by the 'Diffusive Shock' acceleration mechanism, because all the events were 'long-duration events', shock-associated, and their spectra fitted to a power-law ...
DIFFUSIVE-SHOCK-ACCELERATED INTERPLANETARY IONS AT SEVERAL ENERGIES DURING THE SOLAR CYCLE 21 MAXIMUM J. RODRÍGUEZ-PACHECO, J. SEQUEIROS, L. DEL PERAL, E. BRONCHALO and C. CID Dep. Física, Apdo. 20, Univ. de Alcalá, 28871 Alcalá de Henares, Madrid, Spain
(Received 14 May 1996; accepted 23 January 1998)
Abstract. The most intense energetic particle (mainly proton) events in the energy range 36– 1600 keV, during the years of maximum activity of solar cycle 21 (1978 to 1982), have been studied with regard to their spectra, temporal profiles, source location at the Sun, interplanetary plasma parameters and interplanetary magnetic field topology. In all the events, the particles were accelerated by the ‘Diffusive Shock’ acceleration mechanism, because all the events were ‘long-duration events’, shock-associated, and their spectra fitted to a power-law energetic particle spectrum dJ /dE ∼ E −γ with the exponent values ranging from 1.25 up to 1.94, with a mean value of 1.60 ± 0.06. We also show that the spectral indexes γ are related to the shock properties by a linear expression. The solar sources were located on a wide longitudinal belt extending from 50◦ W up to 73◦ E. Neither the spectral indexes nor the shock parameters present any dependence on the source location at the Sun. Finally, only one event showed the complete set of properties that characterize the presence of a magnetic cloud associated with the event.
1. Introduction For more than 4 years the ‘International Solar–Earth Explorer 3’ (ISEE-3) spacecraft remained in an orbit around the Lagrangian point L1, obtaining valuable measurements of the interplanetary populations of energetic particles. Because of the spacecraft’s privileged position, it has been possible to study the relationship between the different fluxes of low-energy (35 < E < 57 keV) and high-energy (1 ≤ E ≤ 1.6 MeV) particles measured by the low-energy proton experiment DFH. The low-energy fluxes are generally related to interplanetary propagation of magnetohydrodynamic perturbations (mainly shock waves). In fact, the connection of the population of particles with energies from 30 keV to 10 MeV with this kind of phenomena has been known for 30 years (Bryant et al., 1962). Furthermore it has been shown that the low-energy particle fluxes behave as a coherent population independent of the solar wind (Sanahuja and Domingo, 1987). In this work the particle fluxes with energies between 36 to 56.5 keV and 1000 to 1600 keV, during the maximum of the 21st solar cycle have been studied in such a way that the events with the highest intensities in both energy ranges have been selected with the purpose of studying their energetic particle source, acceleration Solar Physics 181: 185–200, 1998. © 1998 Kluwer Academic Publishers. Printed in Belgium.
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mechanism and propagation towards the observer. The solar wind plasma parameters and the interplanetary magnetic field (IMF) topology associated with the events have been considered as well. Furthermore, we have also compared these particle fluxes using long temporal averages, with the purpose of obtaining an estimation of the mean low-energy particle fluxes in the interplanetary medium at 1 AU during the period of maximum intensity of solar cycle 21.
2. Instrument Description The ‘Low Energy Proton Instrument: DFH/EPAS’ (Balogh et al. 1978; van Rooijen et al. 1979) is composed of three identical semi-conductor telescopes, namely TEL1, TEL2 and TEL3 with an angle of 30◦ , 60◦ , and 135◦ with respect to the spacecraft spin axis, which is pointing north perpendicular to the ecliptic plane, optimizing the angular coverage and, at the same time, avoiding direct solar radiation on the telescope apertures. Each telescope has a conic aperture half angle of 16◦ and a geometric factor of 0.05 cm2 sr. Eight logarithmically spaced energy channels (E1, ..., E8) are available to measure the total energy loss in the front detector. The lower energy thresholds of these channels are as follows: 35, 56.5, 91, 147, 238, 384, 612, and 1000 keV. The spin of the spacecraft is divided into eight identical sectors of 45◦ each, in which the particle counting rates in each of the energy channel are accumulated, except for channel 8 which is accumulated in only 4 sectors of 90◦ . From these data the directional information of the incoming particles is derived. Finally it should be noted that this instrument is not capable of discriminating between protons and heavier ions, so in the following we will refer to protons or particles indiscriminately.
