Search for periodicities in the IMP 8 Charged Particle Measurement Experiment proton fluxes for the energy bands MeV and MeV

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 114,, doi: /2008ja013181, 2009 Search for periodicities in the IMP 8 Charged Particle Measurement Experiment proton fluxes for the energy bands MeV and MeV M. Laurenza, 1 M. Storini, 1 S. Giangravè, 2 and G. Moreno 2 Received 18 March 2008; revised 25 August 2008; accepted 16 October 2008; published 13 January [1] Past studies revealed that the photospheric magnetic field, as well as many solar activity phenomena, undergoes both periodic and quasiperiodic variations on different time scales. Nevertheless, only a few attempts have been made so far to detect corresponding variations in the occurrence frequency of solar energetic particle events. Here we search for periodicities in the proton fluxes, measured in the interplanetary space, on time scales ranging from a few (>6) Bartels rotations (27 days) up to the Schwabe (11 years) period. We apply the wavelet technique to the proton fluxes recorded by the Charged Particle Measurement Experiment (CPME) instrument aboard IMP 8 spacecraft, from 1974 to 2001, in the energy bands MeV and MeV. The reliability of the obtained results is tested by analyzing the wavelet response to suitable artificial functions. The 9.8, 3.8, and year periods are the most significant found in the interplanetary proton flux. Shorter periods (such as 1 year) are detected in some time intervals, but they are not significant in the whole sequence of data. Citation: Laurenza, M., M. Storini, S. Giangravè, and G. Moreno (2009), Search for periodicities in the IMP 8 Charged Particle Measurement Experiment proton fluxes for the energy bands MeV and MeV, J. Geophys. Res., 114,, doi: /2008ja Introduction [2] Solar activity varies on several time scales, ranging from minutes to centuries. The dominant time scales of variability are the well known 11 year solar cycle (Schwabe s cycle) and the 27 day period related to the synodic rotation of the Sun. On the other hand, the Sun s magnetic activity appears to exhibit both periodic and quasiperiodic variations at other time scales in the range between these two basic periods. The most relevant periods which have been identified in the past are described in the following. [3] Quasiperiodic variations on time scales of the order of 150 days (the so-called Rieger period ) have been observed in several solar activity parameters, such as the monthly mean sunspot number [Wolff, 1983], the hard X-ray flare frequency [Rieger et al., 1984; Dennis, 1985; Bai and Cliver, 1990; Kile and Cliver, 1991] and the sunspot area [Lean, 1990; Ballester et al., 1999]. The effect seems to be absent in some solar cycles (e.g., in cycle 22 [Bai, 1992; Özgüç and Ataç, 1994]). [4] Variations on a time scale of 1 year have been reported in the sunspot area and number series [e.g., Krivova and Solanski, 2002] and in the mean photospheric 1 IFSI-Roma, National Institute for Astrophysics, Rome, Italy. 2 Department of Physics, La Sapienza University, Rome, Italy. Copyright 2009 by the American Geophysical Union /09/2008JA magnetic field [Boberg et al., 2002; Cadavid et al., 2005]. The effect has been explained in terms of the 1.3 years modulation of the Sun s rotation rate, near the base of the convective region, revealed by the heliosismological data at latitudes lower than 30 [Howe et al., 2000; Toomre et al., 2003]. [5] The so-called quasi-biennial oscillations (QBOs) include a variety of quasiperiodic variations, on time scales from 1.5 to 2.5 years, appearing in many manifestations of the solar magnetism (e.g., the number of Ha flares, the solar magnetic field energy index and the sunspot areas [Bazilevskaya et al., 2000]; the coronal hole area and the 10.7 cm radio emission [Valdés-Galicia and Velasco, 2008]). A 2 year periodicity was identified both in nonsymmetric and axisymmetric spherical harmonics of the photospheric field [Stenflo and Güdel, 1988; Stenflo, 1988; Knaack and Stenflo, 2005]. These oscillations seem to occur only at active heliographic latitudes (in the range ±40 ); they tend to disappear during the minimum phase of the sunspot cycle and to be related to the emergence, in the photosphere, of the toroidal magnetic fields [Laurenza and Storini, 2005]. They may have a crucial role in the solar activity phenomena. In fact, it has been proposed that the solar magnetic cycle actually consists of two components [Benevolenskaya, 1995, 1998]: a main component, of low frequency, with a period of about 22 years, and a secondary component, of high frequency, with a period of about 2 years. The superposition of these two components may produce the so-called Gnevyshev Gap [Bazilevskaya et al., 2000, 1of10

