Galactic cosmic ray intensities (GCRs) observed by five neutron monitors (NMs) have been used to study cosmic ray modulations between 1971 and 2007. The influence of interplanetary magnetic polarity (IMF) states has been studied for the A < 0 and A > 0 epochs. A comparison of the spectra for both positive IMF polarities indicated different solar origins. The spectra have different power amplitudes and most peaks of different locations. In addition, the differences in the cosmic ray modulations, conditions for solar activity minima and maxima periods are probably associated with the influence of drift effects. The observed differences are related to the 22-year cycle in heliospheric modulations of cosmic rays, leading to the different shapes of CR maxima and the hysteresis effect. Accordingly, drift effects dependent on the polarity of the global solar magnetic field may play a significant role in the observed differences between maxima and minima periods. The drift mechanism is enhanced during periods of low to moderate SA, i.e., around solar cycle minima, during negative polarity periods, when A < 0.
Journal of Advanced Research (2011) 2, 137–147 Cairo University Journal of Advanced Research ORIGINAL ARTICLE Mid-term periodicities of cosmic ray intensities Mohamed A El-Borie a b a,* , Naglaa A Aly b, Amr El-Taher b Physics Department, Faculty of Science, Alexandria University, Moharam Bak, P.O 21511, Egypt Physics and Chemistry Department, Faculty of Education, Alexandria University, Al-Shatby, Egypt Received April 2010; revised 25 August 2010; accepted 26 August 2010 Available online 26 November 2010 KEYWORDS Astroparticle-nuclear physics; Galactic cosmic rays; Solar activity; Ultra low-frequency power spectra Abstract Galactic cosmic ray intensities (GCRs) observed by five neutron monitors (NMs) have been used to study cosmic ray modulations between 1971 and 2007 The influence of interplanetary magnetic polarity (IMF) states has been studied for the A < and A > epochs A comparison of the spectra for both positive IMF polarities indicated different solar origins The spectra have different power amplitudes and most peaks of different locations In addition, the differences in the cosmic ray modulations, conditions for solar activity minima and maxima periods are probably associated with the influence of drift effects The observed differences are related to the 22-year cycle in heliospheric modulations of cosmic rays, leading to the different shapes of CR maxima and the hysteresis effect Accordingly, drift effects dependent on the polarity of the global solar magnetic field may play a significant role in the observed differences between maxima and minima periods The drift mechanism is enhanced during periods of low to moderate SA, i.e., around solar cycle minima, during negative polarity periods, when A < ª 2010 Cairo University Production and hosting by Elsevier B.V All rights reserved Introduction Study of the modulation of galactic cosmic rays (GCRs) is important because of its potential for revealing the subtle fea* Corresponding author Tel.: +20 16 5042670; fax: +203 391 1794 E-mail address: elborie@yahoo.com (M.A El-Borie) 2090-1232 ª 2010 Cairo University Production and hosting by Elsevier B.V All rights reserved Peer review under responsibility of Cairo University doi:10.1016/j.jare.2010.10.002 Production and hosting by Elsevier tures of energetic charged particle transport in the tangled fields that permeate the heliosphere; as a means of remotely probing the heliosphere; and for learning about the physics of the processes operating on the Sun The charged particles in the solar wind drag the Sun’s magnetic fields with them While one end of the interplanetary magnetic field (IMF) remains firmly rooted in the photosphere and below, the outer end is extended and stretched out by radial expansion of the solar wind The Sun’s rotation bends this radial pattern into an interplanetary spiral shape within the plane of the Sun’s equator The shape of the IMF depends on the Sun’s 11-year of magnetic activity Near activity minimum, the large-scale global magnetism of the Sun can be described as a simple magnet with north and south poles where large, unipolar coronal holes are located The northern pole is of one magnetic polarity or direction and the southern pole is of opposite polarity The negative and positive filed lines meet near the solar equator, where a magnetically 138 M.A