f ~ 0.9 and root-mean-square deviation of 0.40, the confidence interval is 0.77 at the 95% significance level. 4. CONCLUSION In 1991-1992--the onset of the decline phases of the 22nd s.a. cycle--the "Meteor" satellite recorded 57 SPEs. In these events mean relative deviations of the observed values of proton radiation characteristics with E p > 10 MeV from empirical model
distributions for to, Atm, tm and Ym are (48 _+ 6), (80 5: 11), (46 + 6) and (31 + 3)%, respectively. This result allows for the hope that the developed empirical model may be used for assessing the radiation situation in NES when information on the flare characteristics, the synoptic map of the Sun or data on the structure of the large-scale magnetic field of the Sun are obtained.
REFERENCES Avdyushin S. I., Nazarova M. N., Pereyaslova N. K. and Petrenko I. Ye. (1990) Modelling the radiation situation and predicting the parameters of solar proton events. In: Solar Terrestrial Predictions Proceedings of a Workshop at Leura, Australia, 16-20 October 1989, Boulder, CO, Vol. 1, pp. 288-296. Mikirova N. A. and Pereyaslova N. K. (1977) The effect of photospheric magnetic fields on the distribution of solar flare protons. Dokl. A N SSSR 234, 798-801(in Russian). Mikirova N. A. and Pereyaslova N. K. (1983) Quantitative diagnostics of proton flares from X-ray burst data. Sol. dan. 1, 101-105 (in Russian). Pereyaslova N. K., Nazarova M. N. and Mikirova N. A. (1983) Solar cosmic ray parameters related to the structure of coronal magnetic field. Geomag. Aeron. 233, 367-371(in Russian). Pereyaslova N. K., Mikirova N. A. and Nazarova M. N. (1986) A method of forecasting solar cosmic ray events. In: Solar Terrestrial Predictions Proceedings of a Workshop at Meudon, France, 18-22 June 1984, Boulder, CO, pp. 220-227. Smart D. F. and Shea M. A. (1979) A computerized "event mode" solar proton forecasting technique. In: Solar Terrestrial Predictions Proceedings, Boulder, CO, Vol. 1, pp. 406-427.
Pergamon
AN EMPIRICAL STATISTICAL MODEL OF THE RADIATION CHARACTERISTICS OF SOLAR PROTON EVENTS IN NEAR-EARTH SPACE N. K. PEREYASLOVA, M. N. NAZAROVA and I. E. PETRENKO Institute of Applied Geophysics, Rostokinskaya 9, Moscow 129226, Russia Abstract---Characteristics of solar proton events (SPE) with a maximum flux of 1 cm-~ s - ' sr(Ep > 10 MeV) in the Earth's orbit over the last three I 1-year solar cycles are studied using satellite observations. The number of SPEs responsible for strong disturbances in the 22nd cycle has increased considerably. Based on the set of radiation and heliogeophysical parameters, statistical and empirical radiation situation (RS) models are described. The models have been developed from the data on the variations of radiation parameters of solar proton events for the 20th, 21st and 22nd cycles of solar activity. RS models are presented as combined distributions of SPE radiation parameters (statistical model), and as the flare heliolongitude dependencies of temporal and spectral characteristics for two classes of SPE (empirical model). Copyright © 1996 Elsevier Science Ltd
1. INTRODUCTION
I = J J d t = integral proton flux over the whole events;
The state of the radiation situation in near-Earth space (NES) is mainly determined by temporal, spatial and spectral characteristics of the SCR (solar cosmic ray) proton component within the energy range 5-200 MeV, which are caused by solar flares generating protons which penetrate space. The occurrence and intensity of solar proton flares varies considerably with the phase of the I l-year solar activity (s.a.) cycle. The term "near-Earth space" stands for the part of space free from the Earth's radiation belts embracing the area of the open force lines of the geomagnetic field stretching to the magnetotail and reconnecting with IMP (interplanetary magnetic field) force lines, often referred to as "polar caps" or "high-latitude zones of the Earth's magnetosphere". The radiation situation (RS) forecast in the NES is a baseline for predicting radiation conditions on any spacecraft orbit. When developing RS models, statistical methods for investigating solar proton events (SPE) including