2 Figure 1. Time history of (a) the sunspot area and the CPME/IMP 8 proton fluxes in channels (b) P2 and (c) P11. Heavy lines refer to 5-BR running averages. Arrows indicate proton flux values exceeding the scale. and references therein], which is peculiar in the temporal trend of various solar-terrestrial indices [Storini et al., 2003, and references therein] during the maximum phase of the Schwabe cycles (for early works, see Storini [1995, 1998], Storini and Felici [1994], Storini and Pase [1995], and Feminella and Storini [1997]). It has also been emphasized that the Gnevyshev Gap structure and the QBOs in the northern and southern solar hemispheres may be synchronous or shifted in time [Feminella and Storini, 1997; Bazilevskaya et al., 2000]. [6] Periods between 3.4 and 4.4 years have been identified, at different latitudes, in the photospheric field as well as in coronal green line brightness and in the sunspot area [Laurenza, 2006]. These oscillations may be linked to the 3.65 year period in the southern and 3.80 year period in the northern solar hemisphere reported by Berdyugina and Usoskin [2003] in their analysis of active longitudes over the last 120 years. A 3.7 year periodicity has been also reported by Joshi and Joshi [2004] in the N-S asymmetry of the soft X-ray flare index during cycles 21 23; periodicities around years were detected by Vizoso and Ballester [1989] in the N-S asymmetry of flare indices, and periodicities of years by Rao [1973] in spot group indices. These fluctuations may arise from the interaction 2of10

3 Figure 2. (left) WPS versus time and period and (right) GWPS versus period for the proton flux in channel P2. The Morlet function has been used as mother wavelet. In Figure 2 (left), the black dashed line indicates the cone of influence, where edge effects become important. Thick black contours enclose regions of greater than 95% confidence, assuming a white noise background. In Figure 2 (right) the blue dashed line indicates the global significance level. of the QBO of the toroidal magnetic field with the 3.1 year modulation of the poloidal field at latitudes greater than j40 j [Laurenza, 2006]. [7] Several parameters describing solar activity and solarterrestrial relationships were found to oscillate with a period of 5.5 years [Djurović and Pâquet, 1996]. However, Mursula et al. [1997] have suggested that this periodicity is not real, being rather due to the enhanced power of the second harmonic which arises from the asymmetric shape of the sunspot cycle. This view is consistent with the lack of any 5.5 year modulation of the photospheric magnetic flux, reported by Laurenza [2006]. [8] The time variations of the solar activity mentioned above, influence the entire heliosphere. It has been found, e.g., that the solar wind speed fluctuates with a characteristic period of 1.3 years [Richardson et al., 1994; Gazis et al., 1995]. Similar oscillations have been revealed in the north-south component of the interplanetary magnetic field [Mursula and Vilppola, 2004] and in the geomagnetic index ap [Paularena et al., 1995]. More recently, Forgács-Dajka and Borkovits [2007] analyzed statistical properties of data series of different solar/interplanetary parameters finding common periodicities in the range 1 2 years during solar cycles Also the galactic cosmic ray flux is modulated on time scales of 150 days, 1.3 years, 1.7 years, and 11 years [Kudela et al., 2001, 2002; Valdés-Galicia et al., 1996, 2005; Mursula and Zieger, 1999]. [9] On the other hand, typical time scales of the solar energetic particle (SEP) variations have been less extensively studied although they are necessary for the comprehension of the relationship between solar activity variations and the emission of SEPs. Moreover, to estimate the expected flux variations of energetic particles at different energies during the solar cycle is useful in planning interplanetary missions (such as Messenger and BepiColombo), as SEPs can strongly affect the performance of spacecraft and instruments onboard in the inner heliosphere. [10] The frequency of the SEP events seems to undergo a 150 day oscillation [Bai and Cliver, 1990], and