El-Borie et al neutral sheet is dragged out into space by the out-flowing wind The dipole is stretched out at its middle, resulting in two polar monopoles whose magnetic orientation is preserved throughout most of an 11-year activity cycle The polarity of the Sun’s magnetic field reverses during solar activity maximum (i.e., the Sun is directed away during the next cycle, returning to the original direction every 22 yr) The frequency distribution of the cosmic ray intensity (CRI) oscillations in the low frequency range has been examined [1–8] The power spectrum displayed significant peaks of varying amplitude within the solar rotation period (and its harmonics) that changed inversely with particle rigidities The fluctuations of large period (6–11 months) appeared in CRs [5,6,9,10] The comparison of CR power spectra during four successive solar activity minima has indicated that, at low rigidity particles, the spectrum differences are significantly large between the A > and the A < epochs The spectra for even solar maximum years are higher and much harder than those of the odd years The evolution of cosmic ray intensity is different for odd and even cycles, with different time and shape [11] Periodicities of several indices were studied [12], displaying periods of wavelengths of 1.3 yr (15.6 months) and 1.7 yr (20.4 months) Short and intermediate term periodicities of galactic cosmic rays intensity recorded by the Oulu neutron monitor station during the period 1996–2008 were examined [13] by the wavelet technique The study exhibited 14.3 (a) 28.3 13.7 33.3 57.7 (b) 0.8 15.7 46 0.6 23.7 0.4 0.4 25 10.6 0.2 0.2 82 28.3 Kiel 0.8 (c) 0.6 63 15.8 13.7 0.8 11 57.7 9.4 0.6 33.3 25 46 0.4 (d) 19.4 29.5 23.7 0.4 8.2 0.2 0.2 Rome 82 0.8 0.6 28.3 14.3 (e) 29.5 (f) 13.7 46 0.6 25 0.4 23.8 0.4 11 9.3 8.8 0.2 0.01 0.02 0.03 Frequency c / d Fig 1 0.8 33.3 57.7 0.04 0.05 0.05 Normalized PSD 30 0.07 0.09 0.11 0.13 Frequency c / d PSD of: (a & b) Cal, (c & d) Kiel and (e & f) Rome during A1 > (71–80) Normalized PSD Normalized PSD Cal 69.4 0.6 Normalized PSD Daily averages observed by NMs at five locations were recorded, as follows: Calgary (Ro = 1.09 GV; 1971–2007), Kiel 82 0.8 Data and analysis 0.2 0.15 Normalized PSD Normalized PSD a number of short and intermediate term periodicities present between 16 and 500 days in different phases of this cycle Previous study of the daily means of the CRI for four NMs, including Cl (NM), obtained 1.7 yr, 1.3 yr and 150 d peaks It was deduced that the 1.7 yr peak contributed strongly in solar cycle 21, and that the 1.3 yr peak was present in the decreasing phase of cycles 20 and 22 [14] Mavromichalaki et al [15] studied the power spectral density of CRI for the period 1953–1996 for the Cl NM, using three different techniques They found that several peaks occurred around 1.9, 1.7, 1, 0.75, 0.7, 0.6 and 0.4 yr The 1.9 yr ($2 yr variation) was identified along with the annual and other variations in the neutron monitor data a long time ago The aim of this work is to present the power spectra results for the daily averages of the nucleonic intensity recorded by five NMs, which have different cutoff rigidities, over a period up to three solar activity cycles (SACs) in the period 1971– 2007 We investigate the observed differences in the CR power spectra related to different rigidities particles, for A > and A < IMF polarity states, as well as for solar minimum and maximum activity years Mid-term periodicities of CRIs 139 27.7 25.6 13.7 0.8 70.6 0.6 95 0.4 20.7 35 10.8 0.4 10 0.2 0.2 30 Kiel Normalized PSD 19.2 16 (b) 17 27.7 54.6 0.8 16 25.6 (c) 19.2 (d) 14.7 0.8 13.7 0.6 0.6 95 17.2 11 38.3 0.4 9.2 0.4 23.7 69.5 6.8 20.7 0.2 0.2 Rome Normalized PSD 14.7 30 (e) 14.7 19.2 13.7 (f) 0.8 0.8 55.4 16 27.7 0.6 0.6 25.6 12.8 0.4 95 69.4 0.4 35 0.2 0.2 0 0.01 0.02 0.03 Frequency c / d Fig 0.04 0.05 0.05 Normalized PSD (a) 54.6 0.6 Propagation and acceleration of GCRs in the heliosphere is governed by four major mechanisms: diffusion, convection, adiabatic cooling, and gradient and curvature drifts [17] A wavy neutral current sheet separates the heliosphere into two regions of opposite magnetic sense During epochs of positive polarity (e.g., 1971–1979 and 1991–1998), the interplanetary magnetic field (IMF) is directed away from the Sun (A > 0) above the current sheet and toward the Sun south of the current sheet For negative polarity epochs (e.g., 1981–1989), the IMF direction is