The 48-Year Data Analysis Collected by Nagoya Muon Telescope—A Detection of Possible (125 ± 45) Day Periodicity

Abstract

Muons produced by cosmic rays above the atmosphere provide valuable information on the intensity of cosmic rays and variations in the upper atmosphere. Since 1970, the Nagoya University Cosmic Ray Laboratory has been observing the muon intensity using a multi-directional cosmic ray telescope with two layers of 36 plastic scintillators of $1{\mathrm{m}}^2$ each, which measure the muon intensity in different incident directions. The energy of an incident proton that produces a muon incident from a vertical direction is over 11.5 GV. This paper analyzes vertical muon intensities obtained over 48 years from 1970 to 2018 using methods that differ from the East–West method. As a result, a new periodicity of ($125\pm 45$) days and a new periodicity of (4–16) days were found. The latter appears only in winter time, so it may be caused by a synoptic-scale disturbance associated with the arrival of the Siberian cold air mass. On the other hand, the former periodicity may be related to solar dynamo activity. In 1984, the Solar Maximum Mission’s Gamma Ray Spectrometers reported a periodicity of about ($154\pm 10$) days in the flux of solar gamma rays. The ($125\pm 45$)-day periodicity found here is most likely related to solar dynamo activity, since the intensity of cosmic rays around 11.5 GV is affected by the magnetic field induced by the Sun. However, this ($125\pm 45$)-day periodicity differs from the report measured by the GRS instrument in a point that it also appears during periods of low solar activity. Furthermore, it has not appeared often during lower solar activity since 1992. This information is important for future investigation of the origin of this periodicity.

1. Introduction

Around 1960, Japanese cosmic ray researchers discussed the idea of building a device to detect cosmic ray variations with a precision over 10 $\sigma$ or greater. Pursuing this line, it was decided to construct an ultra-high precision meson detector. In fact, the construction of the Nagoya University Multi-Directional Cosmic Ray Telescope began as a part of Japan’s participation in the International Active Sun Year (IASY), which started in the summer of 1968 [1,2]. Data from October 1970 to December 2018 are now publicly available from the website http://crportal.isee.nagoya-u.ac.jp/muon/muon3.html (accessed on 20 February 2023). The same data are also avilable from the website http://cosray.shinshu-u.ac.jp/crest/DB/Public/Archives/ (accessed on 20 February 2023) Nagoya_OLD.php (accessed on 20 February 2023).

The purpose of the installation of this instrument was to search for variations in the heliosphere from cosmic ray muon data. The data obtained from this instrument confirmed that the daily phase variation in the cosmic ray intensity advances during the time of minimum solar activity [3,4], and various other research results [5,6]. Among them, a major finding was the sidereal anisotropy with use of this detector (Nagashima et al. 2012). This implies that the muon telescope has worked very stably for a long time, and a 0.04% minor variation in intensity of cosmic rays has been picked up. They used the multi telescope function and analyzed the differential flux from the East direction minus the West direction (the Elliot method). Applying this method, systematic variations due to temperature and pressure could be found. In this paper, we have analyzed the same data from a different perspective.

2. Data of the Nagoya Multi-Directional Cosmic Ray Telescope

The Nagoya University Multi-Directional Cosmic Ray Telescope consists of 36 plastic scintillators with an area of $1{\mathrm{m}}^2$ and thickness of 5 cm. The telescope functions are realized through a two-layer structure. The two layers, each $36{\mathrm{m}}^2$, are separated by 1.73 m. A 5 cm thick layer of lead is installed between the first and second layers in order to remove the electron and gamma ray components in cosmic ray showers and observe the muon component. The muon flux from multiple directions is observed simultaneously by triggering a combined signal from the plastic scintillators in upper and lower layers. Details are given in the article [2]. In this paper, only vertically incident muon data are analyzed, because we did not apply the East–West method. For the vertical arrival component, the effective solid angle is $10{\mathrm{m}}^2$ steradian (total solid angle × area). The average counting rate is 2,760,000 per hour and the effective cut-off rigidity is estimated at 11.5 GV [2].