QBOs, around the sunspot maximum, besides a modulation over the Schwabe cycle scale [Shea and Smart, 1990, 1994; Bazilevskaya et al., 2006]. Laurenza and Storini [2005] found that the majority of SEPs (84%) occur when the QBO power of the photospheric magnetic field, computed with the wavelet technique, is significant. Their results suggest the emergence of QBO activity pulses with a possible role in SEP generation [see also Bazilevskaya et al., 2006]. However, to our knowledge, no attempt has been done to reveal periodicities in the proton flux with a mathematical technique able to decompose the data series into the time-frequency space. Here we investigate this issue, searching for periodic or quasiperiodic variations of the proton flux measured by the IMP 8 Charged Particle Measurement Experiment (CPME) in two energy windows ( MeV and MeV) on time scales ranging from a few (>6) Bartels rotations to the 11 year duration of the Schwabe cycle. 2. Data Set Used and Method of Analysis [11] This study is based on the data collected by the CPME, aboard Interplanetary Monitoring Platform 8 (IMP 8) orbiting at 35 Earth radii in the period from 1974 to The CPME detects protons in ten differential channels, P1 P11 (channel P6 is missing), covering the energy range from 0.29 MeV to 440 MeV [Armstrong, 1976]. An experiment malfunction occurred in However, the channels P2 ( MeV) and P11 ( MeV) were not affected by this failure, as discussed by Simunac and Armstrong [2004]. Thus we will use only data from these channels, which, on the other hand, give the basic information on interplanetary protons, being placed, respectively, in the low and high portions of the measured energy range. [12] Data have been taken in the form of hourly averages from the Web site of the Johns Hopkins University: sd- Most of the spurious signals, such as those occurring during the spacecraft crossings of the magnetosphere, were already removed Figure 3. Same as Figure 2 using the DOG function as mother wavelet (see the text for details). The arrow indicates a bump of enhanced power at about 2.5 years. 3of10

4 Figure 4. P11. Same as Figure 2 for the proton flux in channel by the investigators. Nevertheless, several spikes were still present, whose instrumental origin was revealed by their short duration (<1 h). After removing these spikes, we averaged data over each Bartels Rotation (BR), obtaining, in both channels, a continuous coverage from BR 1921 to BR 2291 (i.e., from 14 January 1974 to 17 June 2001). [13] We searched for periodicities in the above described data set by using the wavelet transform (WT) [e.g., Daubechies, 1990; Torrence and Compo, 1998]. This technique offers an important advantage with respect to the Fourier transform because it allows localization in time of possible periodicities which are not present continuously in the data set. In fact, it is able to determine both the dominant variability modes and how those modes vary in time, by decomposing a time series into the time-frequency space. [14] A general time series can possess a variety of frequency regimes that may be localized in relatively short time intervals or may span a large portion of the data record. The event occurrence is represented by a set of local parameters characterizing its frequency, intensity, timing and duration. The time-integrated characteristics of these localized signals provide the global information which describes the temporal mean states over some averaging period. Two completely different time series with different local information may result in very similar mean states. Hence, it is important to recognize that it is the totality of both the local and global information that constitutes the true signal. A WT uses base functions (wavelets) that can be stretched and translated in both frequency and time. The windows are adaptive to the entire time-frequency domain, known as the wavelet domain, which narrows while focusing on high-frequency signal and widens while searching the low-frequency background. [15] Mathematically a WT decomposes a signal in terms of some elementary functions called daughter wavelets or, simply, wavelets derived from a mother wavelet, by scaling and translation. The continuous wavelet transform of a discrete data sequence x n, with equal sampling time dt and n =0... N 1, is defined as the convolution of x n with a scaled and translated version of the mother wavelet Y: W n s ðþ¼ XN 1 n 0 ¼0 n x n 0Y 0 ð nþdt * ; ð1þ s where the asterisk indicates the complex conjugate. As seen in equation (1), the transformed signal is a function of two variables: s is the scale parameter and n is the localized time index. Changing the value of s has the effect of dilating (s >1) or contracting (s < 1) the function Y(t). To approximate the continuous wavelet transform, the convolution (1) should be done N times for each scale, where N is the number of points in the time series [Kaiser, 1997]. The algorithm used is described by Torrence and Compo [1998]. [16] The wavelet power spectrum (WPS) is defined as jw n (s)j 2. If a vertical slice through a wavelet plot (at a fixed time) is a measure of the local spectrum, then the timeaveraged wavelet spectrum over all the local wavelet spectra, gives the global wavelet power spectrum (GWPS): W 2 s ðþ¼ 1 N X N 1 n¼0 jw n ðþ s j 2 : ð2þ We assumed two different mother functions, the Morlet (plane wave modified by a Gaussian envelope) and the derivative of a Gaussian (DOG) (with m = 2, the so-called Mexican Hat) ones, whose performances are complementary: in fact, the first supplies a better frequency resolution, while the second allows a better localization of the different frequencies in time. We will compute the WPS and the GWPS in the whole time interval considered, by setting the Morlet wavelet nondimensional frequency (w 0 = 6) and Figure 5. Same as Figure 4 using the DOG function as mother wavelet (see the text for details). Table 1. Results of the Wavelet Analysis for the Proton Flux in Channels P2 ( MeV) and P11 ( MeV) for a P2 IMP 8 Periodicity Data (years) P11 IMP 8 Periodicity Data (years) Morlet DOG Morlet DOG a For both channels, periodicities in bold characters correspond to peaks in the GWPS above the global significance level. Left and right uncertainties were computed as described in section 2. 4of10

5 Figure 6. (a) The theoretical test function F(t) (obtained by summing an 11-year sinusoid with three spikes spaced 2 years from each other) versus time. (b) The local WPS versus time and period for the test function F(t). Thick black contours enclose regions of greater than 95% confidence, assuming a white noise background. The black dashed line indicates the cone of influence, where edge effects become important. (c) The GWPS versus period for the test function F(t). The blue dashed line indicates the global significance level. (d) and (g) Same as Figure 6a for the test functions G(t) and H(t), obtained by applying to F(t) two different upper cutoff (300 and 30, respectively). (e) and (h) Same as Figure 6b, for the test functions G(t) and H(t), respectively. (f) and (i) as Figure 6c, for the test functions G(t) and H(t), respectively. the frequency resolution (d j = 0.125). We chose the scales as fractional powers of 2: s j ¼ s 0 2 jdj for j ¼ 0; 1;...; J; ð3þ J ¼ d 1 j log 2 ðndt=s 0 Þ; ð4þ where s 0 is the smallest resolvable scale and J determines the largest scale. Considering that the set of scales used in the analysis is nonlinear, the uncertainty associated with each scale is asymmetric. The left and right uncertainties (Ds j + =(s j+1 s j )/2, Ds j =(s j s j 1 )/2) are derived from equation (3). As the equivalent Fourier period is proportional to the scale parameter [see Meyers et al., 1993], the uncertainties on period determination are asymmetric as well. [17] Finally, the significance (95%) of the peaks in the power spectra was evaluated against a white noise background, as in the work by Torrence and Compo [1998]. 3. General Features of the Data [18] Figure 1 shows the time history of the proton fluxes in channels P2 (Figure 1b) and P11 (Figure 1c), along with the total sunspot area (Figure 1a). From Figure 1 we notice 5of10

6 energy channels during the maxima of cycles 21, 22, and 23. Figure 7. (top) Time history of the proton flux in channel P2, after applying an upper cutoff of 1500 pfu. (bottom) Same as Figure 2 (WPS and GWPS, Morlet) but using the 1500 pfu cutoff. that the trends of the proton flux (F) in the two channels are different: in channel P11, quiet periods, when F is of the order of 10 3 pfu (1 pfu = 1 particle cm 2 sr 1 s 1 MeV 1 ), alternate with active periods, when F increases by even more than a factor of 10; in channel P2, F fluctuates by several orders of magnitude, but quiet periods are relatively shorter. [19] The above features are consistent with the fact that the Sun emits very frequently protons with energies lower than 1 MeV, but only seldom (in