Third harmonic of the 27 day periodicity of galactic cosmic rays: Coupling with interplanetary parameters

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116,, doi: /2010ja015922, 2011 Third harmonic of the 27 day periodicity of galactic cosmic rays: Coupling with interplanetary parameters I. Sabbah 1,2 and K. Kudela 3 Received 16 July 2010; revised 6 December 2010; accepted 27 December 2010; published 2 April [1] Spectral analysis of neutron monitors and muon telescope daily averages counts shows a significant higher harmonic ( 9 day) of the 27 day variation of galactic cosmic rays (CRs). This quasiperiodicity is also present in the time series of daily averages of the product of interplanetary magnetic field magnitude and the square of solar wind speed (BV 2 ). The wavelet spectrum density of the third harmonic of the 27 day variation of CRs is weakly correlated with the quantity BV 2. This result reflects the coupling between galactic CR modulation and interplanetary parameters. Citation: Sabbah, I., and K. Kudela (2011), Third harmonic of the 27 day periodicity of galactic cosmic rays: Coupling with interplanetary parameters, J. Geophys. Res., 116,, doi: /2010ja Introduction [2] Cosmic ray (CR) variability observed from the ground is affected by many complex mechanisms forming the primary CR flux at different energies in the heliosphere, within the Earth s magnetosphere and in the atmosphere of Earth (review, e.g., in the book by Dorman [2006]). There is a clear diurnal wave that has been studied for a long time (one of the first papers probably published by Singer [1952]). It remains the subject of research in connection with interplanetary magnetic field (IMF) configurations in heliosphere (e.g., see recent papers by Mishra and Mishra [2008], Kudela et al. [2008], and Oh et al. [2010]). At lower frequencies the quasiperiodicity at 27 days is related to the period of solar rotation and the consequences of solar wind structures bounded with the solar surface also discussed for a long time (e.g., by Kane [1957]). Its dependence on solar magnetic field polarity, IMF and solar wind characteristics at different energies of primaries is discussed by Sabbah [2007] and Alania et al. [2008]. The IMF in relation to the fast solar wind plasma streams is discussed by Mavromichalaki et al. [1999] and Rangarajan and Mavromichalaki [1989]. [3] Between the two periodicities, namely 27 day and diurnal variations, there are reported indications about the higher harmonics of interplanetary and geomagnetic characteristics. The second harmonic of a 27 day variation is studied in detail (e.g., by Mursula and Zieger [1996]). Recently, Gil and Alania [2010] reported temporal evolution of the rigidity spectrum of the first (27 day) and the 1 Department of Natural Sciences, College of Health Sciences, Public Authority of Applied Education and Training, Kuwait City, Kuwait. 2 Department of Physics, Faculty of Science, Alexandria University, Alexandria, Egypt. 3 Institute of Experimental Physics, Slovak Academy of Sciences, Kosice, Slovakia. Copyright 2011 by the American Geophysical Union /11/2010JA second (13.5 day) harmonics of the 27 day variation of the galactic CR intensity measured by neutron monitors (NMs) in the period of Description of quasiperiodicities in CR at time scales longer than 27 days can be found in work by Kudela et al. [2010]. [4] In the geomagnetic activity characteristics there is observed 9 day quasiperiodicity. The 9 day periodicity is the third harmonic of the solar rotation period. A study by Střeštík [1998] analyzing long time series ( ) of Ap indices indicated that the 9 day peak exceeds the 95% significance level only slightly. Its presence, however is much stronger for specific shorter time intervals (e.g., for year 2005 Kp index in Figure 2 of the paper by Leietal. [2008]). This approximate 9 day periodicity is also apparent in upper atmospheric processes. Tulasi Ram et al. [2010] indicate 9 day oscillation in the peak value of electron density in the F 2 layer and its phase variation in latitude. It is also observed in thermospheric density [Lei et al., 2008]. Strong 9 and 7 day oscillations have been reported in UV emissions characterizing the column density ratio of O and N 2 in the thermosphere [Crowley et al., 2008]. Total electron content oscillations in a vertical air column of the ionosphere show the oscillation with 9 day period [Jacobi et al., 2007, Figure 1]. The 9 day periodicity is also observed in thermospheric infrared energy budget [Mlynczak et al., 2008]. They linked the 9 day peak in the infrared energy budget to the recurrence of high speed solar wind streams emanating from coronal holes. The 9 day periodic feature in the coronal hole areas determined from GOES/SXI time series of daily images was found by Temmer et al. [2007]. [5] Verma and Joshi [1994] investigated the occurrence rate of solar wind phenomena for time interval They concluded that the 9 day period may be the energy buildup time for coronal hole regions to produce high speed solar wind stream events. High speed solar wind events from the catalog by Mavromichalaki et al. [1988] indicated clear increase in solar wind power spectrum density around 9 days. 1of11