The published observational data are described in UT (universal time) and the barometric pressure fluctuation effects have already been corrected. The counting rate was corrected −0.12%/hPa to the observed pressure. However, temperature fluctuations are not corrected. To remove this variability, for example, the parameter G = (30° N–30° S) + (30° N–30° E) has been introduced, and data analysis has been carried out [7].

Berkova et al. (2016) have proposed to correct the Nagoya muon data for temperature variations in cosmic ray muon flux from meteorological data [8]. However, sometimes the atmospheric temperature of the lower layer differs from the variation in the upper layer (the stratosphere). In such a case, we may also need the information on the stratosphere. In fact, the Japan Meteorological Agency measures the temperature and air density of the stratosphere twice over Wajima. Therefore, for perfect analysis, we may need both pieces of information.

Note that the instruments themselves are located in the thermostatic chamber; therefore, the temperature variation with respect to the trigger rate is negligible. However, the atmospheric pressure variation associated with the temperature variation is still not corrected. Its removal is a challenging task.

We plotted 48 years of public data and found regular one-year variations in the counting rate, reaching a minimum in mid-summer at the end of July and a maximum in winter. The amplitude is approximately 2% or less. In the upper curve of Figure 1, we present the annual variation in the muon vertical flux during 2009 and 2018. Each parameter is given in

Table 1. Fitting parameters.

Year	a	b	p	q
1970	1330.6	0.09085	19.952	−160.88
1971	1840.8	−0.02233	84.376	133.13
1972	1620.6	−0.01785	102.068	139.44
1973	1376.2	−0.00585	32.698	186.15
1974	1321.8	−0.02377	83.296	182.86
1975	1208.7	0.00648	88.557	149.09
1976	1200.9	0.02894	−53.023	296.73
1977	1509.2	−0.01282	105.533	190.32
1978	1426.5	−0.02271	72.131	180.62
1979	1046.0	0.05473	117.321	312.5
1980	1627.0	−0.01527	78.225	132.62
1981	1548.3	−0.01402	37.306	165.22
1982	1365.3	0.00407	177.626	254.96
1983	1355.0	0.02415	111.633	154.34
1984	1522.7	−0.01714	27.319	213.32
1985	1493.3	0.01710	117.354	131.35
1986	1904.1	0.00057	24.554	125.7
1987	1972.3	−0.01467	148.805	138.52
1988	1827.8	−0.00496	95.763	126.91
1989	1647.8	−0.01362	58.353	107.65
1990	1547.8	0.01508	26.976	177.5
1991	1695.0	−0.04247	−1.995	325.36
1992	1549.8	0.03305	110.854	96.2
1993	1742.5	0.01476	109.886	123.26
1994	1821.1	−0.00052	62.230	162.46
1995	1862.7	0.00558	105.588	151.7
1996	1865.9	0.00763	145.005	154.65
1997	1965.4	−0.00884	58.447	132.96
1998	1866.8	−0.00819	64.580	216.17
1999	1813.4	0.00364	120.579	112.76
2000	1660.3	−0.00127	282.026	191.77
2001	1848.9	−0.00938	95.952	188.19
2002	1720.8	0.00320	139.066	150.66
2003	1749.7	−0.01273	82.660	161.79
2004	1762.3	0.01668	117.976	130.47
2005	1711.2	0.03712	196.603	183.7
2006	1958.5	0.00484	91.295	157.43
2007	1970.8	0.01568	135.716	146.45
2008	2024.3	0.01113	107.773	155.81
2009	2082.6	0.00874	104.992	143.77
2010	2062.5	−0.00205	84.536	176.17
2011	2058.9	−0.00649	104.903	188.14
2012	1963.0	0.00731	111.979	180.74
2013	1968.3	0.00344	72.211	194.79
2014	1977.2	−0.01080	96.730	113.81
2015	1862.6	0.00250	79.632	137.22
2016	1913.7	0.00777	84.452	152.93
2017	1971.5	0.00839	138.653	162.34
2018	2022.4	0.0	69.050	153.83