reversed (A < 0) Positive polarity (A > 0) periods are characterized by galactic cosmic rays drifting inward from the pole and exiting along the heliomagnetic equator and the neutral sheet Conversely when A < the drift is inward along the helioequator, neutral sheet and out over the poles It is clear from the CR models that there would be a radial gradient in the CR density and that the gradient would vary with the solar cycles The A < polarity would have a large radial gradient of particles It was also apparent that CR peaks at solar minimum alternated from sharply peaked in the A < polarity state to flat topped in the A > state [18,19] 29.8 Cal 0.8 Solar polarity dependence 0.07 Normalized PSD Normalized PSD Observations and discussion 0.09 0.11 0.13 Frequency c / d PSD of: (a & b) Cal, (c & d) Kiel and (e & f) Rome during A2 > (92–00) 0.15 Normalized PSD (Ro = 2.32 GV; 1971–2007), Climax (Ro = 2.97 GV; 1971– 2006), Rome (Ro = 6.32 GV; 1971–2007) and Huancayo/ Haleakala (Ro = 13.3 GV; 1971–2006) Epochs of positive A > and negative A < IMF polarity states were also determined (epochs of A > are 7/1971–10/1980 and 2/1992–11/ 2000; while epochs of A < are 2/1981–2/1991 and 5/2002– 12/2007) Significant gaps in data have been considered [16] Days of ground-level enhancements (GLEs) caused by solar flares or/and by Forbush decreases (FDs) P 4% have been eliminated from the data Linear trends were performed to compensate for instrumental variations A series of power spectral density (PSD) have been performed and the results were smoothed using the Hanning window function This is necessary since most of the disturbed features completely disappear, while the significant peaks are clearly defined Nevertheless, the particular window chosen does not shift the positions of the spectral peaks Next, each spectrum is independently normalized to the largest peak in the complete spectrum This restriction was chosen in order to avoid spurious strengths often associated with peaks near the start and end of the data set This normalization does not introduce any errors into our identification of the peaks because it changes only the relative amplitude and not the position of the peak spectrum 140 M.A El-Borie et al 19.3 (a) Cal 0.8 13.9 (b) 0.8 17.2 85.3 0.6 61 12.8 54.6 45 0.6 10 27.7 38 0.4 8.4 0.4 7.3 0.2 0.2 Normalized PSD 74.5 Kiel (d) (c) 0.6 0.8 0.6 16.8 13.8 28.8 43.6 56 19.2 0.8 0.4 31.3 10 0.4 22 0.2 0.2 Normalized PSD 0.8 70.6 Rome 19.3 28.8 13.7 (f) (e) 78.8 54 27.7 43 12.6 21.8 10 10.8 9.2 7.3 0.2 0.01 0.8 0.6 16.6 0.6 0.4 0.4 0.2 0.02 0.03 Frequency c / d Fig 0.04 0.05 0.05 Normalized PSD 74.5 (1) The A1 > epoch (1971–1980) displayed remarkable common peaks at wavelengths 1.6, 1.25, $0.37, 0.22 yr (80 d), 57.7 d, 46 d, 33.3 d and 25–28 d (and its harmonics) Other peaks (1 and 0.8 yr) appeared for low particle energy only On the other hand, for the A2 > epoch (1992–2000), significant peaks are confirmed at 1.9 yr, 1.25 yr, 0.7 yr, 0.37 yr, 0.15 yr (55 d), 30 d and 27 d (and its harmonics) A comparison of the spectra for both positive IMF polarities suggests different solar origins The spectra have different power amplitudes and most peaks of different locations (expect 1.25 yr, 0.37 yr, and the effect of solar rotation cycle) (2) The A1 < epoch (1981–1991) reflected high periodicity, which was observed at 5.6 yr, 1.6 yr, 0.8 yr, 0.6 yr, 75–79 d, 43–45 d and 27 d (and its harmonics) On the other hand, the A2 < epoch (2002–2007) indicated different peaks at 1.9 yr, 0.94 yr, 0.56 yr, 71 d, 60 d, 51 d and 27 d (and its harmonics) 0.07 Normalized PSD Normalized PSD 0.22 yr, while the positive solar polarity period A2 > (Fig 5) has common periodicities of 1.9, 0.7, 0.36 and 0.15 yr In contrast, negative solar polarity A1 < (not shown) displayed common periodicities of 5.6, 1.6–1.87 and 0.6–0.8 yr, while negative solar polarity A2 < (Fig 6) has common periodicities at 1.9, 0.93–0.94, 0.56, 0.35–0.37 and 0.16–0.2 yr The comparison of PSDs (Figs 1–6) for the A > and A < epochs shows that: 0.09 0.11 0.13 Frequency c / d PSD of: (a & b) Cal, (c & d) Kiel and (e & f) Rome during A1 < (81–91) 0.15 Normalized PSD A series of PSD have been performed on daily averages of CRIs for periods of different IMF polarity states: A1 > (1971–1980), A1 < (1981–1991), A2 > (1992–2000), and A2 < (2002–2007) The cosmic ray intensity datasets were then separated into different epochs of polarity states A > and A 0, A2 > 0, A1 < and A2 < 0, respectively The first positive solar polarity period A1 > (Fig 1) has displayed common periodicities of 82, 57.7, 46, 33.3, 29.5–30, 28.3, 25, 23.7, 14.3–15.8, 13.7, 10.6–11, 9–9.4 and days, while the second positive solar polarity period A2 > (Fig 2) has common periodicities at 95, 69–70, 54.6–55.4, 35–38, 30, 27.7, 25, 20.7, 19.2, 16, 14.7, 13.7, 10.8–11 and 9.2–10 days Conversely, the first negative solar polarity period A1 < (Fig 3) has shown common periodicities at 70.6, 54–56, 43– 45, 27.7–28.8, 19.3, 16.6–17.2, 13.7–13.9, 10 and 7.3 days, while the second period A2 < (Fig 4) has common periodicities at 89–93, 70.6, 60–60.3, 48.8–51.2, 31, 27–27.7, 22.3, 18– 19, 17, 14.3–14.3, 13.5, 11.3–12.4 10, 9, 7.8 and days More detail is presented in Figs and 6, which display, for the whole considered period, the PSD of CRI observed at Cal, Kiel and Rome during A2 > and A2 < yr, respectively Positive solar polarity period A1 > (not shown) has common periodicities of 2.24, 1.6, 1.25, 1.0–1.12, 0.6–0.75, 0.4 and Mid-term periodicities of CRIs Normalized PSD 17 (b) 0.8 13.5 19 70.6 14.4 0.6 0.6 51.2 12 0.4 27 7.8 9.8 22.3 31 0.2 0.2 60.3 Kiel 17 (c) (d) 0.8 0.8 18 70.6 0.6 14.3 0.6 89 48.8 0.4 27.3 11.3 22.3 31 10 0.4 7.8 0.2 0.2 17 70.6 (e) Rome 14.3 13.5 (f) 0.8 60.3 0.8 51.2 0.6 0.4 27.7 82 0.6 12.4 7.8 22.3 31 0.4 11.6 10 0.4 7.4 0.2 0.2 0.01 0.02 0.03 0.04 0.05 0.05 Frequency c / d Fig Normalized PSD (a) 0.8 93 Normalized PSD Cal Normalized PSD 60 0.07 0.09 0.11 0.13 Normalized PSD Normalized PSD 141 0.15 Frequency c / d PSD of: (a & b) Cal, (c & d) Kiel and (e & f) Rome during A2 < (02–07) Of particular importance is the peak at around 5.6 yr, which may be correlated with the 11-year cycle Significant fluctuations presented at around 5.5 yr were also reported in studies of other solar phenomena [10] Although these peaks may be harmonics of the fundamental sunspot cycle, they deserve attention since their statistical significance and their correlation with other solar and interplanetary phenomena provide means to investigate the physical processes by which the sun influences the heliosphere The existence of the 5.5-year periodicity in sunspot numbers shows that although it is a real periodicity, it is indeed due to the enhanced power of the second harmonic which arises from the asymmetric form of the solar cycle [20] The 5.6 yr variation is probably due to different paths of ion particles in the heliosphere [10,21,22] The observed differences in the cosmic ray spectrum conditions for A > and A < periods are probably associated with the influence of drift effects These results imply that there is a significant difference in the solar modulation of CR during positive and negative polarity magnetic field cycles The fact that CR series obtained at different rigidities show very similar behavior implies that the considered periods reflect a persistent feature of the modulation in the energy range up to several tens of GeV [19] Accordingly, drift effects dependent on the polarity of the global solar magnetic field may play a significant role for the observed differences between positive and negative IMF polarity Recently, Kudela et al [23] studied the PSD of CRI by using the daily averages of CRI at three selected stations: a temporal evolution of the selected quasi-periodicities, especially those of $1.7 yr, $150 days and $26–32 days respectively, was found A single power-law index approximation is appropriate for the whole frequency interval A better approximation is a narrow interval of the frequencies The power spectral density P (f) a fÀn, where n is the power law index, was essentially used in describing the irregularity of the CR time variation At the selected frequencies (f < · 10À2 dÀ1) the spectral density is high and shows significant variations with frequency In order to have a better look at the structure of the spectral density, we have designed a digital filter feedback method to eliminate the intense or/and persistent components The resultant power spectra (after passing through the digital filter) have been fitted with a straight line expressed by a single power law Table lists the n-values of the best-fit power law (fÀn) for the PSD throughout for positive and negative IMF polarities The comparison between positive A > and negative A < solar polarity epochs for all stations shows that negative 142 M.A El-Borie et al 100 1.9 yr (a) Cal 90 80 70 1.25 