3. Data Selection and Analysis The data used when comparing channel E1 (36–56.5 keV) versus channel E8 (1000 –1600 keV) have been averaged over 12 hours, and are expressed in count s−1 , beginning in the first hour of day 228, 1978 and ending with the last hour of day 358, 1982. From the data, the period of five days in October 1982 when the spacecraft crossed the magnetosphere has been excluded. The spacecraft remained in an orbit around Lagrangian point L1 from the beginning October 1978 until the beginning of September 1982. Because the differences of the fluxes measured by each telescope are negligible, only TEL2 data have been used in this work; furthermore, as the main emphasis is on net fluxes, i.e., in the omnidirectional flux without taking into account the possibility of anisotropy, the data from the 8 spatial sectors have been averaged, obtaining a single value for each energy channel of telescope TEL2. This value represents, in counts per second, the net mean flux detected during 12 hours in the
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corresponding energy channel. The results of the temporal evolution of channels E1 (36–56.5 keV) and E8 (1.0–1.6 MeV) are shown in Figure 1. At first sight, it is evident that the less energetic channel shows much more data associated with high fluxes than the high-energy channel (note the different scales). The different behavior of the two channels becomes evident when one of them is plotted versus the other one. Figure 2 shows the measured flux in channel E1 versus the measured flux in channel E8. As can be seen, the data, mainly at low intensities, are very dispersed with little correlation. This dispersion is mainly due to the different properties of the particles associated with each channel: the time that particles take to ‘run’ 1 AU, from their source to the observer is approximately one order of magnitude shorter for the ‘high’-energy channel than for the ‘low’-energy one. Moreover, 1 MeV particles are less sensitive to some magnetic irregularities of the interplanetary magnetic field (IMF) which means that these particles suffer less scattering than particles with energies around 50 keV. As a consequence of these factors, along with the position of the source at the Sun, the two channels do not present the same temporal pattern during a particular event. The different spectral indexes (dJ /dE ∼ E −γ ) of the associated events are also an important factor which contributes to the dispersion shown in Figure 2, when the predominant acceleration mechanism is the ‘diffusive-shock acceleration mechanism’ (Fisk, 1971). The position of most of the points located close to the lower right corner of this figure (i.e., very intense in E1 but with low intensities in E8) are explained in terms of the properties that have just been mentioned above. An example of an event associated with one of these points is shown in Figure 3. Just moving ahead the 12-hour integration period (from the second half of day 94 to the first half of day 95), the position on the E1 and E8 points in Figure 2 can be dramatically different. We can regard these events as affected by ‘temporal shifts’ in the energetic particle profiles. Nevertheless, from these figures we have been able to select the most intense events in both channels. A detailed study of each point – which, it should be remembered, represents net fluxes averaged over 12 consecutive hours – reveal that due to the existence of gaps or discontinuities in the data collection, there are points whose intensities could not be representative of the associated energetic particle event. Since in an event of this kind the fluxes can vary several orders of magnitude in less than 4 hours, the following selection criteria have been established in order to be confident that the 12-hour averages are statistically representative of the nature of the event: (a) All points with a gap in the data of more than 3 consecutive hours in the 12-hour average period are discarded. (b) The total data gap length should not be longer than 4 hours. In this way it can be guaranteed that all the point that fulfill the above criteria are not significantly affected by loss of data during the 12-hour integration period. After applying this criterion to the 12-hour average points, we selected the events associated with the highest intensities in both channels.
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Figure 1. Particle fluxes in counts s−1 measured by channel 1 (E1, upper panel) and channel 8 (E8, lower panel) of the ‘DFH Experiment’ during the maximum of solar cycle 21 (August 1978 – December 1982). Each point represents net flux measured by TEL 2 averaged over 12 hours.