2 monitors and muon telescope and discuss the indications of higher harmonics of 27 day quasiperiodicity, especially at 9 days with those of the interplanetary parameters and geomagnetic activity. Figure 1. Short segments of periodograms of three neutron monitors in the vicinity of the fourth, third, and second harmonic of 27 day periodicity. Fragments of the power spectrum density (by FFT method with Welch window). The intervals of day 182 of 1982 until the end of 2007 are included at all stations. Time is in days on the x axis. All count rates are normalized to 100% for September [6] Sabbah [2007] found that the coronal hole areas are anticorrelated to the amplitudes of the 27 day variation of CR (first harmonic). Sabbah and Rybanský [2006] obtained a better correlation between CR intensity and coronal hole areas than between CR and solar activity. Sabbah [2000] found that the upper cutoff rigidity of the galactic cosmic ray (CR) diurnal modulation is better correlated (r = 0.88) with the magnitude of the product of solar wind speed and interplanetary magnetic field strength (VB) rather than with B alone. This correlation with VB reflects both diffusion of galactic CRs by the IMF and convection with solar wind. He also found that the geomagnetic activity index Ap correlates much better (r = 0.92) with the magnitude of VB rather than with either solar wind speed or IMF magnitude. Sabbah [2007] found that the Ap index is better correlated with BV 2 rather than with BV. Hence we tried to investigate if there is correlation between the 27 day modulation of galactic CRs and interplanetary parameters represented by the quantity BV 2. [7] Here we present the power spectra of CR time series at T < 27 days from long time measurements by neutron 2. Harmonics of the 27 Day Variation at Three Neutron Monitors by FFT [8] We use daily averages of neutron monitors data observed at different locations with different vertical geomagnetic cutoff rigidities (R o ), namely Oulu (0.8 GV), Kiel (2.3 GV) and Lomnický štít (4.0 GV). Hourly averaged data are now available at Days with large ground level enhancements (GLEs) caused by solar flares are eliminated from both data sets. The monthly averaged data sets were normalization to 100% for September [9] The power spectrum in the frequency region between the two (quasi)periodicities namely 27 day and diurnal variation, is rather complicated and affected by various transitional effects in the heliosphere and magnetosphere. This is apparent in Figure 1 during the period Power spectrum density (PSD) of the time series was obtained by fast Fourier transform (FFT) with the rectangular window method. The smooth curve using a cubic B spline connection is used. The spline technique is described (e.g., by de Boor [1978]). [10] Although the structure of power spectrum density is rather complicated, qualitatively the similarity using B spline approximation is apparent at all three NMs. The most pronounced maxima (as well as the variability) are seen in all cases for Lomnický štít (LS). This may be caused by relatively high statistical accuracy with count rate 420 s 1 at the altitude 2634 m. Oulu and Kiel have lower count rates ( 110 and 180 s 1, respectively). Whether the pronounced maxima at LS are higher in comparison with other neutron monitor PSD profiles due to higher count rate or due to the elevation (2634 m) requires further investigation. 3. The Spectra of Solar, Interplanetary, and Geomagnetic Indices [11] The daily data from OMNI web NASA site: omniweb.gsfc.nasa.gov/ow.html were used for inspection of higher harmonics of 27 day period for the interval from 1964 until November 2006 (interval overlapped with available data from Climax NM). Short intervals (<7 days) with gaps were approximated by linear interpolation. For the power spectrum computation, the procedure suitable for unevenly spaced data (Lomb Scargle periodogram described by Scargle [1982]) was used. For the Kp geomagnetic activity the profile of power spectral density is in Figure 2. [12] Power spectrum density was computed in a similar way for solar activity (R) and interplanetary parameters. For solar activity using the index of 10.7 cm wavelength intensity, where the most pronounced peak is situated at 27 day, the higher harmonics were consistently found to be insignificant (e.g., with upper panel of Figure 2 by Crowley et al. [2008]). The result was similar for sunspot number PSD. The solar wind speed (V) however, has clearly pronounced third harmonic of 27 day period. The same is true 2of11