yr 60 0.7 yr 50 40 0.37 yr 30 d 30 0.15 yr 13.6 d 20 10 1.9 yr Kiel Kiel (b) 70 60 0.56 yr 50 0.94 yr 40 0.16 yr 0.37 yr 30 27.3 d 20 1.9 yr 90 80 70 0.7 yr 60 50 40 0.36 yr 30 27.7 d 0.15 yr 13.6 d 20 10 100 1.9 yr Rome 90 80 80 70 60 0.56 yr 0.16 yr 50 0.94 yr 40 0.37 yr 30 26.3 d 20 10 100 (c) 1.9 yr Rome 90 70 60 Relative amplitude % Relative amplitude % (a) 80 100 (b) Relative amplitude % Relative amplitude % 90 0.7 yr yr 50 40 30 30 d 0.15 yr 13.7 d 20 10 0.001 0.01 0.1 Frequency c / d (c) 80 70 60 0.93 yr 50 0.2 yr 0.56 yr 40 0.35 yr 30 27.7 d 20 10 0.001 0.01 0.1 Frequency c / d PSD of Cal, Kiel and Rome during A2 > (92–00) Fig polarity epoch A1 < (1981–1991) has a higher power index than those of the A1 > 0, A2 > 0, and A2 < periods PSD of cosmic rays has been calculated from hourly averaged counts observed by underground muon telescopes located at Mawson over the low-frequency range 2.7 · 10À7 to 1.4 · 10À4 Hz [24] The spectra are flatter and have lower power when the interplanetary magnetic field (IMF) is directed Table Cal 10 100 Fig 1.9 yr 90 Relative amplitude % Relative amplitude % 100 PSD of Cal, Kiel and Rome during A2 < (02–07) away from the Sun above the current sheet (A > 0) than when the IMF is directed toward the Sun above the current sheet (A < 0) The spectra imply that heliospheric magnetic turbulence may be more variable on time scales of several years than that previously suspected The n-values of the best-fit power law (fÀn) for positive and negative IMF polarities Period Cal (Ro = 1.09 GV) Kiel (Ro = 2.32 GV) Cl (Ro = 2.97 GV) Rome (Ro = 6.32 GV) Hu/Ha (Ro = 13.3 GV) A1 > (71–80) A1 < (81–91) A2 > (92–00) A2 < (02–07) m1 (75–76); A > m2 (85–86); A < m3 (94–95); A > M1 (79–80) M2 (89–90) M3 (00–01) 1.37 ± 0.03 1.78 ± 0.03 1.5 ± 0.03 1.22 ± 0.02 0.6 ± 0.02 1.45 ± 0.02 0.9 ± 0.016 0.84 ± 0.14 1.4 ± 0.02 0.88 ± 0.01 1.42 ± 0.02 1.65 ± 0.02 1.62 ± 0.03 1.16 ± 0.014 0.7 ± 0.013 1.4 ± 0.02 0.8 ± 0.01 0.77 ± 0.01 1.3 ± 0.01 0.84 ± 0.014 1.3 ± 0.03 1.88 ± 0.03 1.68 ± 0.03 1.36 ± 0.023 0.7 ± 0.01 1.52 ± 0.02 0.64 ± 0.01 0.83 ± 0.017 1.3 ± 0.02 1.2 ± 0.02 1.43 ± 0.02 1.67 ± 0.025 1.64 ± 0.022 1.34 ± 0.022 0.6 ± 0.02 1.24 ± 0.02 0.6 ± 0.013 0.23 ± 0.01 1.61 ± 0.02 0.87 ± 0.02 1.3 ± 0.02 1.7 ± 0.02 1.2 ± 0.03 1.27 ± 0.03 0.5 ± 0.02 1.2 ± 0.03 0.77 ± 0.02 0.43 ± 0.02 1.4 ± 0.04 0.7 ± 0.04 Mid-term periodicities of CRIs 143 Solar minima and maxima Solar minima Solar minimum is the period of least solar activity in the solar cycle of the Sun During this time, sunspot and solar flare activity diminishes, and often does not occur for days at a time The date of the minimum is described by a smoothed average over 12 months of sunspot activity, so identifying the date of the solar minimum usually can only happen six months after the minimum takes place At a solar minimum, there are fewer sunspots and solar flares subside Sometimes, days or weeks go by without a spot Periods of solar activity minima are determined as; m1 (1975–1976), m2 (1985–1986), and m3 (1994–1995) Figs 7–9 display the PSD of daily averages of galactic CRIs recorded by Kiel, Rome and Hu/Ha, during the three consecutive solar minimum periods m1, m2, and m3, respectively The actual frequency range is from 0.003 to 0.5 dÀ1 Most detectors presented well-defined peaks within the solar rotation period (27 d) and its first-two harmonics The plots indicated that 100 28.5 d Kiel (a) 146 d 80 70 68 d 60 Relative amplitude % Relative amplitude % 90 46 d 50 13.8 d 40 9d 30 7d 20 10 90 80 256 d Rome (b) 70 146 d 60 50 Relative amplitude % Relative amplitude % 100 28.5 d 103 d 40 46.5 d 68 d 30 13.8 d 20 10 9d 100 80 256 d Hu / Ha 146 d (c) 28.5 d Relative amplitude % 90 Relative amplitude % the amplitude (or the magnitude) of 27 d and 13.5 d fluctuations are greater during the A > epochs (Figs and 9) than for the A < state Previous works [19,25] have presented clear evidence for an increase in the size of the recurrent CR modulations by about 50% during the A > epoch compared with during the A < epoch The rigidity dependence of CRI modulations for the low solar activity periods (1975–1976, 1985–1986 and 1994–1995) was apparent The rate of CR variations was larger in magnitude during 1975–1976 than during 1985–1986 PSD for the period 1975–1976 (Fig 7) shows that there are some noticeable peaks at frequencies 45–250 d which may indicate an unstable variation The 146 d (0.4 yr) is a common periodicity for considered NMs