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Figure 2. Particle fluxes detected in channel E8 versus particle fluxes detected in channel E1. All the data are 12-hour averages expressed in counts s−1 . Note the different scales and the data dispersion. The points associated with the most intense events are located over the upper part of the graph. Note as well the existence of an area (lower-right corner) with points related to very intense events in channel E1 but with low or moderate intensities in channel E8.
4. Results and Discussion
Once the most intense events have been selected, and in order to perform a complete study, they were studied considering all the channels of the instrument and using 1-hour averages expressed in particles s−1 sr−1 cm−2 keV−1 . These were 14 events associated with the highest intensity points that fulfilled the former criterion. For every event, we have studied its spectrum, solar source location, solar wind plasma parameters, and the IMF topology that accompanied the event arrival. The
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Figure 3. Channel E1 and E8 plot of the 5 April 1979 event. This is a clear example of how a temporal shift of the maximum fluxes in the two channels and the 12-hour integration periods together, may produce very different points in E1 versus E8 plots (Figure 2). The broken lines show the two 12-hour integration periods corresponding to two different points of Figure 2.
data referring to the plasma parameters and IMF are 1-hour averages, and they were obtained from the OMNIWeb data explorer. 4.1. S PECTRAL
INDEXES
The energetic particle fluxes of all the events, at the time of the shock passage, were found to fit a power-law energetic particle spectrum dJ /dE ∼ E −γ with the exponent values ranging from 1.25 up to 1.94, with a mean value of 1.60 ± 0.06. All the events were found to be associated with an interplanetary shock wave whose solar wind velocity compression ratio, K = v2 /v1 , ranged between 1.20 and
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TABLE I Events with the highest intensities in 36 – 56.5 keV and 1.0 – 1.6 MeV. The table shows the event number, date (day/month/year), spectral index, solar wind velocity compression ratio, source position at the Sun, and maximum fluxes (particles s−1 sr−1 cm−2 keV−1 ) in 1-hour averages reached by channel E1 and E8, respectively. Event No.
SC date
γ
K
Source
Peak E1
Peak E8
1 2 3 4 5 6 7 8 9 10 11 12 13 14
25 Sept. 1978 14 Dec. 1978 5 Apr. 1979 6 June 1979 18 July 1980 26 Apr. 1981 11 May 1981 17 May 1981 13 Oct. 81 1 Feb. 1982 6 June 1982 11 July 1982 6 Sept. 1982 24 Nov. 1982
1.39 1.58 1.73 1.56 1.85 1.70 1.72 1.33 1.25 1.94 1.71 1.86 1.49 1.27
1.52 1.23 1.42 2.11 1.42 1.62 1.42 2.23 1.94 1.28 1.20 1.53 1.49 2.84
35N – 50W 16S – 48W 26S – 14W 17N – 14E 11S – 06E 14N – 50W 09N – 42E 10N – 16E 16S – 30E 16S – 13E 09S – 72E 17N –73E 13N –33E 11S – 36W
751 1206 2242 1729 1644 1330 1387 1510 1938 1225 1406 630 1653 1159
7.16 4.53 4.66 21.24 6.06 6.19 10.32 19.41 40.29 5.89 6.59 6.92 11.72 5.83
2.84 with a mean value of 1.66 ± 0.13 (v2 is the solar wind velocity after the shock passage, i.e., downstream velocity, and v1 is the solar wind velocity before the shock passage, i.e., upstream velocity). The event dates (sudden commencement day, month and year), spectral indexes, and solar wind compression ratios along with others features that will be discussed later on, are shown in Table I. The event with highest K (K = 2.84, γ = 1.27) was event number 14 and the event with the lowest K (K = 1.20, γ = 1.72) was event number 11. The fact that the events are shock-associated, that all the events are long-duration events (not ‘spike’-like events), and that the energetic particle fluxes present a power-law spectrum, suggest that these particles were accelerated by the diffusiveshock acceleration mechanism. Nevertheless, with the aim of confirming the acceleration mechanism, we have studied the possible relationship between the spectral indexes and the solar wind velocity compression ratio. In Figure 4 we have plotted the former versus the latter for the 14 events. As can be seen, these two parameters seem to be correlated with the γs decreasing with increasing Ks. This correlation is not unexpected because several works (Axford, Leer, and Skadron, 1977; Bell, 1978; Blandfor
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Figure 4. Spectral indexes versus the solar wind velocity compression ratio, K. Filled points represent the fourteen most intense events that fitted to a linear regression (solid line). When two more points, associated with events very intense in channel E1 but with moderate intensities in channel E8, are considered (empty circles), then it could be reasonable to assume that the dependence of γ on K could be γ = (a1 K + a2 )/(b1 K + b2 ), with the a’s and b’s as constants (dotted curve).