connection with flares or shocks driven by coronal mass ejections (CMEs)) those with energies of hundreds of MeV. The quiet level, observed in channel P11, should be identified with the interplanetary particle background, to which largely contribute the galactic cosmic rays (GCRs). On the other hand, the GCR contribution is nearly negligible at energies lower than 1 MeV, so that the fluxes observed in channel P2 are, at any time, primarily of solar origin (hereafter referred to as solar cosmic rays, SCRs). On the contrary, in channel P11 the SCRs become dominant only in the active periods. [20] The long-term variations of the proton fluxes, apparent in Figure 1, depend on the different behavior of the two populations of cosmic rays (GCRs and SCRs). In both channels, the basic modulation occurs on the Schwabe period. In channel P2, the modulation is in phase with the sunspot cycle, as the observed protons are produced in solar events which occur more frequently in periods of high activity. On the other hand, in channel P11 one observes opposite trends during quiet and active periods, as GCR and SCR are affected in opposite ways by the solar activity phenomena: in fact, when the solar activity is high, the SCR fluxes tend to increase (because flares and CME/shocks are more frequent), while the GCR fluxes tend to decrease (because the interplanetary perturbations more effectively shield the heliosphere from the incoming charged particles). [21] We also emphasize the evidence of the Gnevyshev Gap structure in the proton time behavior for both the 4. Results From the Wavelet Analyses [22] Figures 2 and 3 show the WPS and GWPS of the fluxes observed in channel P2, computed by using as mother function the Morlet and the DOG, respectively. Figures 4 and 5 are similar plots for channel P11. As expected (see section 2), the Morlet GWPS supplies a better frequency resolution, while the DOG WPS allows a better localization of the observed periodicities in time. Inspection of Figures 2 to 5 reveals the periods listed in Table 1. We note that, in the GWPS (solid blue lines in Figures 4 (right) and 5 (right)) of both channels, peaks are present at 9.8 years (Morlet) and 10.2 years (DOG). However, in the Morlet spectra the 9.8 year period for channel P2 is under the cone of influence (dashed thick line in Figure 2 (left)), while for channel P11 the corresponding peak falls below the level of global significance (dashed blue line Figure 4 (right)). The 9.8 and 10.2 year periods coincide within the errors and are also in close agreement with the duration of the sunspot cycles 21 and 22 (10.25 and 9.70 years, respectively). [23] Not surprisingly, the Schwabe modulation is better observed in channel P2, as in channel P11 the opposite trends of the SCR and GCR fluxes overlap each other. [24] In the Morlet GWPS of the channel P2, two other peaks are detected at 3.8 and 2.2 years, both above the global significance level. The 2.2 year period is also consistent with the bump at 2.5 year period found in the DOG GWPS (indicated by the arrow in Figure 3). Inspecting the Morlet WPS, one notes that both periods are locally significant, being their power enclosed in the black thick contours (i.e., those representing the 95% confidence level): the 3.8 year period is localized from 1975 to 1985, and the 2.2 year period is localized from 1988 to A minor, but locally (around 1990) significant, peak at 0.9 year is also present in the WPS, even though it is below the global significance level. [25] In the Morlet GWPS of the channel P11, several peaks are present (at 5.8, 2.7, 1.7, and 0.8 years), but only that at 1.7 years is above the global significance level. All these periods, on the other hand, become significant in time intervals centered about 1990, as seen in the WPS. In particular, the 1.7 year period (which coincides within the errors with the significant peak at 1.8 years in the DOG GWPS) is localized from 1986 to1992. [26] It should be pointed out that a peak in the WPS, even being locally or globally significant, can be fictitious [Laurenza et al., 2008]. In fact, the wavelet analysis is subject to errors when applied to discontinuous data, such as the proton fluxes considered here which fluctuate from one Bartels rotation to the other by even more than 1 order of magnitude (see Figure 1). Thus, we now turn to investigate this issue by applying the wavelet analysis to suitable test functions. 5. Test of the Wavelet Analysis Results With Theoretical Functions [27] To evaluate the reliability of the wavelet analysis performed in section 4, we applied this technique to a test 6of10

