The existence of cosmic ray sidereal anisotropies of galactic and solar origins with energies lower than 104 GeV and their modulation caused by the presumed behavior pattern of the heliomagnetosphere and of its neighboring gaseous matter in interstellar magnetic field
© The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB 2012
Received: 21 August 2011
Accepted: 26 February 2012
Published: 16 August 2012
It is shown that the sidereal anisotropy (SiA) of cosmic rays (CRs) with energies smaller than 104 GeV consists of three kinds: one (GA) is of galactic origin from the direction ΦG (αG = 0 hr; δG = −20°), and the other two (tail-in TA and nose-in HA) are of solar origin from the respective directions ΦT (αT = 6 hr; δT ∼ −24°) and ΦH (αH = 18 hr; δH > 0°) and supposed to be produced by the acceleration of CRs on the tail and nose boundaries of the heliomagnetosphere (HMS). This conclusion was arrived at in 1995 after a long-term delay since the beginning of CR observations in the early 20-th century. This delay was mainly due to the inconsistency among observations caused by the belief that the sidereal anisotropy must be unidirectional in space. The inconsistency has been solved at least qualitatively by the discovery of GA and TA. These anisotropies, including also HA, are subject, respectively, to their proper solar modulations in the HMS characterized by a polarity reversal every 11 years of the solar polar magnetic field and solar activity dependence with an 11-year periodicity. By using these modulation patterns, the origins of the three anisotropies have been determined. TA and HA thus determined inversely produce the following kinds of evidence and problems in the HMS: (1) the structure of the HMS, (2) acceleration of CRs on the boundary of the HMS, (3) CR Lens Effect of the HMS for the sharp concentration of TA and HA, (4) the proper motion (VHMS) of the HMS relative to neighboring stars, (5) the proper motion of interstellar gaseous matter (including the magnetic field) relative to neighboring stars, and (6) the existence of the Subordinate HMS surrounding the HMS for the explanation of the duality of the motion of the HMS and also of the absence of the Compton-Getting (C-G) effect on the HMS. The present paper not only presents a brief summary of the studies of CR sidereal anisotropy made by many researchers during the 20th century leading to the present understanding, but also presents some problems to open up a new vista of the future.
The sidereal anisotropy SiA of CRs has been inferred indirectly from observations of the sidereal daily variation (S i D) on the ground ever since the discovery of CRs (e.g. Forbush, 1937a, b, 1939). Recently, due to greatly improved observational methods, the direct observation of SiA has become possible in the high-energy region by observations with cosmic ray and gamma-ray detectors (e.g. Amenomori et al.,2004, 2005; Guillian et al., 2007; Abdo et al., 2008; Abbasi et al., 2010). This method is, however, not applicable to SiA in the lower energy region as cosmic rays cannot maintain their direction hindered by the influence of the heliomagnetic and geomagnetic fields. In such a low-energy region, S i D, with the frequency 366 cycles/yr must be detected under the following difficult condition that it is always superposed by the solar daily variation (S o D) with the adjacent frequency of 365 cycles/yr produced inside the HMS and disturbed by the daily variations of the Earth’s atmospheric pressure, temperature and wind velocity. If S o D is constant, its yearly average in units of sidereal time, called the spurious sidereal daily variation (SS i D), becomes zero and does not affect S i D. Practically, however, as S o D is supposed to be almost always disturbed by various kinds of noises, the elimination of SS i D is indispensable. In addition to such indirect influences upon S i D, some of the HMS-phenomena, which directly influence S i D, have been discovered successively during a long elapsed time, such as the polarity reversal every 11 years of the solar polar magnetic field. It is not an exaggeration to say that the history of the study of S i D in the low-energy region (≤104 GeV) has been the history of the study of the direct and indirect influences upon S i D. In the following, we present a brief summary of the study of SiA of CRs made by many researchers with a dedicated attention to the direct and indirect influences in order to reach a better understanding of the nature of SiA and the features associated with it.
2. Influence of SSiD on SiD
The attempt to eliminate SS i D from the observed S i D of CRs has continued ever since the observation of S i D began in the early 20th century. Besides the well-known atmospheric influence on S i D (e.g. Myssowsky and Tuwim, 1928; Sekido,1943; Duperier, 1944, 1949; Olbert, 1953; Jacklyn, 1954; Trefall, 1955; Dorman, 1957; Wada, 1960), some of the elimination methods are presented in advance to simplify the following discussion on S i D.