and Ostricker, 1978) have suggested that the spectral index γ depends solely on the hydrodynamic shock strength H as γ = (H + 2)/(2H − 2) ,
(1)
where H is given by the ratio between the downstream and upstream plasma density. Nevertheless, using the solar wind velocity compression ratio instead of the density ratio, the correlation with the spectral index seems to be linear (γ = aK + b), as Figure 4 suggests. After making a linear regression, we have obtained for the correlation coefficient a value of r = 0.7 with a = − 13 and b = 29 : γ = (− 13 )(K − 23 ) .
(2)
The discrepancy of the spectral-exponent dependence on the shock-wave parameters could lie on the event selection criterion. This conflictive point will be discussed later in Section 4.4. 4.2. S OURCE
LOCATION AT THE
S UN
In order to determine the origin and properties of the events, we have looked for their sources at the Sun. To achieve this goal, two papers of Cane (1985,
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1986), where she discussed the evolution of shock waves in the interplanetary (IP) medium, and events of energetic particles related to different types of solar flares have been used. Also, for those events not discussed in those references, we have searched for their sources related to long-duration X-rays flares that occurred in the two days prior to the energetic particle event arrival, due to the fact that these kind of flares are the best proxies for coronal mass ejections (CMEs) and for gradual energetic particle events (Rodríguez-Pacheco et al., 1997). The information about long-duration X-ray flares was obtained from the ‘Solar Variability Affecting Earth’ files provided by NOAA. For every event, the source location on the Sun is shown in column 5 of Table I. The peak flux in channel E1 and in channel E8 are also shown in this table (columns 6 and 7, respectively). Attending to the work of Cane (1985), in which she suggests that shock waves originating in western latitudes are weaker than central and eastern shocks (10◦ W –45◦ E), we should expect that the source heliolongitude associated with the fourteen events under consideration (we have to bear in mind that they are the most intense in the 36–1600 keV range during the years of maximum activity of solar cycle 21) would fall into the second group (i.e., central and eastern longitudes). Nevertheless, the data shown in Table I indicate that the heliolongitude dispersion of the energetic particle event’s heliolongitude source is quite high, ranging from 50◦ W up to 73◦ E. In order to check any possible dependence of the solar wind velocity compression ratio ‘K’ and of the spectral exponent ‘γ’ on the source location at the Sun, we have plotted them versus the source heliolongitude in Figures 5(a) and 5(b), respectively. As can be seen, neither the solar wind velocity compression ratio versus the source heliolongitude plot (Figure 5(a)), nor the spectral exponent versus the source heliolongitude plot (Figure 5(b)), indicates any possible correlation between them. We can only say that the events with the highest Ks and lowest γs fall in a longitudinal belt extending from 36◦ W (event 14) up to 30◦ E (event 9). The possible correlation with the source location study was completed by checking any possible dependence of the peak fluxes during every event in both channels on the source heliolongitude. Figure 6(a) represents the maximum flux in channel E1 versus the source heliolongitude. Figure 6(b) is similar to the former but for the maximum flux in channel E8. Again the dispersion is quite high, mainly in Figure 6(a), suggesting that these sets of parameters are not related. Anyway, we think that Figure 6 is particularly interesting because the maximum flux in channel E8 is almost constant around 6 particles s−1 sr−1 cm−2 keV−1 along the heliolongitude interval, with the only events with peak fluxes higher than the former value located in the 14◦ –42◦ E longitudinal belt, i.e., falling in the strongest shock heliolongitude interval defined by Cane (1985). Finally, the nature of the two ‘unusual’ events with source heliolongitudes above 70◦ E (events numbers 11 and 12) will be discussed in the following section.
