The influence of the sidereal cosmic-ray anisotropies originated on the tail- and nose-boundaries of the heliomagnetosphere (HMS) upon the solar cosmic-ray anisotropy produced inside the HMS
© 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 2010
Received: 7 January 2009
Accepted: 26 February 2010
Published: 6 August 2010
The solar diurnal variation of cosmic rays was considered to be fully explained by the diffusion-convection theory. Recently, however, it has been found that the geographic latitude distribution of the yearly averaged diurnal variations observed with the neutron monitors and the muon telescopes on the ground does not agree with that expected from the theory. The difference between the two distributions is observed almost every year, and it is especially remarkable in the solar activity minimum period in the positive polarity state of the solar polar magnetic field, when the diurnal variation reduces its magnitude and shifts its phase towards the morning side. It is shown that such a difference is produced by the seasonal variation of the sidereal heliotail-in and helionose-in anisotropies with respective right ascensions of 6 h and 18 h according to the following process. Generally, if any sidereal anisotropy from the right ascension α is subject to the seasonal variation with its maximum and minimum at the times when the Earth is closest to and farthest from the source of the anisotropy, respectively, located through its direction at the boundary of the HMS, it produces a yearly averaged residual flux from 0 h LT in solar geographic polar coordinates regardless of its direction (α). This residual flux from 0 h LT produces the difference mentioned above.
The modulation of galactic cosmic rays in the heliomagnetosphere (HMS) has been considered to be described by the diffusion-convection theory first proposed by Parker (1958) and theoretically formulated by Gleeson and Axford (1967). On the basis of this theory, many authors have numerically solved the so-called diffusion-convection equation and tried to explain various modulation phenomena (e.g. Gleeson, 1969; Fisk, 1971; Dorman and Milovinova, 1973; Kota, 1975; Moraal and Gleeson, 1975; Earl, 1976; Jokipii and Kopriva, 1979; Moraal et al., 1979; Jokipii and Davila, 1981; Bieber and Pomerantz, 1983).
The solar diurnal variation of cosmic rays was also one of the subjects of the modulation. The most remarkable feature of the variation is seen in its phase shift from the evening side to the morning side with the two solar-cycles’ periodicity corresponding to the polarity reversal of the solar polar magnetic field from the negative (N-) to the positive (P-) state, as will be shown later (cf. Nagashima et al., 1986).
The theoretical simulation of the variation with a special emphasis on the effect of the polarity-dependent heliolatitudinal drift motion of cosmic rays that have been pointed out by Jokipii and Kopriva (1979) could explain the observed shift and showed that the diurnal variation is fully explained by the diffusion-convection theory (Munakata and Nagashima, 1986). Recently, however, this conclusion has been contra-indicated by the following evidence. As stated in Abstract, the observed geographic latitude distribution of the yearly averaged diurnal variations largely deviates from that derived from the solar anisotropy (FDC) due to the diffusion-convection of cosmic rays with any reasonable rigidity spectrum. It will be shown in the following sections that such a difference would come from the seasonal variation of the sidereal heliotail-in anisotropy (FT) of cosmic rays from a right ascension (αT) of 6 h and the declination (δT)of −24° and also of the helionose-in anisotropy (FH) from αH = 18 h and δH > 0°, both of which are thought to be produced respectively by the cosmic-ray accelerations on the tail and nose boundaries of the HMS (cf. Nagashima et al., 1998, 2005).
In 1998, the existence of such a sidereal anisotropy called the tail-in anisotropy FT(αT = 6 h) and of its seasonal variation was discovered by observations at Hobart underground muon station (geographic lat. (λ)43°S, long. (φ) 147°E; median energy (Em) 184 GeV; Jacklyn, 1966, 1986; Nagashima et al., 1995, 1998). However, its residual flux FTSO in the geographic coordinates was not explicitly found by observations because of the large influence of FDC. The existence of FTSO is confirmed in the present analysis and provides a firm basis for the interpretation of the above-mentioned difference between the distributions of the yearly averaged diurnal variations observed and those theoretically derived by the diffusion-convection of cosmic rays.
2. Solar Diurnal Variation of Cosmic Rays
The solar anisotropy F(y) of cosmic rays with an amplitude F(y) and a phase Φ(y) at a time y (0–1) in a unit of 1 year produces the diurnal variation D(j, y) with an amplitude D(j, y) and a phase ϕ(j, y) at a station j. For the convenience for the following discussion, y = 0 is set at the time of the December solstice. The yearly averages of these variables are expressed without y. The observed D(j, y)s used in the following analysis are those of neutron monitors (Em ∼ 20 GeV) at the old and new WDC-C2 Centers for Cosmic Rays*1 and the muon telescopes at Nagoya (Em ∼ 60 GeV, λ = 35.1°N, φ = 137°E; Sekido et al., 1975; Fujii et al., 2000) in the period of 1965–2007.