. We can recognize that the signals oscillated quite regularly. This phenomenon is caused by the expansion of the atmosphere during the summer season, which increases the altitude at which muons are generated. In other words, the expansion of the atmosphere produces pions higher up in the altitude, increasing the muon decay distance and decreasing the number of muons, which is known as a negative temperature effect.

As a first step in the removal process of the “temperature effect”, we corrected the inter-annual variation by approximation using trigonometric functions as $\mathrm{average}\_\mathrm{flux}=a+bt+psin\left(2\pi t/\tau \right)+qcos\left(2\pi t/\tau \right)$ where $\tau =24\times 365.25\mathrm{hour}$ (one solar year). The fitting curve is drawn over the raw data (on the upper curve of Figure 1) and we can recognize that the fitting curve quite well expresses the original variation in the muon intensity. Each parameter of ecah year is deduced from the data set starting from 1 January 00:00 UT to 31 December 24:00 UT and they are provided in Table 1 as indicated before. The difference between the fitting value and the original data (difference = flux- average_flux) is shown in the lower part of Figure 1. We analyzed this “difference data”. The results of analysis based on the dataset are given in the next section.

3. Wavelet Analysis and Main Results

Before we present the results of the wavelet analysis by the Morlet wavelet function, we note one important record found in this data base. Only one clear GLE (Ground Level Enhancement) event was observed throughout the entire period (14 October 1970∼31 December 2018); the event was associated with a flare of X9.8 on 29 September 1989 at 11:33 UT. The time profile is shown in Figure 2 and the energy spectrum is shown by the red line in Figure 3. The flare induced a CME (Coronal Mass Ejection) shock that accelerated the protons of warm particles [9] generated at $\mathrm{W}90$∼$\mathrm{W}95$ on the solar surface to higher energies and transported them to the Earth [10,11,12]. No other clear GLE events were found in this data base. As can be seen from Figure 3, the GLE of the 29 September 1989 event had the hardest energy spectrum among the GLEs found in solar cycle 22.

We have searched whether any periodicity is hidden in the data set. For this purpose, we have applied the wavelet analysis to the “difference data” using the software of Matlab [13]. The results are shown in Figure 4. The vertical and horizontal axes are given by “day values”. (1) Black dots are concentrated between days 4 and 16 (4–16) of vertical axis. (2) Peaks corresponding to 27-day variations are discretized. (3) Then, the presence of day ($125\pm 45$) is seen in the first half of the period dominantly; however, the pronounced ($125\pm 45$)-day oscillations can be recognized through the 21st, 22nd, 23rd and 24th periods of solar activity.

Quite surprisingly, the 125 day activity appeared in the lowest time of solar activity between 1976 and 1986. However, it does not appear in the subsequent minimum periods after 1992 which may be a key to elucidating the phenomenon of decreasing trend of solar activity and an extension of the 11-year cycle. These periods are summarized in

Table 2. The number of abscissa represents the day from 14 October 1970.

Abscissa (Days)	Calender Year	Solar Activity	Solar Cycle
1700–2200	10 August 1975–6 March 1977	minimum
3000–3200	17 June 1979–2 February 1980	maximum	21st solar cycle
4000–4700	20 August 1982–30 April 1984
5400–5800	18 June 1986–4 August 1987	minimum
6800–7000	20 May 1990–8 December 1990	maximum	22nd solar cycle
7300–7700	11 October 1991–15 November 1992
11,000	9 June 2002	maximum	23rd solar cycle
11,600	24 March 2004
12,000	11 May 2005
15,000	6 October 2013	near maximum	24th solar cycle

.