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Figure 5. (a) Variation of K over the heliolongitude of the associated solar source. As in Figure 4, filled circles represent the fourteen most intense events in both channels, and the empty ones represent events very intense in channel E1 but not in channel E8. (b) Similar to (a) but showing the γ variation on the source heliolongitude.
Figure 6. (a) Variation over the heliolongitude of the associated solar source of the 1-hour average maximum fluxes (peak fluxes) detected during every event for channel E1. Filled symbols represent the fourteen most intense events in both channels, and the empty ones represent events very intense in channel E1 but not in channel E8. (b) Similar to (a) but showing the variation with the source heliolongitude of the 1-hour average maximum fluxes detected during every event for channel E8.
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4.3. S OLAR
WIND PHYSICAL PARAMETERS AND
IMF
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TOPOLOGY
During the past years, several studies have provided strong evidence (Reames, 1990a, b, 1993; Kahler, 1992; Gosling, 1993) for two types of solar energetic particle (SEP) events: ‘impulsive’ events (3 He-rich, solar-flare accelerated) and ‘gradual’ events. Particularly, the energetic particles associated with gradual events are accelerated by interplanetary traveling shocks that are driven by fast coronal mass ejections (CMEs) (Sheeley et al., 1983, 1985). Nowadays, it is widely accepted that the interplanetary signatures of the CMEs are (Gosling, 1990, and references therein): depressed temperatures of solar wind plasma protons, enhanced solar wind helium abundances, magnetic-field-aligned, bi-directional solar wind electron heat fluxes, bi-directional energetic ion flows, low-variance magnetic field enhancements that often include smooth rotations of the magnetic field direction in so-called ‘magnetic clouds: MC’, and low plasma β (ratio of the particle to magnetic field pressures). When an interplanetary traveling shock is observed before these signatures, it is assumed that the spacecraft have entered into CME material forming the shock driver. These entries are also associated with depressions in the energetic ion intensities. In this section we study the possible presence of magnetic clouds following the shocks that are associated with the events under consideration. The presence of the magnetic cloud is studied, examining the following set of parameters associated with the events: energetic particle profiles, plasma velocity (vsw ), plasma temperature (Tsw ), plasma number density (ρsw ), and magnetic field topology: module (B), and X (Bx ), Y (By ) and, Z (Bz ) components (GSE coordinates). All the data that we have used were 1-hour averages. For every event, and when the data were available, the plasma beta and the expected temperature were calculated, using the well-established association between the solar wind velocity and the proton temperature (López, 1987). Table II shows the sudden commencement (SC) time (day, month, year), the source location, and the following energetic particle, plasma and magnetic field signatures (d.o.y.-UT hour): depression in the energetic proton flux (8↓), proton temperature depression (T ↓), plasma beta depression (β↓), magnetic field enhancement (B↑), and finally, magnetic field smooth rotation (B←-). As can be seen, only one of the fourteen events (number 1) presented evidences, in all the parameters under consideration, of a magnetic cloud (MC) driving the shock. But unfortunately, this event is even affected by a data gap in the plasma temperature. For the rest of them, we can only say that four of them (events numbers 9, 11, 13, and 14) presented evidences of MCs but the absence of data (mainly in the plasma temperature and number density) does not allow us to assert that they were driven by MCs. Anyway, and despite this handicap, we can say that nine of the fourteen events under study did not show all the specific features of a magnetic cloud associated with the shock. Events number three and eight presented sudden decreases in the energetic proton counting rate, proton temperature and in the plasma beta, but failed with magnetic-field-specific features. This could mean
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TABLE II Energetic particles, plasma and magnetic field properties associated with the most intense energetic particle events detected during the years 1978–1982. The column’s legends are the following: event number, time (year-d.o.y-UT hour), source location at the Sun and d.o.y. and hour of sudden decrease in the energetic particle flux, plasma temperature and plasma beta, low-variance magnetic field enhancement and smooth rotation of the magnetic field direction. Data marked with ∗ means that these periods contain gaps. Event No.