Type-1.—The East-West difference method.
Type-2.-The Farley-Storey method.
Type-3.—Correction for stationary solar anisotropy (CSSA).
Ex. 1—Some correction effects, shown in Fig. 4, indicate that almost all the s with the phase in the 4th quadrant (18 hr–24 hr), observed by telescopes pointing to the northern hemisphere, change their phases to the 1st quadrant (0 hr–6 hr) indicating that the contain a very large SSiD. In Figs. 4(a) and 4(b), the process of the correction method is shown.
Ex. 2—The correction would produce a serious influence on the interpretation of the sidereal anisotropy. The following is another example. In 1966, the bi-directional sidereal anisotropy model was presented by Jacklyn (1966), which was the first concrete anisotropy model ever derived from the observations of sidereal diurnal and semi-diurnal variations by the underground muon telescopes at the northern and southern stations Budapest (47°N) and Hobart (43°S) in the period 1959–1962. The outline of his result is explained by the schematic diagram of the observation in Figs. 5(a) and (b). In it, the resultant of the observed and expressed by dotted curve shows a sharp peak at 18 hr in the N-hemisphere and 6 hr in the S-hemisphere, suggesting that some concentrated CRs are arriving, respectively, from opposite directions probably along a straight line. This is called bi-directional anisotropy, being in accord with the L. Davis model for a pitch angle anisotropy of intensity (Davis, 1954). This model was soon afterwards reconfirmed by directional observations in the N- and S-hemispheres, making use of the Cerenkov detecting telescope at Nagoya (γ = 35°) (Sekido et al., 1968, 1971), and also by the ion-chamber data at the northern and southern stations Cheltenham (γ = 39°N) and Christchurch (γ = 44°S), (Nagashima et al., 1968). However, the shown in Figs. 5(a) and (b) were not corrected by the CSSA method which was not known in those days. The real SiD1 has been obtained later by adding the conjugate vectors and according to the simplified CSSA, as shown in Fig. 5(c). S i D 1 is common in both hemispheres and the resultant of S i D 1 with or produces a sharply concentrated variation with a phase of 6 hr common in both hemispheres, asshown in Fig. 5(d), suggesting the disappearance of the essential properties of the bidirectional anisotropy model.
On looking back to 1971, we notice that we abandoned at that time the most important principle that sidereal anisotropy should be studied by analyzing at least the sidereal diurnal and semi-diurnal variations and then composing them following the procedure which successfully discovered the bi-directional anisotropy. If this principle has been applied at that time, we would have noticed immediately after the disintegration of the bi-directional anisotropy that the diurnal and semi-diurnal variations at Budapest and Hobart had a common peak at 6 hours, in the N- and S-hemispheres, suggesting the existence of a sharply concentrated uni-directional anisotropy from 6 hours, as shown in Fig. 5(d). Because of this failure in 1971, almost 25 years passed before its discovery in 1995 (Ref. 3). It is further noted here that, during this lost period, only one paper was presented, by Cutler and Groom (1991), concerning the study of the sidereal anisotropy by composing the 1st, 2nd and 3rd harmonic components, and a considerably interesting image of the anisotropy was obtained (cf. Ref. 3).