4. Discussion

Before we compare present results with preceding results, we leave a short note here. The present detector has been working stably since 1974. In the early stage between 1970 and 1974, the gain of the photomultipliers dropped slightly down and we observed this effect. In Figure 5, we present the zoomed results of the wavelet analysis, picking up the year 2018. One can clearly recognize 24 h periodicity owing to the diurnal variation arising from the Earth’s rotation. Furthermore, one may notice a (120∼240)-hour variation. This periodicity will be discussed in the next section. Incidentally we can also recognize 27-day (=648 h) variation due to the solar rotation. Now we enter into the main part of the discussion of the ($125\pm 45$)-day variation.

4.1. Comparison with the Results of Preceding Studies

In 1984, the Gamma Ray Spectrometer (GRS) on board the SMM satellite detected gamma rays from the Sun in the range between 300 keV and 100 MeV. In the dataset, Rieger et al. (1984) [14] have found a periodicity of $(154\pm 10)$ days. In the paper, they have discussed the periodicity, which may be related to the dynamo motion of the Sun. This is because the periodicity is quite near the periodicity of g-mode found by Wolf [15]. Recent development may be found in the references of the paper by Mathur et al. (2008) [16]. Bai and Sturrock also interpreted its origin [17].

Ichimoto et al. (1985) [18,19] have analyzed the $H_{\alpha }$ solar flare data during solar cycles 20 and 21. Then, they have found not only a prominent periodicity of day 154, but also 115- and 92-day periodicity in both the northern and the southern solar hemispheres. Their results are consistent with our muon observation data.

Among the error bars, the present periodicity coincides with the GRS periodicity. Furthermore, the flux of cosmic rays in the energy range between approximately 10 and 30 GeV strongly receive the influence of the magnetic field induced by the Sun. Therefore, both may be related with each other. So, we carefully compare with the time when a $(125\pm 45)$-day periodicity was observed. The observed year by the GRS was in fall between 1980 and 1983. This duration completely coincides with our observation time of a ($125\pm 45$)-day periodicity.

Katsavrias, Preka-Papadema and Moussas analyzed the data collected by the ACE satellite located at the L1 Lagrangian point. This paper is henceforth referred to as the KPM paper [20]. The KPM paper describes the results of the periodic analysis of a number of solar and geomagnetic parameters, using the NASA OMNI web database during 1966 to 2006. Among them, we selected the physical quantities in which the ($125\pm 45$)-day cycle appears, including solar wind velocity and temperature, plasma pressure and density, interplanetary magnetic field strength, Alfvén Mach number and plasma beta. However, the ($125\pm 45$)-day cycle is noticeable in the time from 1982 to 1989. This time, the ($125\pm 45$)-day periodicity was probably the most strongly realized.

On the other hand, in the cosmic ray data, $(125\pm 45)$-day cycles appear around the peak of active solar time. They continue for quite a long time, as shown in Figure 4. They are summarized in Table 2. Quite surprisingly, the $(125\pm 45)$-day periodicity is also recognized at very quiet time of solar activity in 1976 and 1986. The origin of the $(125\pm 45)$-day periodicity is still an interesting subject for future investigation.

4.2. Comparison with Observations of the 10.7 cm Solar Radio Wave

We searched another evidence on the solar activity. For this purpose, a periodic analysis was carried out for the daily average data of the 10.7 cm solar radio intensity. The results are compared with the variations in cosmic ray muon intensity. Along with sunspots, the radio emission with 10.7 cm wavelength from the solar surface is an indicator of sub-coronal activity on the Sun. To facilitate comparison with the observations of cosmic ray muon time profile in the present study, a wavelet analysis was carried out on the solar radio data for almost the same period. The analysis was conducted from 14 October 1970 to April 30 April 2018. The basic data are shown in Figure 6 [21], while Figure 7 shows the results of the wavelet analysis.