3 Figure 2. Lomb Scargle periodogram that Scargle [1982] computed for Kp ( ). (bottom) The computed values for each of the frequency points; the line is the confidence level at (top) The smoothed PSD values (adjacent average smoothing with five points). for the magnitude of IMF (B) and for the quantity BV 2. This is seen in Figure On the Significance of Higher Harmonics of the 27 Day Period in CR Time Series [13] To understand the significance of quasiperiodicities in CR time series one has to assume the fact that PSD of CR at NM and muon detectors energy has a character of power law decrease f n, where n is 1.7, but it is not constant in the whole interval of frequency below that corresponding to 5 days and, especially at higher energies, the index n depends in the polarity of solar magnetic field [Sabbah and Duldig, 2007]. The spectral index is most probably controlled by that of IMF spectra. That is shown to be variable over the years and possibly depends on the position in the heliosphere. In work by Burlaga and Ness [1998] the slope of PSD in the frequency range between and Hz varies from 1.5 in year 1987 to 2.0 for In Figure 7 of that paper it is seen that also the slope of PSD of IMF is different for different years corresponding to different phases of solar cycle activity. [14] Revealing these quasiperiodicities in the presence of the underlying spectral density of the IMF variations, which takes a power law form, is not a trivial task. Figure 4 shows the spectra for the longest time series of CR measurements observed with Climax NM (R o = 2.92 GV) at ( sr.unh.edu/neutronmonitor/neutron_mon.html). [15] While 27 day and 13.5 day increase is seen in spectra, only marginal signatures of increases for the third harmonic ( 9 day) can be observed. The tests of sensitivity of the analysis were undertaken by adding different levels of total power of that wave to the signal of Climax NM normalizing it to unity. The threshold for 95% is obtained for the level of monochromatic wave power [16] The contribution of different quasiperiodicities to the power of the signal is not constant in time. For nonstationary time series like those of CR, the wavelet transform providing the information about time evolution of various periodic contribution to the signal is widely used. For identification of the intervals, where the 9 day quasiperiodicity is remarkable we used that method and checked where that quasiperiodicity can be observed clearly (with respect to other waves ). We inspected the whole interval from 1964 until 2006 and found that only in selected intervals such periods are seen with significance. Since the slope of PSD is rather high ( 1.78 in Figure 4), we used the Fourier filtering and reconstruction in the interval of frequencies d 1. One example of the segments, where the 9 day period is significant, is in Figure 5 during the time interval 5 June 1979 to 2 November [17] Continuous wavelet time frequency spectrum technique was used. Morlet wavelet mother function with the wave number 26 is adapted. More information about wavelet techniques can be found at wavelets or Wavelet analysis described in detail by Torrence and Compo [1998] was used. [18] Lomb Scargle periodograms were computed for three NM (Climax, Oulu and Huancayo (R o = GV) and the vertical component of the surface muon telescope located at Nagoya ( u.ac.jp/ste www1/div3/ muon/muon1.html). We see a significant increase at the third harmonic of 27 day period and at the second harmonic for the time interval analyzed. This is apparent at three NMs (at Oulu the third harmonic has even higher 3of11