Ex. 3—The simplified CSSA method applied to the conjugate stations Cheltenham (γ = 39°N) and Christchurch (44° S) is presented in the following. The long-term averages of ’s at these stations are shown in Fig. 6, together with that at the equatorial station Huancayo (γ = 12° S), (cf. Ref. 3). In it, the north-south difference of ’s at Cheltenham and Christchurch is clearly seen. In those days of the analysis (1976), this difference was misinterpreted by Nagashima and Mori (1976) as being due to some north-south asymmetric sidereal vectors being superposed on a common sidereal vector, in spite of the earlier findings of their real origin in 1971 by Nagashima and Ueno. Fortunately, the decomposed vectors and shown in Fig. 6 can be identified with those derived from the simplified CSSA method at the two conjugate stations Cheltenham and Christchurch. The persistent difference between S i D 1 ’s at these stations is shown by their phase dif-ference classified into morning (0–12 hr) and evening (12–24 hr) sides by the open and solid circles in Fig. 7. This asymmetry is very stable as can be seen also in the summation dial of the yearly vectors shown in Fig. 8(a). On the other hand, S i D 1 almost coincides with at Huancayo, indicating the negligible influence of at the equatorial station Huancayo (cf. Fig. 6). It is emphasized that these two vectors show remarkable yearly fluctuations, especially in the period 1948–1957, of the positive polarity (P-) state of the solar polar magnetic field shown in Fig. 8. Especially, the solar activity minimum period in the P-state seems to be a special epoch for the appearance, or the phase change, of the sidereal anisotropy, which occurs every 22 years. The occurrences of the event have been successively observed in 1954 (Conforto and Simpson, 1957), in 1975–1976 (Swinson, 1976; Nagashima et al., 2010) and in 1996 (Nagashima et al., 2010).
Ex. 4—The simplified CSSA was applied also to S i D 1 ’s and AS i D 1 ’s at the conjugate neutron monitor stations in the N- and S-hemispheres which were artificially made by averaging respectively the s and of almost all the data of 473 station-years in the northern stations and 147 station-years in the southern stations in the period of 1958–1979. The averaged and are shown in Fig. 9(a) with the labels N or S. Their sum and difference between the N- and S-hemispheres express respectively and those residuals shown in Figs. 9(b) and 9(c). and in Fig. 9(c) are almost the same in magnitude and their phases are, respectively, in the proper directions of 18 hr and 0 hr in the N- and S-hemispheres, justifying inversely the simplified CSSA method applied to the artificial conjugate stations. The phase of the real S i D 1 is 6.8 ± 0.3 hr and almost coincides with that observed at Hobart (γ 43°S; E m 184 GeV) as shown in Fig. 4(a). However, the phases at London (γ 52°N; 60 m.w.e.) and those in Figs. 4(a) and 4(b), deviate toward the mid-night side from 6 hrs. The deviation increases with the increase of cosmic-ray energy and reaches at the maximum ( = 6 hr) in the energy region ∼104 GeV observed by air showers at Mt. Norikura (36°N, 133°E) (cf. figure 9 in Ref. 3). Such an energy dependence was found in a wide range of rigidities (90–660 GeV) with the OHMA in the period 1976–1984 by Bercovitch (1984), as shown in Fig. 10.
In spite of such differences in phase in the low- and high-energy regions, the coincidences in phase observed by the neutron monitor (Ex. 4, ∼20 GeV, 1983), ion-chamber (Ex. 3, ∼67 GeV, 1976) and the underground muon telescope (Ex. 2, ∼184 GeV, 1966) seem to suggest the existence of some sidereal anisotropy in the low-energy region in space from α = 6 hours (Nagashima et al., 1983a, 1984). But this was not accepted unanimously at that time for the following reasons: (1) the difference of the phases in the low- and high-energy regions mentioned above cannot be explained by the difference between CR deflections produced by the single anisotropy in the HMS, (2) the signal of the anisotropy in the low-energy region (∼20 GeV) would be difficult to maintain its shape until its arrival at the Earth because of disturbance in the HMS and therefore the observed S i D 1 might be some residual of SS i D, and (3) the CSSA-method was not unanimously accepted in those days. Therefore, it took about another 20 years for the confirmation of such an anisotropy.
Although all the events corrected by the CSSA method do not directly connect with the image of sidereal anisotropy, they will be used to specify the discussion for the determination of the anisotropy, without any explanation of their complicated derivation process.