SC time
Source
8↓
T↓
β↓
B↑
B←-
1 2 3 4 5 6 7 8 9 10 11 12 13 14
78-268-07 78-348-02 79-95-01 79-157-20 80-200-20 81-116-07 81-130-22 81-137-23 81-286-23 82-32-12 82-157-03 82-192-11 82-248-22 82-328-09
35N –50W 16S – 48W 26S – 14W 17N – 14E 11S – 06E 14N – 50W 09N – 42E 10N – 16E 16S-30E 16S-13E 09S-72E 17N-73E 13N-33E 11S-36W
269-18 348-22 95-09 158-04 201-00 No No 138-06 287-16 No 157-14 No 249-12 328-21
269-10∗ 349-00 95-12 158-04 No data No data No data 138-06 No data No data No data No No data No data
269-18 No 95-12 No No data No data No data 138-06 No data No data No data No No data No data
269-18 No No No No No No No 287-16 No 157-21 192-14 No data 328-20
269-18 349-00 No No 201-00 No No No 287-18 No 158-06 No No data 328-20
that these events were followed by ‘ejecta’ without the typical magnetic features of a magnetic cloud. Finally, we have to mention that the plasma parameters. magnetic field topologies and energetic particle profiles (simultaneous and similar profiles in all the energetic channels throughout the entire event) of the two events associated with solar sources with heliolongitudes above 70◦ E (Figure 7), suggest that they arrived at the spacecraft position close to a presumably previous magnetic field boundary crossing, and were connected to the ‘rear’ front of the shock (which explains their extremely high source heliolongitudes). 4.4. L OW- INTENSITY
EVENTS
Turning our attention back to Figure 2, we can observe that there was a particular kind of events that presented very high fluxes at low energies, but very low fluxes at high energies (lower right corner of this figure). As has been already said, most of these points were associated with events affected by ‘temporal shifts’. Nevertheless, we have found two events whose high-to-low-energy flux ratio was extreme, and not associated with any ‘temporal shift’ in the energetic particle profiles. Just
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Figure 7. Magnetic field module and GSE coordinates (B, Bx , By , and Bz ), plasma number density and velocity (nsw and vsw ) and energetic particle profiles in channels E1 and E8, of the 6 June events (events number 11). The solid line indicates the shock arrival at the spacecraft. The possible presence of a previous current sheet crossing, suggested by the magnetic field decrease and rotation and number density increase, is indicated by the broken lines. Note the similar energetic particle profiles in both channels.
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TABLE III Similar to Table I but for the two events that showed relatively very low fluxes in the high-energy channel (E8) Event No.
SC date
γ
K
Source
Peak E1
Peak E8
15 16
27 Aug. 1978 20 Dec. 1980
2.55 2.77
1.39 1.37
15N – 15E 10N – 07E
949 1643
0.06 0.08
for the sake of completeness, we have studied them in the same way as that for the previous fourteen points. Both events also fitted to a power-law energetic particle spectrum, dJ /dE ∼ E −γ , which, along with their long durations, suggests that the acceleration mechanism involved is the same as that of the previous fourteen events, i.e., diffusive shock acceleration mechanism. The event dates (sudden commencement day, month and year), spectral indexes, solar wind compression ratios, source location, and peak fluxes in channels E1 and E8 are shown in Table III. These points are represented by empty circles in Figures 4, 5, and 6. As can be seen, both events presented high gamma values, very low values in E8, and near-central-meridian heliolongitudes. Particularly, in view of Figure 4, we can see that they do not fit the linear regression performed over the most intense events. Moreover, if we take into account the position over Figure 4 of these low-intensity events, we can say that the discrepancy between our result about the dependence of γ on K (Equation (2)) and that obtained by others authors already mentioned in Section 4.1 (Equation (1)), could be due to the fact that we have restricted our study to the most intense events (with the lowest gamma), where the non linear equation written above approaches a linear behavior. In order to clarify this point, in Figure 4 we have also plotted (dashed curve) a function similar to the latter but with K as independent variable instead H : γ = (K + 1.5)/(2K − 1.5) .
