Preliminary analysis of two-hemisphere observations of sidereal anisotropies of galactic cosmic rays

Transcription

1 JOURNAL OF GEOPHYSCAL RESEARCH, VOL. 103, NO. A1, PAGES , JANUARY 1, 1998 Preliminary analysis of two-hemisphere observations of sidereal anisotropies of galactic cosmic rays D. L. Hall, 1 K. Munakata, 1 S. Yasue, 1 S. Mori, C. Kato, 1 M. Koyama, 1 S. Akahane, 1 Z. Fujii, 2 K. Fujimoto, 2 J. E. Humble, A. G. Fenton? K. B. Fenton, and M. L. Duldig 4 Abstract. By using the two-hemisphere network of underground muon telescopes we have examined the average sidereal daily variations in the count rates recorded by 48- component muon telescopes. The telescopes respond to primary cosmic rays with rigidities between -140 and 1700 GV and view almost the entire celestial sphere. We have modeled the data by using Gaussian functions, and we have related the Gaussian parameters to the recent tail-in and loss cone anisotropy model proposed by Nagashima et al. [1995a, b] to explain the sidereal daily variations. We have used the model parameters to derive the rigidity and latitude spectra of the galactic anisotropies and find them to be qualitatively in agreement with Nagashima et al.'s predictions. The results indicate, however, that the tail-in anisotropy is asymmetric about its reference axis, whereas the loss cone anisotropy is more symmetric. We show that these characteristics of the galactic anisotropies may explain the north-south asymmetry observed in the amplitude of the sidereal diurnal variation derived from Fourier analysis techniques. 1. ntroduction al., 1995; Munakata et al., 1995]. This is called the north-south asymmetry of the sidereal diurnal variation. Long-term observations of the count rates of cosmic rays Recently, one possible explanation of this asymmetry has recorded by underground muon telescopes have consistently been proposed [Nagashima et al., 1995a, b] and is called the reported the existence of an average diurnal variation in side- tail-in and loss cone anisotropy model. n proposing this model real time [Fenton and Fenton, 1975; Cutler et al., 1981; Ueno et the researchers compared the time profiles of the average al., 1984; Cutler and Groom, 1991; Fenton et al., 1995]. Histor- sidereal daily variation determined from various surface and ically, this variation has been studied in an attempt to elucidate underground muon telescopes. They postulated that there are the origin of galactic cosmic rays with energies between a few two distinct anisotropic distributions of galactic cosmic rays in hundred GeV and a few thousand GeV. The observations from the heliosphere; one of these is a loss cone, or deficit in flux, underground muon telescopes also provide interesting com- distributed symmetrically about an axis aligned with declinaparisons with those made from air shower experiments which tion (8) 20 ø north and right ascension (RA) 12 sidereal hours. respond to primary cosmic rays with energies more than an The other anisotropy should be an excess flux having an axis of order of magnitude higher [e.g., Nagashima et al., 1989, and symmetry with RA of 6 hours sidereal time and 8 of 24 ø in the references therein; Aglietta et al., 1996]. Most investigators southern hemisphere. t was suggested that the direction tohave concluded that the variation is small (<0.1%) and the ward this excess was close to the inferred direction.of the apparent right ascension of its maximum is somewhere in the heliomagnetotail, opposite to the proper motion of the solar early hours of the local sidereal day. Presently, no common system, and the anisotropy was thus dubbed the tail-in anisotconsensus exists about the nature of the production mecha- ropy. nism of this variation or its exact direction in the local region This paper presents the preliminary results of an extensive of the galaxy. nformation about declination can only be ob- investigation of the sidereal daily variation. n recent years we tained by making multiple observations of various regions of have formed the two-hemisphere network (THN) of underthe sky, and this was not possible until recently. With multidi- ground muon telescopes. We have recently analyzed the data rectional telescopes the amplitude of this variation was shown collected by the THN and present some of these results here. to be distributed asymmetrically about the celestial equator Considering the recent model put forward, we have attempted [Ueno et al., 1984]. t has now been conclusively demonstrated to depart from conventional Fourier analysis techniques and that the sidereal daily variation will be recorded with a larger used nonlinear iterative fitting procedures to model the daily amplitude in its first (diurnal) harmonic when viewed from variations by Gaussian functions. The fitting procedure proaround the midlatitudes in the southern hemisphere [Mori et duces parameters which can be directly related to the model's details. We will present these parameters and show how they Department of Physics, Faculty of Science, Shinshu University, may explain the N-S asymmetry and be the cause for some Matsumoto, Japan. refinements to the model of Nagashima et al. [1995a, b]. 2Solar-Terrestrial Environment Laboratory, Nagoya University, Nagoya, Japan. 3physics Department, University of Tasmania, Hobart, Australia. 4Australian Antarctic Division, Kingston, Tasmania. 2. Method of Analysis Copyright 1998 by the American Geophysical Union. Paper number 97JA /98/97JA Telescopes in the THN The THN of underground muon telescopes is composed of the multidirectional underground muon telescopes located at

2 368 HALL ET AL.: SDEREAL ANSOTROPES OF GALACTC COSMC RAYS Table 1. Stations and Their Component Underground Muon Telescopes Number of Viewing Years Detector Component Vertical Count Latitude Rigidity Station Analyzed Type Telescopes Rate, 103 h-1 Range Range, GV Mawson GM, P øS 165 Cambridge GM øS-0 ø Misato S øS-59øN Sakashita S øS-77øN Matsushiro S øS-90øN Liapootah S øS-21øN Poatina GM, P øS 1400 The instruments are described as having a detector type of either Scintillator telescope (S), proportional counters (P), or Geiger-Muller counters (GM). The Mawson underground muon telescope consisted of three GM telescope sections until 1982, which were then progressively replaced by proportional counter telescope sections. The Poatina underground muon telescope was also originally composed of three GM telescope sections and has progressively been upgraded by the inclusion of two proportional counter sections since Misato (vertical depth of 34 m water equivalent (mwe)), Sakashita (vertical depth of 80 mwe), and Matsushiro (vertical depth of 220 mwe) in central Japan and Liapootah (vertical depth of 154 mwe) in Tasmania, Australia. Along with the THN we have included the data from the underground muon telescopes located at Mawson (vertical depth of 31 rowe) in Antarctica and Cambridge (vertical depth of 36 mwe) and Poatina (vertical depth of 365 mwe) in Australia in the database for this paper. The telescopes respond to primary cosmic rays with median rigidities in the range GV and have asymptotic viewing cones [Rao et al., 1963] covering almost the entire celestial sphere. The details of these instruments have been presented by Mori et al. [1976], Fujimoto et al. [1984], Mori et al. [1989], and Humble et al. [1992] and are summarized in Table 1. variation recorded by each instrument. This was also performed in antisidereal time. Errors of each average hourly deviation were calculated from the scatter of the yearly averaged values about the final means. To obtain the diurnal variations recorded by instruments with median rigidities <500 GV, an additional correction needed to be made. This correction takes into account the annual modulation of the solar diurnal signal produced from the solar semidiurnal anisotropy, which is a sidereal variation also present in these data. The correction procedure uses the relation between the sidereal and the antisidereal diurnal vari- ations produced from the solar diurnal variation and has been outlined by Nagashima et al. [1985] and verified by K. Munakata et al. (Solar semidiurnal anisotropy of galactic cosmic ray intensity observed by the two-hemisphere network of sur Analysis face-level muon telescopes, submitted to Journal of Geophysical Research, 1997). We corrected all the data recorded by the instruments in Table 1 with median rigidities <500 GV for atmospheric pressure variations. For Poatina data prior to 1992, pressure effects were removed by using the barometric pressure recorded at the Liaweenee air shower array and the Palmerston power station in the highlands of central Tasmania. Since 1992 a pressure recorder has been operating at the Poatina site, and the corrections were made using those pressure data. To remove any transient variations not associated with the galactic anisotropy (for example, Forbush decreases), we subtracted the 24-hour The diurnal variations obtained by the above method typically show peaks close to 0600 local sidereal time and/or minima around 1200 local sidereal time [cf. Nagashima et al., 1995a, Figure 1]. This 6-hour separation between maxima and minima leads us to ask the question: s harmonic analysis necessarily the best method for examining such data? Certainly, in the past, it has been the best available method, but in this paper we have attempted to extract information from these data by assuming