4 is not observed during the whole time span of the data. The quasiperiodicity of the third harmonic is not a narrow peak, but it is composed of several transient increases in the vicinity of that frequency. [19] Using Fourier filtering and consequent reconstruction of Climax NM time series in the range f = d 1 and integrating the PSD with the frequency step of 0.01, we obtained the frequency time picture of character of PSD in the vicinity of the second and third harmonic. The results are shown in Figure 6. [20] We see from Figure 6 the variability of WSD at 9 day quasiperiodicity as well as 13.5 day during the interval analyzed. To check which parameter of interplanetary physical characteristics is related to the variability of WSD for the two intervals, we have collected data on IMF B (magnitude, nt) and solar wind speed (in km s 1 ) from OMNI data for each day of the analyzed interval. The value BV 2 was constructed and averaged over 100 days to compare it with the pattern of WSD near the third harmonic of basic 27 day period. Figure 7 presents the result. [21] For both plots the pattern is inconsistent with r =0, although the estimate of correlation coefficient is relatively low. For second harmonic the probability that correlation is zero for the general population from which we have sample correlation coefficient computed, is just 0.01, and for the third harmonic it is < It should be mentioned that the difference between the two correlation coefficients is statistically significant; the higher coefficient is for the third harmonic. The probability that both estimated correlation coefficients are equal is Figure 3. The normalized spectrum (from Lomb Scargle periodogram, smoothed similarly to Figure 2 by five points) of the daily values of (top) solar wind speed V, (middle) magnitude of IMF B, and (bottom) BV 2 for the interval Method is the same as in Figure 2. significance than the second harmonic). At Nagoya the increase is not as clearly pronounced as at lower energies but still significant at the level Such pattern, however, 5. Discussion and Summary [22] Spectral analysis of CRs and interplanetary data reveals the following. [23] 1. The 9 day periodicity is also evident in the spectra of the quantity BV 2. We confirmed on rather long time series of interplanetary and geomagnetic parameters the significant presence of 9 day periodicity (in Kp, in IMF B magnitude, in solar wind for epoch when interplanetary characteristics are available along with Climax neutron monitor data). [24] 2. We indicated the similarity of the power spectrum density in the vicinity of 9 and 13.5 day quasiperiodicity as measured on three neutron monitors and Nagoya muon telescope with the highest increases for high mountain neutron monitor having relatively high statistical accuracy. [25] 3. We found that the quasiperiodicity near third harmonic of 27 day period in CRs is rather complicated and not monochromatic if described over a long time period. [26] 4. We found that the wavelet spectrum density in the vicinity of the second and third harmonic of the 27 day variation weakly correlates with BV 2 with better correlation for the third harmonic. This reflects both diffusion of galactic CRs by the IMF and convection with solar wind. Since BV 2 is well correlated with the geomagnetic activity index, it follows that the third harmonic should be correlated with the Ap index. [27] Future studies include work on case studies as well as the presence of the third CR harmonic for different solar cycles, its phases and polarity of solar magnetic field. These can give more detailed information on the processes con- 4of11

5 Figure 4. Power spectrum density for Climax NM, 1951 to 30 November The best power law fit for n is Correlation coefficient of the fit is FFT method with Welch window was used. 5of11

6 Figure 5. (a) The wavelet time frequency spectrum of the Climax neutron monitor. The abscissa is in days from 1 January The color codes used are gray (10% 50%), cyan (50% 90%), and green (90% 95%). The Morlet mother function with the wave number parameter (the number of oscillations within the wavelet itself) of 26 is used. Period is in days; frequency is in d 1.(b e) Lomb Scargle periodogram with critical limit significance levels with red noise signal best fit. Red noise is present when the background power decreases with increasing frequency. Data were used during the time interval 5 June 1979 to 2 November Increases around second harmonic ( d 1 ) and around the third one ( 0.11 d 1 ) are seen for three neutron monitors. 6of11

7 Figure 5. (continued) 7of11

8 Figure 5. (continued) 8of11

9 Figure 6. (top and middle) The wavelet spectrum density (WSD) of Climax NM for the time interval with Df =0.01d 1 in time (x axis) versus frequency (y axis). Color code is the value of WSD. The values in the time domain are integrated over DT = 100 days. Horizontal cut is at approximately 9 days; a vertical cut is for the event displayed in detail at T = 5600 where the second as well as third harmonic is seen. (bottom) The solar activity as measured by the R index. Days are numbered from 26 March WSD was computed with the same method as in Figure 5 and averaged over the frequency domain with Df = 0.1 d 1. The x axes in Figure 6 are days starting from 26 March of11

10 Figure 7. (left) Scatterplot of WSD near the third harmonic ( f = d 1 ) versus BV 2 averaged over each 100 day period under examination. (right) The same for the second harmonic ( f = d 1 ). Log log plots provide the fit characterized by the linear correlation coefficients r. trolling the CR modulation and are in progress using the database collected during the present study. [28] Acknowledgments. I. Sabbah is grateful to Essam Khamis, vice president of the Alexandria University, and to M. Ismail, dean, and O. El Shazly and A. Ibrahim, vice deans, of the Faculty of Science, Alexandria University, for their support and encouragement. K. Kudela wishes to acknowledge VEGA grant agency project 2/0081/10 for support. We are grateful for the National Science Foundation grant ATM for Climax and Huancayo data and to Zenjiro Fujii for Nagoya muon data. We acknowledge the use of OMNI data from the National Space Science Data Center. We thank anonymous reviewers for their comments. 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