Our results reflected the fluctuations 45 d, 66 d, 100 d and 256 d (0.7 yr) On the other hand, the period 1985–1986, displayed well defined peaks at 64 d, 79 d, 114 d (0.3 yr), and 170–200 d (0.45–0.55 yr) Thus, the observed CR maximum spectra P27 d is at different frequencies Sometimes this maximum occurs at 27 d or 256 d At other epochs (Fig 8) the time of high power is between 170 d and 205 d So, the different spectrum behaviors may be rigidity-dependent fluctuations The different CR power spectra at low energies during consecutive solar minimum periods are due to the gradient and curvature drifts of charged particles in the global magnetic field [21,26] The net CR modulations at low rigidities indicated that the amplitude of 70 60 102 d 60 d 50 47 d 40 13.7 d 9d 30 20 10 0.001 0.01 0.1 Frequency c / d Fig PSD of Kiel, Rome and Hu/Ha during minimum solar activity m1 (75–76) 100 90 80 70 60 50 40 30 20 10 100 90 80 170 d (a) 79 d 114 d 60.3 d 29 d 19 d 10 d 171 d 70 60 50 40 30 20 10 100 90 80 70 60 50 40 30 20 10 0.001 Kiel Rome (b) 79 d 114 d 64 d 29 d 19 d 10 d 205 d Hu / Ha (c) 114 d 79 d 64 d 18.3 d 0.01 0.1 Frequency c / d Fig PSD of Kiel, Rome and Hu/Ha during minimum solar activity m2 (85–86) 144 M.A El-Borie et al Relative amplitude % 100 205 d Kiel 90 80 70 (a) 102 d 60 27.7 d 79 d 50 40 38 d 13 d 30 20 A < solar minima epochs are significantly large The CR PSD is harder by a factor of two during the A < epoch (1985–1986) than during the A > epochs According to the change in the polarity of the IMF from the A > state to the A < epoch that occurred in 1979/1980, the intensity spectra shifted toward higher-energy particles Consequently, the intensities of high-energy particles are larger (and the intensities of low-energy are smaller) during the A < than the A > of solar minimum periods In addition, the dependence of the power index n on the solar activity for solar minimum years is generally absent For high-rigidity particles, the rigidity dependence of CR modulations is small or nearly missing since no modulation is expected for CR with energy above 100 GeV [7,19] In conclusion, a soft PS of CR is obtained for the A > epochs solar minima relative to A < epochs, and this is in accordance with the predication of the driftmodel Solar maxima Solar maximum is contrasted with solar minimum Solar maximum is the period when the Sun’s magnetic field lines are the 100 9d Rome Relative amplitude % 256 d (b) 28.5 d 37 d 103 d 13.8 d 57 d 9d 6d 205 d Hu / Ha 28.5 d (c) 85 d 102 d 0.01 36.5 d 14 d 9d 0.1 Kiel (a) 205 d 70 60 27.7 d 78.7 d 50 48.7 d 40 30 8d 20 10 90 205 d 146 d Rome 80 (b) 28.5 d 70 60 78.7 d 50 40 14 d 30 8d 20 10 Relative amplitude % Relative amplitude % Relative amplitude % 80 100 10 100 90 80 70 60 50 40 30 20 10 100 90 80 70 60 50 40 30 20 10 0.001 146 d 90 Relative amplitude % modulation for the 20th cycle was larger, while at high rigidities no remarkable changes were obtained Also, the CRI was more strongly affected by a factor of two during the A > epoch [27,28] In conclusion the PSD for solar minima activity reflected different peaks of different magnitudes and locations The work of El-Borie and Al-Thoyaib [6] displayed a broad peak near 250–300 d ($0.7–0.8 yr), which has been observed for the solar minima epochs They attributed these periodicities to the changes in the coronal holes and to the active solar regions related to the coronal hole boundaries [20] Our spectrum showed a significant peak at 256 d (0.7 yr) which agrees with the work of [5,6] Joshi [29] studied the power spectra for Cl during the period 1989–1991 and found a periodicity of 170 days This periodicity was related to a strong magnetic field, as CRs are associated with magnetic clouds The magnetic clouds are associated with shocks, coronal mass ejections and geomagnetic storms The decreases in CRI are mostly caused by interplanetary transients originating from solar coronal holes and solar flares [30,31] Table shows the values of the power index for the considered stations Comparing periods of A > and A < for years of solar minima, we found that the power law index n has a higher value for period of A < (1985–1986) than for A > yr (1975–1976 and 1994–1995) The observed differences of CR power spectrum between the A > and the Frequency c / d Fig PSD of Kiel, Rome and Hu/Ha during minimum solar activity m3 (94–95) 100 90 80 70 60 50 40 30 20 10 0.001 205 d Hu / Ha (c) 146 d 25.6 d 49 d 14 