each peak and minimum in the data are due to independent effects. We fit a model comprising two running average from each hourly record of a month. Propor- Gaussian functions and a constant term to the data recorded tional and Geiger counter data are prone to large, transient by all the telescopes in Table 1; i.e., level shifts in data. n the case of Geiger counter data this is usually due to the counters' rapid deterioration in detecting D(t)=A exp - +A2exp - +C efficiency and the periodical adjustments to the high voltage '2 applied to the counters' anodes to maintain efficiency. Propor- (1) tional counters are much more stable, but data can have level shifts associated with electronic failure of the experimental system. For these data we first normalized the mean of each day's data to the yearly average hourly count rate. Each corrected hourly count rate for a month was binned according to its local sidereal hour, and the average sidereal hourly count rate for each month was obtained. The average hourly count rate from all the months was then calculated, providing 24 (average) hourly values obtained from the complete set of data for each instrument. The mean of these hourly values was calculated, and the percentage deviation of each hourly value from the mean was calculated to obtain the average daily One Gaussian has positive amplitude (A ) and represents the tail-in anisotropy of Nagashima et al.'s [1995a, b] model. The other Gaussian has negative amplitude (A2) and represents the loss cone anisotropy. Note that for the duration of this paper, unless otherwise noted, we will refer to the height/depth of the Gaussian functions as "amplitude," and that this should not be confused with the more usual amplitudes of fitted harmonic functions. Both Gaussian functions have arbitrary centers (tl, t2) and widths (0'1, 0'2)' The fitting is nonlinear and thus subject to the intricacies of iterative programming (s.ee, for example, Press et al. [1990]). We found that the solutions to the iterative fitting of the data from some of the components

3 HALL ET AL.' SDEREAL ANSOTROPES OF GALACTC COSMC RAYS 369 (usually with poor statistics) depended on the initial conditions in the compute.r code. This was probably a result of the code finding a relatively low value of X 2 but not recognizing the existence of a solution with a slightly lower value of X 2. To maximize our chances of determining the absolute minimum for X 2, for each set of data the same set of (various) initial conditions was used, and the best solution (lowest X 2) from the results was chosen. Any solutions with an error in the amplitude of 4 times the amplitude, or greater, were rejected from the intermediate results. The diurnal variation (by definition) is cyclic. Gaussian func- tions are not. n order to model the variation a little more accurately, we actually fit two sets of these Gaussianseparated by 1 day to 48 hours of data and obtained the best fit solutions to the central 24 hours of data. Figure 1 shows the results of such an analysis. The daily variations are a subset of those recorded from 17 years of continuous operation of the Sakashita underground muon multidirectional telescope. The components shown here are north pointing (N), vertical (V), south pointing (S), and farther south pointing (2S), having central latitudes of view of 65øN, 45øN, 5øS, and 23øS, respectively. The individual best fit Gaussians superposed on the best fit constant terms are shown by the dashed lines, while the overall fit is indicated by the solid line. The fitted constant term C is usually small with most values between +_0.01%. n Figure 1, C is 0.00%, 0.013%, %, and 0.003% for the N, V, S, and 2S telescopes, respect.ively. Note that each set of data from nonvertical telescopes in the figure has been shifted in time according to the difference between the vertical asymptotic longitude of view and the corre.sponding longitude of view of the telescope. This m o 80 6o Tail-in m= tx)ss cone m= ' (East) Longitude (West) Figure 2. Best fit centers of the Gaussians (see equation (1)) as a function of viewing longitude. The slopes (m) are slightly different. meant a 2 hour shift to earlier times for the north pointing telescope and a 1 hour shift to later times for the two south pointing telescopes. The best fit Gaussian amplitudes, centers, and widths de- rived from the data recorded by all the instruments in Table 1 can be examined for dependencies on viewing latitude, rigidity, and other variables. We report here the results of these examinations. We stress, though, that we are not claiming that harmonic analysis of cosmic ray data is now defunct; we have just simply examined whether or not another technique