Figure 7 shows the existence of a strong ($125\pm 45$)-day cycle around 3900 days on the abscissa; the 3900th day corresponds to around 15 June 1981, which indicates that 1979–1981 was the most active period of the 21st solar cycle.

4.3. Comparison with Oulu Neutron Monitor Data

Next, we analyzed the observed data at Oulu cosmic ray station in Finland, where cosmic ray intensity is measured by the neutron channel. We report the results of analysis. The period analyzed was from 14 October 1970 to 31 December 2018—the same period in which the data were obtained by the Nagoya muon telescope. The results of the wavelet analysis are shown in Figure 8. It is interesting to note that although the $(125\pm 45)$-day period is not predominant throughout the 48-year period, peaks near 64 days were observed in June 1991 (7600 days) and around November 2003 (12,000 days) when the solar activity was the maximum. It is nearly half of the ($125\pm 45$)-day periodicity. This may reflect the influence of the continuous occurrence of giant flares around June 1991 and the GLE in 2003. The strong amplitude near day 4096 corresponds to the 11-year cycle of solar activity. It should be noted here that the GLE of the 29 September 1989 was also recorded in the data set of Oulu. However, the existence of the ($125\pm 45$)-day periodicity is unclear. This may be the effect arising from the difference of the threshold energy between the two stations, Oulu (0.78 GV) and Nagoya (11.5 GV).

5. Discussion on (4–16) Day Periodicity

Finally, the five-day oscillations are discussed. A characteristic feature of the data may be pointed out that they appear with (4–16)-day oscillations during the winter season. To investigate the cause of this periodicity, the vertical variation in the altitude at 100 hPa above Wajima was investigated. A radiosonde was flown over Wajima (37.4° N, 136.8° E) twice a day at 09:00 and 15:00 JST to investigate the upper-level atmospheric condition.

The results are shown in Figure 9. The 100 hPa altitude in summer is approximately 1000 m (∼8%) higher than that of winter. The figure shows that the atmosphere expands and the 100 hPa point moves upwards during the summer season. As the atmospheric density decreases, the muon flight distance increases, so the muon decay probability with the energy around 2 GeV increases. Therefore, muon flux decreases.

On the other hand, the fluctuation of the muon intensity that appear with a period of (4–16) days in winter is induced by the periodic arrival of Siberian cold air masses over Japan (Figure 10). This is caused by synoptic scale disturbances that appear at high latitudes in the Northern Hemisphere. These oscillations cannot be removed by our trigonometric approximation. The oscillation of the upper atmospheric are eastward propagating waves in the Northern Hemisphere with a wavelength of about 4000 km to 6000 km and a wind speed of 40 m/s. Our analysis shows that meteorological phenomena are closely related to cosmic ray intensity.

6. Concluding Remarks

We have analyzed 48 years of observations by the Nagoya muon telescope without using the East–West method ([22] and references, therein). Present analysis shows that the effect of temperature fluctuations on the intensity of cosmic rays can be removed throughout the year, but some amplitude of the cosmic rays exceeds the effect of temperature fluctuations during the winter season. This arises from the arrival of Siberian cold air mass to Japan in winter time.

On the other hand, the existence of an effect on the intensity of ∼20 GeV cosmic rays with a periodicity of ($125\pm 45$) days has been confirmed. Taking into account the preceding researches, a new candidate of ($125\pm 45$)-day periodicity may be deeply related with the solar dynamo mechanism. It appears both during the peak and quietest periods of the solar activity.

This new fact may be a key to understanding the origin of this oscillation. If the oscillations only appear during the periods of high solar activity, it may be possible to assume that a large number of energetic particles are produced on the solar surface during the active time; however, if they also appear during the quiet period, it may be necessary to consider another origin. For example, there could be magnetic field oscillations in the heliosphere that we do not understand well, which could affect the intensity of cosmic rays. However, the origin of the ($125\pm 45$)-day periodicity is still a matter for future investigation.