d 8d 0.01 0.1 Frequency c / d Fig 10 PSD of Kiel, Rome and Hu/Ha during maximum solar activity M1 (79–80) Mid-term periodicities of CRIs 145 most distorted due to the magnetic field on the solar equator rotating at a slightly faster pace than at the solar poles The Sun takes about 11 yr to go from one solar maximum to another and 22 yr to complete a full cycle (where the magnetic charge on the poles is the same) Since the drift modulation processes are charge/polarity dependent, the 22 yr solar magnetic field cycle is visible in CR data, e.g., in the different shapes of maxima of GCRs intensity cycles In Figs 10–12 we plot the PSD of CRIs during the maximum solar activity years (1979–1980, 1989–1990 and 2000–2001) in the frequency range between · 10À3 dÀ1 and 0.5 dÀ1 Results indicated a flat spectrum for frequencies P0.12 dÀ1 However, most peaks are wider than those in Figs 7–9 and have a double-peak structure Note that the process of CRI modulation in and around solar maxima is complicated, with probably many modulating factors involved The plots further confirmed the peak of 146 d (0.4 yr), which has been observed during solar minima, confirming the existence of such periodicity in the CRI spectrum; and a broad peak at 170 d, narrower peaks at 45–90 d, as well as the solar rotation period and its harmonics In addition, the plots indicate that the three maximum solar activity periods reflected different long-term behaviors The processes responsible for long-term variations are different 100 170.6 d 68 d 50 40 93 d 27.7 d 16.5 d 30 20 10 100 90 170.6 d Rome (b) 80 70 60 68 d 50 93 d 40 57 d 27.7 d 30 13 d 20 10 100 90 80 70 60 50 40 30 20 10 0.001 170.6 d Hu / Ha (c) 27.7 d 51 d 68 d 0.01 16.5 d 0.1 146 d 90 Relative amplitude % 70 60 (a) Kiel Relative amplitude % 90 80 Relative amplitude % Relative amplitude % Relative amplitude % Relative amplitude % 100 from the ones that cause short-term variations Figures indicate a complicated structure of the spectra resulting from the superposed of the profiles with the different periodicities The total profile is determined by different periodicities rather than a superimposition of different periodicities which are stable in time Shorter periodicities have different probabilities of occurrence in different epochs It should be noted that extremely large Forbush decreases were observed in the 1989–91 period Also, the total solar magnetic flux from the active regions in 1989–91 significantly exceeded those observed in 1979–81 [32] Furthermore, there are significant differences between individual spectral maxima for different solar epochs Table shows the values of the power law index n for maximum solar activity epochs We note that the power law index n during M2 (1989–1990) has a higher value than M1 (1979– 1980) and M3 (2000–2001) On the other hand, for the 1989– 1990 solar maximum, the power spectra are generally harder (by a factor of two) than those for the 1979–1980 and 2000– 2001 periods Thus, the CR power spectra for even-cycle solar maximum years are higher and much harder than odd cycles At low frequencies, our results indicate that the CR power spectra exhibited a complex structure for different epochs This is probably due to the combinations of different transient Frequency c / d Fig 11 PSD of Kiel, Rome and Hu/Ha during maximum solar activity M2 (89–90) (a) Kiel 80 64 d 70 60 29 d 50 13.8 d 46.6 d 40 30 20 10 100 90 80 70 60 50 40 30 20 10 100 90 80 70 60 341 d (b) Rome 146 d 64 d 30 d 42.7 d 340 d 50 40 30 20 10 0.001 146 d 13.8 d Hu / Ha (c) 64 d 29 d 13.8 d 5d 0.01 0.1 Frequency c / d Fig 12 PSD of Kiel, Rome and Hu/Ha during maximum solar activity M3 (00–01) 146 factors with unstable periodicities growing and decaying throughout the entire period Our observations indicated the significance of drift effects on the modulation of CRI at time scales of one month or more At high frequencies, corresponding to a few days to one month, our results indicated that there are significant differences between the individual spectra maxima for different cycles We obtained a good correlation between the CR PSD and the polarity of the solar polar magnetic field In addition, our results indicated that PSD at around 27 d periodicity is correlated with changes in the magnitude of solar activity However, the decrease in CRI levels (and the increase in CRI modulations) around maxima of solar activity is different in the last three solar maxima