can be useful ( 0.1-0, Right ascension (sidereal hours) Figure 1. Average hourly percent deviations of the Sakashita underground muon north (N), vertical (V), and south (S and 2S) telescopes from 1978 to Vertical lines are shown at 0600 and 1200 local sidereal time. The individual best fit Gaus- sians superposed on the best fit constant terms are shown by the dashed lines, while the overall fit is indicated by the solid line. 3. Results and Discussion 3.1. Central Positions of Fitted Gaussians n any analysis of diurnal variations recorded by multidirectional telescopes the RA of the anisotropies (usually taken as the phase of the first harmonic) is an important parameter, indicating the azimuthal direction of a referenc. e axis of an anisotropy. This direction, calculated from the temporal variations of cosmic ray data, can be subjec.t to modulation by the Earth's magnetic field [Rao et al., 1963] and possibly the interplanetary magnetic field [Nagashima et al., 1982]. Even without these modulations the maximum variation in the count rates recorded by east pointing, vertical, and west pointing instruments should be obse.rved earliest by the east pointing telescope, latest by the west pointing telescope, and at an intermediate time by the vertical instrument. Figure 2 shows the best fit centers (tx, t2) of the two Gaussians plotted with respect to the offset of the asymptotic longitude of view of the instruments. All offsets have been referenced to the vertical direction (i.e., 0 ø longitude) by the geometrical position of the center of the corresponding telescope's direction of view. We note that the values of t and t 2 show that east viewing telescopes detect the anisotropies earlier than west viewing telescopes, as expected. Furthermore, we have confirmed from the coupling coefficients theory [Nagashima, 1971; Fufimoto et al., 1984] that a linear dependence of these observations is to be expected. We therefore have a high degree of confidence in this technique. The values of the slopes are very similar to those obtained from an examination of the coupling coefficients, but owing to the reasons outlined below, it is not very

4 370 HALL ET AL.' SDEREAL ANSOTROPES OF GALACTC COSMC RAYS Tail-in m= _ hrs per GV Loss cone... rn= _ hrs per GV 0 ' 100 Pmed (GV) looo Figure 3. Rigidity dependence of the fitted Gaussian centers. There is almost no dependence, as inferred from the statistically insignificant slopes (m). butions are independent of rigidity (the fitted lines have zero slope within errors) Rigidity and Latitude Distributions Figure 4 shows our attempts at deriving the rigidity spectra of the two distributions. n order to accurately obtain such a quantity the data must first be free from latitude variations. We have ignored any such variations and used the entire data set regardless of the latitude from which the observations were made. At first this may seem erroneous, but we have examined any correlation between our data set's latitudes of view and median rigidities and found almost zero correlation. Therefore we believe that the effects of latitude in our rigidity spectra will be distributed randomly about the true rigidity spectrum and just contribute to the scatter in the data. Some justification for this assumption is given in the following paragraph. Both spectra appear to be the same, having spectral indices of around The spectrum of the tail-in anisotropy is consistent with that determined by Nagashima et al. [1995a], but without data from instruments responding to higher-rigidity particles it is impossible to fully determine the rigidity dependencies of the practical to attempt to derive other quantitative information such as the rigidity spectra of the anisotropies from these comparisons. Figure 5 shows the latitude distributions of the fitted amplitudes (A and A2) of the Gaussians. The amplitudes are normalized to 500 GV by the rigidity spectra shown in Figure The difference between the slopes of the two distributions 4. We have fitted Gaussian functions to these distributions could have been accounted for by different spectral indices to the anisotropies, but we will show that this is not possible. The difference between the two distributions may indicate that the upper cutoff rigidities of the two anisotropies are different, with one anisotropy having a greater proportion of its distribution subjected to geomagnetic deflection and modulation. We tested this possibility by calculating the distribution of expected phases which result from an anisotropy with a positive spectrum and a low upper cutoff rigidity (500 and 1000 GV) and compared this with the distribution of expected phases obtained from assuming a high cutoff rigidity (10000 