7 Figure 8. (a) (top) Time history of the proton flux in channel P11, after applying an upper cutoff of 10 2 pfu. (bottom) Same as Figure 2 but using the 10 2 pfu cutoff. (b) Same as Figure 8a but using a cutoff of pfu. function F(t), plotted in Figure 6a, which resembles the basic features of our experimental data. F(t) was obtained by superimposing on a sinusoid (of 11 year period and amplitude of 1) three spikes (spaced by 2 years from each other and having amplitudes of 300, 3000, and 300, respectively). The results of the analysis (assuming the Morlet as mother function) are shown in Figures 6b and 6c. [28] In the GWPS (solid blue line in Figure 6c), a single peak at 11 years stands out, above the global significance level. In addition, three more periods (2, 1, and 0.7 years) are present and appear to be locally significant in the WPS, their power being enclosed in the thick black contours of Figure 6b); the two shortest ones are clearly artifacts, produced by the strong discontinuities occurring in F(t) at the times of the spikes. We then introduced an upper cutoff to the values of F(t), reducing the amplitudes by 1 (Figure 6d) or 2 orders of magnitude (Figure 6g). As seen in Figures 6e, 6f, 6h, and 6i, the fictitious periodicities tend to disappear with decreasing the cutoff, whereas the actual 2 year oscillation is more evident and becomes globally significant. In particular, for the higher cutoff (300) the 2 year oscillation becomes significant both locally (Figure 6e) and globally (Figure 6f) and is clearly disentangled in the WPS from the spurious periods. Moreover, when further decreasing the upper cutoff (30), the power associated with the spurious periods falls also below the local significance level in the WPS. We then conclude that the use of an upper cutoff to high discontinuities helps to discard eventual spurious frequencies, although not compromising the detection of real periodicities or local oscillations (except, obviously, those strictly related to values exceeding the cutoff). 6. Wavelet Analysis With an Upper Cutoff in the Observed Proton Fluxes [29] The tests carried out in section 5 suggest that the true periodicities present in our data set may be disentangled from possible spurious harmonics, by setting a suitable 7of10

8 Table 2. Same as Table 1 by Using Only the Morlet Mother Function and the Upper Cutoff Approach in the Data Series for a P2 IMP 8 Periodicity Data (years) a See the text for details. P11 IMP 8 Periodicity Data (years) upper cutoff to the observed fluxes. Figures 7 and 8 and Table 2 summarize the obtained results. [30] For channel P2, an upper cutoff of 1500 pfu was adopted (Figure 7). Two periodicities (3.8 and 2.2 years) discussed in section 4 are still present, in both WPS and GWPS. According to the analysis performed in section 5 the power of spurious periods is expected to fall below the significance level. We thus conclude that both the above periods are most probably real. Concerning other periods, we note that 0.9 and 0.5 year are significant for short time intervals, even though the corresponding peaks fall below the global significance level. [31] Concerning channel P11, we assumed two different cutoff: 10 2 pfu (Figure 8a) and pfu (Figure 8b). The new results differ substantially from those reported in section 4. In fact, from Figure 8b (where the lowest cutoff is used), the 5.8 and 2.7 year periods are revealed to be artifacts, as they disappear as peaks in the GWPS. The 1.7 Figure 10. Power, normalized to the 95% significance level, versus time for different periodicities, as reported in legends. (top) P2 channel. (bottom) P11 channel. Upper cutoff (1500 pfu for P2 and pfu for P11) were applied to the proton fluxes. and 0.8 year periods are confirmed in the WPS, even though they barely reach the global significance level (Figures 8a and 8b). On the other hand, a 3.8 year periodicity stands out both in the WPS and the GWPS. Inspection of Figure 9, where GWPS with and without cutoff are compared for both energy channels, strengthens previous conclusions. [32] The time intervals in which the different periodicities are observed are better seen in Figure 10, where the wavelet power corresponding to the most relevant periods (obtained by using the cutoff approach) are plotted as a function of time for the channels P2 (Figure 10, top) and P11 (Figure 10, bottom). Figure 9. (top) The GWPS in channel P2 with the 1500 pfu cutoff (dashed thick line) and without cutoff (solid thick line) versus period. The global significance levels are represented by the thin dashed and solid lines, respectively. (bottom) Same as Figure 9 (top) for the flux in channel P11 (assuming a pfu cutoff). 