solar activity cyclicity were used. On the basis of investigations of SPE radiation characteristics and their variations in 1965-1989 a statistical model as an SPE number distribution according to radiation characteristics and an empirical model in the form of SPE radiation characteristic dependencies on the heliolongitude of the flareproton source for two classes of events were developed (Avdyushin et al., 1990). The system of "Meteor" satellites provides regular recording of the SPE protons. For the period from 1990 to December 1992, 80 SPEs were recorded. Their flux and spectral characteristics were evaluated:
Jm = proton flux at the SPE maximum; y, = spectral index at the SPE maximum in power representation of the integral proton spectrum J( > E) = A E - "~.The proton sources have been identified and temporal characteristics of events have been determined: to = time from the beginning of H~ flare observations till the proton arrival in the Earth's orbit; tm= time from flare onset till the SPE maximum; Atm = time from SPE onset till its maximum; T = SPE duration. 2. A STATISTICAL MODEL OF RS IN THE NES A statistical model taking into account events recorded in 1990 is given in Fig, 1. As is seen from the histogram the values of J~ and I did not exceed 105 cm -~ s -~ sr -m and 2 x 10 "cm -2, respectively. The spectral index varied within 0.5--7, the most probable value being 1 < Ym< 3. SPE distributions over Jm and I are satisfactorily described by log-normal functions. For temporal characteristics the approximate analytical equations are obtained (Table 1). 3. EMPIRICAL MODEL OF SPE RADIATION PARAMETERS
451
Investigations, described in Mikirova and Pereyaslova (1977), Pereyaslova et al. (1983); Pereyaslova et al., (1986) and Smart and Shea (1979) of the relations of radiation characteristics with flare heliolongitude, the structure of the coronal magnetic
N. K. PEREYASLOVA et al.
452 250
50 -
50 200
50 - -
Jm
150
30
I
"Ym
30
100 50
10
c~
10
-
[
105
107
o
e~
o
100
102
104 crn-2s-lsr-1
10 9
I0 II cm -2
0
L
i 1--,--,
2
4
6
70
250 70
e~ 200
z
5o
150
50
100
.~ N 3o
50
50 At m
50
tm
3o
30
I0
10
30
8 I0
~
10
I 0 30 60 90 h 0 30 60 90 h 0 30 60 90 h 0 8 16 20 day Fig. 1. Proton event distributions over radiation parameters during the 1965-1990 period. field and the intcrlocation of the source and the proton detector were used when developing an empirical model of SPE temporal and spectral characteristics. This model, together with flux parameters, determines the radiation situation in the NES. In accordance with the obtained dependencies (Mikirova and Pereyaslova, 1977; Pereyaslova et al., 1983), all SPEs with proton flux in the maximum being Jm --> 1 crn -2 s - l sr -~ for protons with E~ > 10 MeV were divided into two classes. The first class includes events for which the flare and the base of the Earth-Sun force line are located in a single unipolar solar region, the second class of events includes the location of the flare and the base of the Earth-Sun force line in different unipolar regions. Taking into account circumsolar propagation and hcliolongitudinal dependencies for radiation characteristics---t0, t~, Arm at T--two classes of SPEs were obtained. Figure 2 illustrates the SPE radiation parameters for protons with Ep > 10 McV as a function of the flare heliolongitude using the data for the 20th, 21st and 22nd (1990 inclusive) s.a. cycles. The data are averaged within a 30° heliolongitude interval. Standard deviation from the mean value is shown in each heliolongitude interval. The dependencies were Table 1. Analytical equations for the approximation of SPE distribution over radiation characteristics Radiation parameter
Approxnnate equations
to, h
N = 327e-o.:s,o+ 56c-o.~,o
Arm, h
N = 227e-°'°~- + 16c -°'°sA'N = 351e-°°~'N = 569e-°"2r + 77e -°'~°r
t®, h T, day
,~= ~ ~ ~ : ~ "~ .~ E"
10
2 class
1 class
~5,_. 9= ., .~ 30 ~ ,,~ ~ < 20 lO o
I
2 class
I
;
lcl"s
40
~ 30
2 class
20 [" E
10
~
3
I
.I.
1 class
t
v~~' ~ .~ .
2 r 1 E 90 °
2 class
[ - ~ l c l a s s 60
30
0
30
60
90 ° W
Fig. 2. Heliolongitudinal dependence of radiation parameters for two SPE classes in the 20-22 solar cycles.