Summary and conclusions The most common method for studying variation of time series is based on the power spectrum analysis In our analysis, we have used the daily average CR counting rates observed with five NMs, whose geomagnetic vertical cutoff rigidity Ro covers the range 1.1 GV Ro 13.3 GV A comparison of the spectra for both positive IMF polarities suggests different solar origins The spectra have different power amplitudes and most peaks of different locations (expect 1.25 yr, 0.37 yr, and the effect of solar rotation cycle) The A1 < epoch (1981–1991) reflected higher periodicity, which was observed at 5.6 yr, 1.6 yr, 0.8 yr, 0.6 yr, 75–79 d, 43–45 d and 27 d (and its harmonics) The 5.6 yr variation is probably due to different paths of ion particles in the heliosphere [e.g., 19] On the other hand, the A2 < epoch (2002–2007) indicated different peaks, at 1.9 yr, 0.94 yr, 0.56 yr, 71 d, 60 d, 51 d and 27 d (and its harmonics) The observed differences in the cosmic ray spectrum conditions for A > and A < periods are probably associated with the influence of drift effects These results imply that there is a significant difference in the solar modulation of CR during positive and negative polarity magnetic field cycles Accordingly, drift effects dependent on the polarity of the global solar magnetic field may play a significant role for the observed differences between positive and negative IMF polarity The rigidity dependence of CRI modulations for the low solar activity periods (1975–1976, 1985–1986 and 1994–1995) was apparent The observed CR maximum spectra P27 d are at different frequencies Sometimes this maximum occurs at 27 d or 256 d The period of 1975–1976 PS (Fig 7) shows that there are some noticeable peaks at frequencies 45–250 d, which may indicate an unstable variation The 146 d (0.4 yr) is a common periodicity for considered NMs Our results reflected the fluctuations at 45 d, 66 d, 100 d and 256 d (0.7 yr) On the other hand, the period 1985–1986 displayed well defined peaks at 64 d, 79 d, 114 d (0.3 yr) and 170–200 d (0.45– 0.55 yr) Thus, the observed CR maximum spectra P27 d are at different frequencies Sometimes this maximum occurs at 27 d or 256 d At other epochs (Fig 8) the period of high power is between 170 d and 205 d So, different spectrum behaviors may be rigidity-dependent, and this is due to the gradient and curvature drifts of charged particles in the global magnetic field The PSD for solar minima activity reflected different peaks of different magnitudes and locations The observed differences of the CR power spectrum between the A > and the A < solar minima epochs are significantly M.A El-Borie et al large The CR PSD are harder by a factor of two during the A < epoch (1985–1986) than during the A > epochs A soft PS of CR is obtained for the A > epochs solar minima relative to A < epochs, and this is in accordance with the prediction of the drift-model The process of CRI modulation in and around solar maxima is complicated, with probably many modulating factors involved Our results confirmed peaks of 146 d (0.4 yr), a broad peak at 170 d, and narrower peaks at 45–90 d, as well as the solar rotation period and its harmonics In addition, the plots indicated that the three maximum solar activity periods reflected different long-term behaviors Shorter periodicities have different probabilities of occurrence in different epochs The power law index n during M2 (1989–1990) has a higher value than M1 (1979–1980) and M3 (2000–2001) For the 1989– 1990 solar maximum, the power spectra are generally harder (by a factor of two) than those for the 1979–1980 and 2000– 2001 periods Thus, the CR power spectra for even-cycle solar maximum years are higher and much harder than those for odd cycles At low frequencies, our results indicate 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Power spectra of cosmic ray intensity for years of solar activity In: Proc int cosmic ray conf (Hamburg), vol 9; 2001 p 3877–80 [6] El Borie MA, Al Thoyaib SS Power spectrum of cosmic- ray fluctuations... On mid-term periodicities in cosmic rays: utilizing the NMDB archive, in: Proc 31st inter cosmic ray confer (Lodz); 2009 p 1126 [24] Sabbah I, Duldig ML Solar polarity dependence of cosmic ray. .. S, Gali M In: Proc 15th int cosmic ray conf (Plovidiv), vol 11; 1977 p 287–90 [2] Attolini MR, Cecchini S, Guidi I, Galli M The shape of the power spectrum of cosmic ray at ground level up to ·