7. Discussion [33] As we have already pointed out, the basic modulation of the proton fluxes, in both the energy channels considered, occurs on the Schwabe period. The variations with the sunspot cycle are present even in channel P11 where, during quiet periods, the GCRs (whose flux is anticorrelated with the solar activity) become dominant over the SCRs. On the other hand, we found that the proton fluxes also vary on the following time scales, shorter than the Schwabe period: 8of10

9 [34] 1. The period T = 3.8 years has been singled out in both energy channels and approximately in the same time interval ( ), corresponding to the active phases of the solar cycle 21. As mentioned in section 1, a modulation on similar time scales (from 3 to 4 years) was identified in different solar indices. In particular, Laurenza [2006] has shown the solar origin of this mode of variability which might arise from an interaction between the variations of the toroidal and poloidal components of the solar magnetic field (occurring on time scales of 2 and 3 years, respectively) [Laurenza, 2006]. She also found that the wavelet power spectrum of the photospheric magnetic field exhibits a 3.7 year periodicity at low latitudes only in solar cycle 21 [Laurenza, 2006]. Present results are in good agreement with such findings. [35] 2. For the periods T = 1.7 years and T = 2.2 years, in both the energy channels, the proton fluxes undergo QBOs with a period of about 2.2 and 1.7 years for P2 and P11, respectively. This modulation is better observed from 1988 to 1993, i.e., around the sunspot maximum of the cycle 22. First, we stress that the lack of the QBOs in the proton fluxes near the sunspot minima is consistent with results obtained studying also other phenomena of solar activity (see section 1). Moreover, the year period for the channel of higher energy (P11) coincides with that found in energetic solar electron fluences by Chowdhury and Ray [2006] and in the solar toroidal field variations ( [Laurenza, 2006; Laurenza and Storini, 2005]). The above findings suggest the QBOs to be the most prevalent quasiperiodicity in solar activity phenomena. [36] 3. For the period T = 0.8 to 0.9 years, variations on a time scale of 1 year ( year period) are not significant in the GWPS. Nevertheless, they are locally detected in both channels during somewhat different time intervals. The best evidence is obtained in cycle 22 ( in channel P2; and in channel P11, see Figure 10). A detailed study is needed to investigate the possible link with other quasiperiodic variations on similar time scales found in different solar and interplanetary parameters (see section 1). [37] Finally, we stress that the lack in our data of a significant 5 6 year modulation supports the view that this periodicity, observed in the sunspot number, could be an artifact produced by the asymmetric shape of the solar cycle [Mursula et al., 1997]. Moreover, the 150 day modulation can be only marginally investigated with our data set, due to the 27 day averaging procedure. Nevertheless, inspection of Figure 9 shows minor peaks at year in the GWPS. 8. Conclusions [38] The performed analysis has shown that the solar proton fluxes, in the energy windows MeV and MeV, are modulated (see Figures 2 5) on time scales similar to periodicities detected from the photospheric field and other parameters characterizing solar activity phenomena (see section 1). As expected, the basic modulation of both proton fluxes (IMP 8 CPME-P2 and IMP 8 CPME-P11) has the Schwabe period, which, in the time interval considered, is 10 years. Moreover, the wavelet technique used in this work demonstrates the following: [39] 1. There are other significant variations on time scales of 3.8, (QBOs), and years. We stress that the periods obtained from the two proton channels are nearly identical (see Table 2). [40] 2. The 3.8 year modulation (see Figure 10) occurs from 1976 to 1986 for P2 and from 1979 to 1989 for P11, while the QBOs are detected during the active phases of cycle 22 ( in P2 and in P11). [41] 3. 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