GV). We confirmed that an anisotropy with a high upper cutoff which indicate that the loss cone is centered (with respect to celestialatitude) at 8 ø in the northern hemisphere, while the tail-in anisotropy is centered at 5 ø in the southern hemisphere. These positions are qualitatively in agreement with Nagashima et al's [1995a, b] model but much closer to the celestial equator than the model would suggest. Furthermore, the results suggest that the loss cone extends much farther southward than the model would imply. With regard to our determination of the rigidity spectra of the anisotropies we have renormalized all the original amplitudes in Figure 4 by these two latitude distributions and repeated the spectral determinations. We obtain the same results (within errors) but note that the scatter rigidity would result in a much steeper distribution of observed in both distributions is markedly reduced, such that in each phases than that of an anisotropy with a low cutoff rigidity. The coupling coefficients used for such a comparison were those case the values of chi-square have decreased by more than a factor of 2 compared with those of the original determinations applicable to the harmonic formalism of diurnal anisotropies, of the spectral indices. The marked improvement in the fits so any quantitative analysis of the comparison to obtain a most leads us to conclude we were justified in originally ignoring the likely upper cutoff rigidity to the anisotropies would be inac- latitude variations. curate. n the rest of this paper, t and t 2 are all normalized to the vertical viewing direction by the fitted lines in Figure 2. Figure 3 shows our examination of t and t 2 for rigidity effects. We see that essentially, the positions of the two distri- Without doubt the most interesting result of this paper is obtained when we examine the latitude distributions of t and t 2. Figure 6 presents these distributions. The loss cone's center (t2) is essentially constant with respect to the declination of effects. Loss cone anisotropy rigidity spectrum m= Tail-in anisotropy rigidity spectrum. 0..L..... _.,... _'i...,, i O.Ol o.ool loo Pmed (GV) 1ooo t...i. 1oo Pmed (GV) 1ooo Figure 4. Rigidity spectra of the two anisotropic distributions.

5 HALL ET AL.' SDEREAL ANSOTROPES OF GALACTC COSMC RAYS 371 :. : øo Latitude (deg) Latitude (deg) Figure 5. Latitude distributions of the amplitudes of the two anisotropic distributions. view. Conversely, t appears to depend strongly on the declination of view. There are two implications of this result. First, the results in Figure 6 may imply that the loss cone's distribution is symmetric about its reference axis, while the tail-in anisotropy may be asymmetric. Second, the results in Figure 6 may explain the N-S asymmetry of the sidereal diurnal variation mentioned in section 1. From Figure 6 it is obvious that the temporal separation of the maximum and minimum of the data depends on the latitude of view of the telescope. f one refers to the data presented in Figure 1, the effect is even more ysis techniques to obtain the 24-hour wave contained in such data. n trying to understand these anisotropic distributions it would be interesting to view them as contour or color maps in the celestial and galactic coordinates. n the future we plan to present these results elsewhere, but for now we simply note that the loss cone would be centered high in the northern galactic hemisphere (about 75 ø latitude), while the tail-in anisotropy would be located around equatorial to midsouthern latitudes. striking. The position of the loss cone (deficit in flux) appears to have had little change in the four charts, while the tail-in 4. Conclusion anisotropy has clearly changed position. n Figure 1 we can see We have fitted a model comprising two Gaussian functions that the loss cone has RA scattered between 1300 and 1400 (equation(1)) to the average sidereal daily variations recorded sidereal time for all four sets of data. Also in Figure 1 there is a monotonic change in the RA of the tail-in anisotropy from about 0400 sidereal time, as observed by the 2S telescope, to 0800 sidereal time, as observed by the N telescope. From Figure 6, in the southern hemisphere the temporal separation of the anisotropies closer to 12 sidereal hours (9.25 hours at 45øS), while in the northern hemisphere this separation is by 48 components of the two-hemisphere network of underground muon telescopes. The Gaussian model is a good representation of the daily variations in the data and is useful for obtaining parameters which can be used to examine a recent model of the galactic anisotropy [Nagashima et al., 1995a, b]. The technique yields logical directions (t 2 and t ) of the loss cone and tail-in anisotropies when considered in relation to the closer to 6 sidereal hours (5.75 hours at 45øN). We postulate viewing directions of the component telescopes, similar to the that this may naturally explain why the first harmonic of the daily variation derived from southern hemisphere data is larger more usual method of harmonic analysis. We have shown that the assumption in the Nagashima et al. model, that the two than that derived from data recorded in the northern hemiconstituent anisotropies' directions were independent of rigidsphere. An example of this RA dependence can also be seen clearly in Figure 1 of Mori et al. [1995] from the high rigidity data observed at the Matsushiro underground station. n the future we plan to simulate this effect and to use Fourier anality, is valid. The analysis has also shown that the two anisotropies have similar rigidity spectra. We agree that the model of Nagashima et al. [1995a, b] can explain the northern and southern hemisphere observations of the sidereal diurnal variation but that it may need to be refined to take into account some asymmetry of the tail-in anisotropic distribution. Nagashima et al. claimed that the tail-in anisot- 24 ropy should be symmetric about a reference axis with declina- O Tail-in tion 24 ø south and right ascension 0600 sidereal time. We have., - Loss cone... i... ;... shown that the tail-in anisotropy may be asymmetric about its reference axis. We believe that the results indicate that this 20- ß 'i... it""i 16- asymmetry an underground muon telescope's 12- ß... ' '.'... i $'"'!!... :... i! Latitude (degrees) Figure 6. Latitude distributions of the fitted Gaussian centers to the two anisotropic distributions. is manifested as a maximum in the daily variation of count rate, having a right ascension related to the declination of view. From our analysis it appears that the loss cone component of the model is much more symmetric about its reference axis, close to 1300 sidereal time. Furthermore, the analysis and results suggesthat the asymmetry in the tail-in anisotropy may cause the temporal separation of the maximum and minimum in the daily variation to be about 3 sidereal hours closer in the northern hemisphere than in the southern hemisphere. This may produce a larger first harmonic in southern hemisphere data which are analyzed by Fourier techniques and may naturally explain the observed north-south asymmetry in the amplitude of the first harmonic of the sidereal daily variation.

6 372 HALL ET AL.: SDEREAL ANSOTROPES OF GALACTC COSMC RAYS n the future we plan to repeat this analysis but to separate the data into two sets according to the polarity of the Sun's magnetic field. n this way we can examine whether or not some relationship between the galactic anisotropies and the magnetic polarity of the heliosphere exists. t may also be possible to separate the data according to solar activity (for example, the solar minimum and maximum periods) and to investigate the effects of solar activity on the galactic anisotropies. We also plan to examine the modeled count rates and to chart them in celestial and galactic coordinates to obtain a better understanding of the anisotropies' origins. Acknowledgments. This work was supported by research grants from the Japanese Ministry of Education, Science, Sports and Culture, the nternational STEP project (representative S. Kato, Kyoto University, Japan), and the Australian Research Council. This work was carried out by the joint research program of the Solar-Terrestrial Environment Laboratory, Nagoya University. D. L. H. was supported by the Japan Society for the Promotion of Science through a postdoctoral fellowship. Shinshu University greatly appreciates financial support from the Hitachi-Device Co., Oki-Denki Co., and Toshiba- Jyouhou Co. The authors gratefully acknowledge the help received from the TasmanJan Hydro-Electric Commission and would also like to thank K. Newman and V. Newman at Tarraleah in Tasmania, Australia, for their invaluable assistance during periods of maintenance work at Liapootah. The Editor thanks J. A. Lockwood and the other referee for their assistance in evaluating this paper. References Aglietta, M., et al., A measurement of the solar and sidereal cosmic-ray anisotropy at E 0 10 TM ev, Astrophys. J., 470, , Cutler, D. J., and D. E. Groom, Mayflower mine 1500 GV detector: Cosmic ray anisotropy and search for Cygnus X-3, Astrophys. 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( jøhn'humble@utas'edu'au) Z. Fujii and K. Fujimoto, Solar-Terrestrial Environment Laboratory, Nagoya University, Nagoya 464, Japan. (Received March 26, 1997; revised June 20, 1997; accepted August 13, 1997.)