3.SiA in the HMS
Since the discovery of the polarity reversal of the solar polar magnetic field (Babcock, 1959; Howard, 1974a, b), its influence has been discussed actively in considerations of cosmic-ray intensity variations (e.g. Moraal, 1976; Nagashima, 1977 and references therein; Kuzmin et al., 1977; Nagashima and Morishita, 1980a, b; Kota and Jokipii, 1983; Nagashima, 1990 and references therein; Nagashima et al., 1991; Belov, 2000, references therein; Duldig, 2000 and references therein) and the cosmic-ray solar diurnal variation (Duperier, 1946; Thambyahpillai and Elliot, 1953; Gleeson and Axford, 1967; Kota, 1975; Moraal, 1976; Jokipii and Kopriva, 1979; Mori et al., 1981; Bieber and Pomerantz, 1983; Munakata and Nagashima, 1986; Nagashima et al., 1986 and references therein). The observational data of the cosmic-ray sidereal anisotropy, however, were limited in those days, but the theoretical expectation of the polarity dependence has been proposed by many authors in considering the interaction between interstellar and interplanetary magnetic fields, (e.g. Davis, 1954,1955; Sarabhai and Subramanian, 1966; Schatten and Wilcox, 1969; Marsden et al., 1976; Nagashima and Mori, 1976; Davies et al., 1977; Benko et al., 1979; Krainev, 1981). On the other hand, another approach to study S i D 1 has been made by putting special emphasis on the behavior of the CR orbits arriving at several specific stations from a specified SiA, (e.g. Speller et al., 1972; Marsden et al., 1976; Davies et al., 1979). As part of further progress of such studies, the general formulation of the solar modulation of the axis-symmetric SiA from an arbitrary direction was presented (Nagashima et al., 1982 Nagashima and Morishita, 1983, called hereafter Refs. 1 and 2; Yasue et al., 1985). According to this formulation, S i D 1 and S i D 2 produced by this modulation can be expressed respectively by the linear combination of the vectors selected from the eight basic vectors in the geographic coordinate depending on the direction and constituent of SiA. Hereafter, this formulation of the modulation is called the modulation model. The most characteristic feature of the modulation is that S i D 1 produced by SiA from the direction of the equatorial region is greater in the N- state than in the P-state, while, from the direction of the polar region, it is greater in the P-state than the N-state, or becomes almost equal in both states.
In addition to these problems, the following most important and difficult one must be added. In the northern hemisphere, the phase of the first harmonic vector S i D 1 of the sidereal anisotropy SiA varies from 0 hr to 6 hr depending on the energy; on the other hand, the phase of the second harmonic vector S i D 2 is ∼6 hr regardless of E m (Nagashima and Mori, 1976; Fujii et al., 1984; Mori et al., 1989; and references therein). On the contrary, in the southern hemisphere, and are all 6 hrs regardless of the energy. The solution for these problems will be discussed in the next section.
In relation to these phenomena, it would be worthwhile to mention that the anomalous enhancement of S i D 1 in the equatorial zone was observed at Sakashita (540 GeV) by Ueno et al. (1984) and at Matsushiro (220 m.w.e.) by Mori et al. (1989, 1993), which was not certain whether it is due to the North-South asymmetric distribution, or the equatorial anomaly. Although the anomaly failed to be explained by the unidirectional anisotropy, it is conducive to the determination of GA and TA that follows.
4. GA and TA of Three Kinds of Sidereal Anisotropy in the HMS
Nagashima et al. (1998) were indicating that at energies less than 104 GeV the amplitude of TA was decreasing with increasing energy, giving strength to the conclusion that TA was of solar origin. Remarkably, since that time it has been reported from a number of advanced experiments that TA continues to exist at energies in the multi-TeV region, raising new questions regarding the evidence for the solar origin of TA.
According to the previous analysis (cf. Ref. 3), the space distribution of the T-anisotropy (or TA) responsible for these can be expressed by a directional excess flux confined in a cone with a half opening angle from the direction approximately coincides with the heliomagnetotail direction inferred from the direction of proper motion of the solar system (Campbell and Moore, 1928), although it is emphasized that this is different from the inferred tail direction ) opposite to the relative motion of the solar system to the neutral gas (Ajello, 1978; McClintock et al., 1978). This difference will be discussed later.
5.Modulation of Anisotropies in the HMS
It is emphasized here that seems to be the same as to be produced by the C-G effect by the motion of the HMS, as their phases are considered to be the same as each other (18 hr). But, they differ in the following points. First of all, is a broad sinusoidal diurnal variation with a declination distribution of cos δ-type and has a flat energy spectrum (Gleeson and Axford, 1967). On the other hand, shows the sharply-concentrated diurnal variation with an N–S asymmetric δ-distribution (cf. Fig. 24) and has a soft energy spectrum which almost disappears in the energy region ≥300 GeV (cf. Fig. 19). Furthermore, is greater in an AN-period than a QN-period (cf. Eq. (5)). This is against the galactic origin hypothesis as Cg(tSi) must be smaller in the A-period than the Q-period like the behavior of the modulation pattern of , (cf. Eq. (1)). Therefore, the C-G effect of CRs cannot be observed in an energy region less than 104 GeV, as pointed out previously (Ref. 3).