SOLAR PROTON
EVENTS IN NEAR-EARTH
SPACE
453
Table 2. Regression equation between SPE radiation characteristics and flare heliolongitude from the 1965-1990 data Parameter
SPE class
to, h
Approximate equations
1 2 1 2 1 2 1 2
Arm, h tin, h ~
2.36 11.2 5.32 19.1 7.67 26.2 2.08 2.90 --
SPE number taken into account
0.0332 + 0.00043. 2 0.0453. + 0.000622 0.0182 + 0.000122 0.1603. + 0.002422 0.048,~ + 0.00043.2 0.1743. + 0.00153. 2 0.0053. + 0.000053. 2 0.0023. + 0.000033. 2
183 118 186 110 179 158 189 170
(a)
4
•
3
--J.
•
2
•
6
•
•
•
•
•
Q
•
1 • Q
0O
00 •
•
•
•
• 9
•
~
t
0
•
•
Q 0O
•
•
•
0
•
I
I
I
1
2
3
(b) 3
-
.
." ~ •
1
f.
.
.~~-.,
•
•
~~."
•
•
.j~~
D
•
o
-1
I
I
I
1
2
3
X-ray intensity IogF x (mlerg cm-2s -]) Fig. 3. Correlations between the proton flux during the event maximum and maximum X-ray burst intensities (a) for class 1 of SPE and (b) for class 2.
454
N . K . PEREYASLOVA et al.
approximated with second-order parabolas; calculations were carried out using the least squares method. Regression equations are presented in Table 2. Similar distributions were obtained for the protons with Ep > 30, 60 MeV. A relation is established between the maximum proton flux with Ep > 10 MeV and the maximum X-ray burst intensity within 1-8 A, accompanying the flare--the source of proton injection (Mikirova and Pereyaslova, 1983). To forecast the maximum proton flux, functions of the predicting variables for two classes of events were obtained. Figure 3 shows the correlation dependence between Jm values and Fx--the maximum value of X-ray burst intensity. Regression equations for two classes of SPEs: log Jm = 0.75(Iog Fx)2 -- 1.71 log Fx + 1.88 class 1 log Jm = 0.82 log F~ -- 0.09 class 2 For SPE of class 1, J~ dependence on Fx is satisfactorily described by the second-order equation (parabola); for SPE of the second class, linear dependence with a correlation coefficient o f ~ 0.9 and root-mean-square deviation of 0.40, the confidence interval is 0.77 at the 95% significance level. 4. CONCLUSION In 1991-1992--the onset of the decline phases of the 22nd s.a. cycle--the "Meteor" satellite recorded 57 SPEs. In these events mean relative deviations of the observed values of proton radiation characteristics with E p > 10 MeV from empirical model
distributions for to, Atm, tm and Ym are (48 _+ 6), (80 5: 11), (46 + 6) and (31 + 3)%, respectively. This result allows for the hope that the developed empirical model may be used for assessing the radiation situation in NES when information on the flare characteristics, the synoptic map of the Sun or data on the structure of the large-scale magnetic field of the Sun are obtained.
REFERENCES Avdyushin S. I., Nazarova M. N., Pereyaslova N. K. and Petrenko I. Ye. (1990) Modelling the radiation situation and predicting the parameters of solar proton events. In: Solar Terrestrial Predictions Proceedings of a Workshop at Leura, Australia, 16-20 October 1989, Boulder, CO, Vol. 1, pp. 288-296. Mikirova N. A. and Pereyaslova N. K. (1977) The effect of photospheric magnetic fields on the distribution of solar flare protons. Dokl. A N SSSR 234, 798-801(in Russian). Mikirova N. A. and Pereyaslova N. K. (1983) Quantitative diagnostics of proton flares from X-ray burst data. Sol. dan. 1, 101-105 (in Russian). Pereyaslova N. K., Nazarova M. N. and Mikirova N. A. (1983) Solar cosmic ray parameters related to the structure of coronal magnetic field. Geomag. Aeron. 233, 367-371(in Russian). Pereyaslova N. K., Mikirova N. A. and Nazarova M. N. (1986) A method of forecasting solar cosmic ray events. In: Solar Terrestrial Predictions Proceedings of a Workshop at Meudon, France, 18-22 June 1984, Boulder, CO, pp. 220-227. Smart D. F. and Shea M. A. (1979) A computerized "event mode" solar proton forecasting technique. In: Solar Terrestrial Predictions Proceedings, Boulder, CO, Vol. 1, pp. 406-427.