D(j, y) reverses its direction toward 18 h ∼ 24 h from ∼ 12h ∼ 18 h LT at stations with high latitude-like phase displacements, while it rotates its direction anticlockwise toward 0 h ∼ 6 h from ∼ 6h ∼ 12 h at stations with low latitude-like phase displacements (cf. Fig. 7). For the sake of convenience, these two types of variation are called the loop-type and the morning-type, respectively. Almost all the phase shifts toward the nocturnal side occurred in January of 1996, and its duration period of the reversal depends on λ and the cut-off rigidity pc at the station; it is less than several solar rotations.
The magnitude R(j) of the total sum of D(j, y)’s in the respective duration periods in Fig. 8 shows a north-south (N-S) asymmetric latitude distribution which has the maximum at Hermanus (λ = 34.4°S), a considerably large value even at the South Pole (λ = 90°S), and almost no response at the northern high-latitude stations Inuvik (λ = 68.4°N), Thule (λ = 76.6°N), and so forth. Note that the exceptionally large R(j) observed at Climax (λ = 39.4°N), Rome (λ = 41.9°N), and Jungfraujoch (λ = 46.6°N) in the northern hemisphere in Fig. 8 seems not to be contradictory to the N-S asymmetry, as will be explained later, and also that R(j)’s of the morning-type variation at Tokyo (λ = 35.8°N), Nagoya (λ = 35.1°N) and Beijing (λ = 40.1°N) are excluded from the figure because of their different character.
The reversed vectors at Hermanus do not overlap with or cross other vectors before or after the reversal, which is contrary to those at other stations, and seem to show the anticlockwise movement with time if the three vectors right before the reversals are included (cf. Fig. 7).
In relation to this movement of D(j, y) at Hermanus, the precursory phenomena of the phase anomaly seem to have appeared as the amplitude reduction of D(j, y) at other stations in the several periods of Oct. Nov., and Dec. 1995 (cf. Fig. 7).
The influence of F(y)T also appears in the anomaly-enhanced period (AEP) in the next winter season shown by the bold-faced symbols with the mark B in Fig. 7. Although these vectors do not show the clear phase reversal, their movements can be regarded as the phase anomaly as will become clear later. Among them, D(j, y)’s at Hermanus and Potchefstroom show a morning-type variation in the period from around November that is different from the looptype variation starting from January in the previous season. This difference in type would be due to the difference of ϕ(j, y)DC’s between the two periods, as will be made clear later. In the same period, D(j, y) at the low-latitude station Beijing also starts its phase change toward ∼6 h LT, and this can not be explained by the diffusion-convection theory. In marked contrast with the clear plateau-type variation at Beijing (λ = 40.1°N; pc = 8.9 GV), D(j, y) at Tokyo (λ = 35.8°N; pc = 11.5 GV) shows only a small change, and the one at Nagoya (λ = 35.1°N, pc = 11.9 GV) does not show any recognizable change. This would be due to the fact that the larger anomaly would be more likely to appear for larger |Δϕg(j, y)|, as its values at Beijing and Tokyo are larger than that at Nagoya by about 1.5∼2 h and ∼1 h, respectively (cf. Yasue et al., 1982; Fujimoto et al., 1984). The reason for the Δϕg(j, y)-dependence of the anomaly will be made clear later.
In the next section, a detailed explanation will be given for the origin of the phase anomaly, and at the same time it will be shown that this phase anomaly could explain the D-anomaly pointed out previously.
3. Influence of the Tail-in Anisotropy on the Solar Anisotropy
The tail-in anisotropy is the sharply concentrated excess flux FT with axis-symmetric distribution along the direction of α = 6 h and δ = −24°.
FT is thought to be produced by the acceleration of galactic cosmic rays on the tail boundary of the HMS.
FT increases and decreases in the P- and N-states, respectively, and varies proportionally to the solar activity.
The magnitude of FT at the Earth’s orbit is influenced by the strong magnetic field near the Sun and shows its maximum at the December solstice, when the Earth is closest to the tail and its minimum when it is the farthest from the tail, at the June solstice. Therefore, the tail-in anisotropy is expressed by F(y)T at a time y (0–1) in 1 year intervals in the sidereal polar coordinate system (r,α,S) and also by F(y)TSO in the geographic polar coordinate system (r,θ,ϕ).