6. Origin of GA, TA and HA, and the Related Discussion
6.1 Origin of GA, TA and HA
The structure of the HMS is surrounded by the nose-and tail-boundaries, and has a wavy neutral sheet at the heliomagnetic (HM) equatorial plane which divides the HM polarity states in the N- and S-hemispheres.
CRs are assumed to be accelerated uniformly all over the boundaries depending on the solar activity.
Modulation pattern of sidereal anisotropy by GA, TA, and HA.
22 yr period
11 yr period
Solar (Tail boundary)
Solar (Nose boundary)
The polarity dependence of Eq. (6) can be realized if the HMS tail is extended long enough to achieve the CR flux from the total sum of Rb larger than that of the tail-end region (Re) near the central line of the neutral sheet.
6.2 Direction of nose head of the HMS in space
The nose direction of the HMS can be determined by observation on the basis of the model. As pointed out earlier, the T- and H-anisotropies are observed in the respective directions and , both of which could be considered to constitute a straight line through the Sun; that is, the center line of the neutral sheet of the HMS. Therefore, the motion of the HMS would be in the direction and should produce the C-G effect of CRs from the direction of 18 hr. Contrary to this expectation, the C-G effect could not be observed (Nagashima et al., 1998). The non-existence of the effect is of importance with regard to the interaction between the HMS and the interstellar gaseous matter (IGM), as will be discussed in the next section.
6.3 The duality of the motion of solar system in space
On the other hand, the neutral particles in the IGM could not recognize the existence of the SuHMS owing to their long scattering mean free path in comparison with the scale of the SuHMS. Therefore, the particles are able to freely pass through the SuHMS and the HMS with the velocity and produce the motion observed in the solar system (cf. Fig. 28).
As above, the introduction of the two proper motions and relative to the neighboring stars could explain the duality of the motion of the HMS in space and prove also the absence of the C-G effect of CRs at low energies due to the motion of the HMS by the interaction of the SuHMS surrounding the HMS. Furthermore, the interaction of the SuHMS with the HMS can contribute to the acceleration of CRs at the boundary of the HMS required for the origin of TA and HA.
Finally, it is noteworthy that the existence of the motion of IGM relative to the neighboring stars has been found by the duality of the motion of the solar system in space probably for the first time.
6.4 Influence of TA and HA on SoA
On the contrary, S o D 1 (Hermanus) belongs to the X-type and almost all the characteristic points on the diagram are in the left-outside region of the net area. Such a deviation from the net area is not attributable to statistical errors, as almost all the deviations are distributed in the left-side area with respect to the iso-p u line of 103 GV. It is also noted that this area is forbidden, not only for the points derived from SoA with the present spectrum form but also for those with any reasonable spectra as far as SoA is an unidirectional form. Therefore, the distribution of the points is of the X-type and clearly indicates the existence of . However, there are two exceptional points similar to the 3 exceptional cases at Nagoya, which show very small R’s in the solar activity minimum periods (1996, ’97) as S o D 1 (Hermanus) of the X-type changed to the Y-type due to a phase shift toward ∼12 hours for a decrease of solar activity. It is emphasized that the appearance of these Y-type s at the two stations were in the same Q-period but occurred in different polarity states. Hermanus observed them in the N-state, while Nagoya observed them in the P-state. This is due to the phase shift with decrease of solar activity from ∼18 hr to ∼12 hr at Hermanus in the P-state and from ∼15 hr to ∼12 hr at Nagoya in the N-state, showing a good agreement with the solar modulation of the phase of S o D 1 mentioned earlier (Munakata and Nagashima, 1986).
It is emphasized that the influence of the sidereal anisotropies on the solar diurnal variation is not negligibly small.