(3)
Finally, we have to point out that the two low-intensity events that we have selected were presumably associated with magnetic clouds, because their plasma and magnetic field parameters (Table IV), along with their temporal profiles, are consistent with those of these interplanetary structures.
5. Conclusions In this work the most intense energetic particle events in the energy range between 36 and 1600 keV during the period of maximum activity of solar cycle 21 have been studied. The particle fluxes were expressed in particles s−1 sr−1 cm−2 keV−1 .
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TABLE IV Similar to Table II but for the two events that showed relatively very low fluxes in the high-energy channel (E8) Event No.
SC time
Source
8↓
T↓
β↓
B↑
B←-
15 16
78-239-02 80-354-05
15N –15E 10N –07E
239-14 354-11
239-21 354-12∗
239-19 354-13∗
239-19 354-11
239-19 354-11
The solar wind physical parameters and the interplanetary magnetic field topology associated with the energetic particle events were studied as well. When considering every event, all the data used were 1-hour averages. After applying a data selection criterion that related to data gaps, the number of selected events was 14. All the fourteen events were long-duration, shock-associated, and their spectra fitted to a power-law energetic particle spectrum dJ /dE ∼ E −γ with the exponent values ranging from 1.25 up to 1.94, with a mean value of 1.60 ± 0.06. We conclude that the particle acceleration mechanism predominant in these events was the ‘diffusive-shock acceleration mechanism’. We have studied the shocks related to the solar wind velocity compression ratio K = v2 v1 (i.e., the ratio between the downstream to the upstream velocity). The values of K ranged between 1.20 and 2.84 with a mean value of 1.66 ± 0.13. We have also found that the spectral exponent γ depends on the solar wind velocity compression ratio. This dependence was found to be linear, as Equation (2) shows, with a correlation coefficient of r = 0.7. This result differs from that presented by several authors who showed a dependence of the spectral exponent on the hydrodynamic shock strength H given by Equation (1). The study of two different events which showed very high intensities at low energy but very low intensities at high energies solved this discrepancy, suggesting that it could be due to the fact that we have restricted our study to the most intense events (with the lowest gamma) where the nonlinear equation written above approaches a linear behavior. The study of the energetic particle profiles and solar source along with plasma physical parameters and the interplanetary magnetic field topology associated with the energetic particle events lead to the following conclusions. All the events were associated with solar sources whose heliolongitudes spanned a considerable range from 50◦ W up to 73◦ E, i.e., much wider than the longitudinal belt proposed by several authors for the most intense shocks. Neither the spectral exponents, nor the solar wind velocity compression ratio, nor the peak fluxes in channel E1 and channel E8 showed a dependence on the heliolongitude of the solar source. Nevertheless, both the events with the highest K (lowest γ) and the events with the highest channel E8 peaks were associated with sources between 36◦ W and 30◦ E for the former, and 14–42◦ E for the latter, i.e., falling in the strongest shock heliolongitude interval defined by previous works.
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Finally we have to mention that the study of the plasma and magnetic field parameters suggests that the most intense events were not accompanied by interplanetary magnetic clouds, but the absence of data does not allow us to be confident about this conclusion. Nevertheless, this study indicates that the two events with solar sources heliolongitudes higher than 70◦ E were connected with the rear shock front and associated with a previous magnetic field boundary crossing.
Acknowledgements This work has been supported by the ‘Comisión Interministerial de Ciencia y Tecnología (CICYT)’ under grant ESP97–1776. The authors also wish to thank the referee for helpful comments and the OMNI-Web data system.
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