The existence of CR sidereal anisotropies GA and TA was discovered in 1995 by the analysis of the observation of sidereal diurnal variations at the underground stations Hobart and Sakashita, and the ground station Nagoya, being incited by the casual finding of the seasonal variation of the sidereal diurnal variation at Hobart and also assisted by the acknowledged elimination method for the spurious sidereal variation produced by the CR solar anisotropy (cf. Table 1). The discovery enabled a unified explanation to be offered at least qualitatively for those conflicting observed phenomena of the sidereal variations in the past.
The sidereal diurnal variations and produced by GA and TA and another one by HA (cf. Table 1) are subject, respectively, to the three kinds of HMS modulation characterized by the polarity reversal of the solar polar magnetic field with 22-years periodicity and the solar activity dependence with 11-years periodicity (cf. Table 1). These modulation patterns together with the theoretical modulation model of CRs in the spherical HMS can determine their origins; one (GA) is of galactic origin from α = 0 hr and others (TA and HA) are, respectively, the sharply-concentrated CR fluxes along the neutral sheet of the HMS from α = 6 hr and 18 hr. The sharp concentration of the anisotropies can be produced by applying the CR-Lens-Effect of the HMS to the accelerated CRs on the boundary of the HMS with the short nose and the long tail together with the wavy neutral sheet.
The duality of the motion of the HMS observed, respectively, by the CRs and the neutral particles suggests the existence of the proper motion V IGM of the interstellar gaseous matter (IGM) including the magnetic field. produces the electromagnetic interaction between the HMS and IGM and forms the disturbed region surrounding the HMS, called the Subordinate HMS (SuHMS), which prevents the C-G effect expected to be caused by the relative motion between the HMS and the low energy CRs in IGM. In the high-energy region, however, as CRs can freely pass through the IGM and the SuHMS, the C-G effect can be observed in the direction of . On the other hand, as the neutral particles cannot recognize the existence of the SuHMS owing to their long scattering mean free path compared with the scales of the SuHMS, the particles can pass through the SuHMS with the velocity V IGM and produce the motion of V np observed on the HMS. As above, the solar modulation of CR sidereal anisotropies are intimately correlated with the behavior pattern of the heliomagnetosphere (HMS) and also with the CR solar diurnal variation produced by the diffusion-convection process inside the HMS. One of the most remarkable results of the present analysis is that the motion of the interstellar gaseous matter (IGM) relative to the neighboring stars could be estimated for the first time by using the duality of the velocities and .
However, the sidereal anisotropies of CRs and their related phenomena are not completely solved yet, as they are based on basic assumptions such as the acceleration of CRs on the boundary of the HMS, the motion of IGM in space, the formation of the SuHMS surrounding the HMS and so on. It is necessary to confirm these assumptions theoretically and experimentally not only for the sidereal anisotropies of CRs but also for the further development of the interaction between the HMS and the interstellar medium.
The authors express their sincere appreciation for the long-term continuous observations of cosmic ray diurnal variations performed with the neutron monitor network in the world by many researchers, with the ion chambers at Godhaven, Cheltenham, Huancayo and Christchurch by the Late Dr. S. E. Forbush and his colleagues, and at Yakutsk by the Late Professor Emeritus Yu. G. Shafer, Dr. G. B. Shafer and their colleagues, with the underground muon telescope at Cambridge, Hobart by the Late Drs. A. G. and K. B. Fenton, Dr. J. E. Humble and their colleagues, with the muon telescopes at Mawson, Antarctica by one of the authors (R. M. J.), Drs. J. E. Humble, M. L. Duldig and their colleagues and expeditionists, with the underground muon telescopes at Misato and Matsushiro by one of the authors (S. M.) and his colleagues, with the muon telescopes on the ground at Nagoya and the underground station at Sakashita by the Late Professors Emeritus Y. Sekido, K. Murakami and H. Ueno, the Late Dr. K. Fujimoto and their colleagues, with the air shower observation at Mt. Norikura (the University of Tokyo) by the Late Professor H. Ueno and his colleagues at Nagoya University and, finally, for the positive support for the data analysis of the World Data Center C2 for Cosmic Rays by the Late Dr. Y. Miyazaki, Dr. M. Wada, one of the authors (I. K.) and their colleagues. Without these observations and the analysis, the present result could not be obtained.
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