Their phase ϕ(j, y) in the second quadrant (90°–180°) of the harmonics coordinates in Fig. 13 shows the morning-type variation, while in the third quadrant (180°–270°) it shows the evening-type.
The morning- and evening-type variations are enhanced with the advancement and the retardation, respectively, of ϕ(j, y).
At the boundary between the morning- and evening-type regions, the variation of D(j, y) is small, as is observed at Rome in Fig. 13, indicating the transition between the two types.
These characteristics are most clearly observed in the variations from late 1993 to early 1994 in Fig. 13 and can safely identify them as being due to the phase anomaly. Among these variations, the one at Beijing stands out. As has been pointed out previously, this kind of variation at Beijing can be observed almost every year in the P-state (1989–2000), with its maximum in 1993–1994 (cf. Fig. 6). Nevertheless, the phase anomaly was discovered first in the solar activity minimum period (1995–1996) when the phase anomaly at Beijing shows rather a negligibly small value. This is due to the following reason. The enhancement of the phase anomaly is proportional to the ratio , which is variable depending on the cut-off rigidity at each station. In the solar activity maximum periods, the enhancement of the phase anomaly in the low latitude region (Beijing) can be observed, but the one in the high latitude region is difficult to be recognized, as D(j, y)DC in the region is very much larger than that at low latitudes (cf. Fig. 6). On the contrary, in the solar activity minimum period, although D(j, y)TSO becomes smaller with the decrease of the solar activity (Nagashima et al., 2004, 2005), the corresponding D(j, y)DC also decreases much more severely and produces large values of β, especially in high latitudes (cf. Fig. 6). This causes clear enhancement of the phase anomaly in almost all of the latitude regions in the solar activity minimum period (1995–1996), (cf. Fig. 7).
The above analysis reveals that the two anisotropies FT and FH would influence the solar anisotropy (FDC) and would produce the previous D-anomaly in Section 1. We now attempt to explain the D-anomaly by using FT as a representative for the two anisotropies.
Even if the separation would be successful, the obtained FTSO and FHSO could not provide any information on the sidereal anisotropies (FT and FH) responsible for them, because they can be produced by any sidereal anisotropies from arbitrary right ascensions (αS) as long as they are subject to the seasonal variation with their maximum and minimum at the times when the Earth is closest to and farthest from their sources, respectively, as has been pointed out in Introduction. Their responsible origins can be inferred only from D(j, y)TSO and D(j, y)HSO superposed on D(j, y)DC. As has been pointed out previously, the seasonal variation of D(j, y)TSO indicates that F(y)T is maximum near the December solstice (α = 6 h), with a sharply concentrated flux from the southern hemisphere δ = −24°, while that of D(j, y)HSO is produced by F(y)H, which is a maximum near the June solstice (α = 18 h) with a broad peak at the northern hemisphere (δ > 0°). As the directions of these fluxes inferred from the present analysis coincide fairly well with those obtained by the previous analyses of the sidereal diurnal variations (Nagashima et al., 1998; Nagashima and Fujii, 2006), the origin of the excess flux from 0 h LT can be regarded as being due to the sidereal heliotail-in and helionose-in anisotropies.
Finally, it should be noted that the present conclusion does not necessarily refute the following possibility as the origin of the D-anomaly. The sidereal anisotropy which produces the required seasonal variation is not necessarily persistent throughout a year. The most extreme case of such an anisotropy is the cosmic-ray flux produced by the acceleration in a short-term period at a point on the boundary of the HMS. Such a flux is thought to be produced very frequently at any one time at any one place, as the acceleration would not always be limited only to the tail and nose boundaries, although its mechanism itself can not be directly confirmed. If such a flux happens at a point when the Earth crosses the line through the point and the Sun, it can be regarded as a kind of seasonal variation of the anisotropy required for the D-anomaly. As such happenings would be very frequently expected, their overall contribution to the D-anomaly would not be negligible.
The yearly averaged solar diurnal variation of cosmic rays observed with the neutron monitors and the muon telescopes on the ground does not coincide with that expected from the diffusion-convection theory. Their difference is due to the excess flux from 0 h LT which is the yearly averaged flux in solar geographic polar coordinate, of the seasonal variation of a sidereal anisotropy having right ascension α with its maximum and minimum, respectively, at the times when the Earth is closest to and farthest from its source. The present analysis found two kinds of anisotropy: one shows a maximum near the December solstice (α = 06 h), with a sharply concentrated flux from the southern hemisphere (δ = −24°), and the other shows a maximum near the June solstice (α = 18 h), with a broad peak in the northern hemisphere (δ>0°). The anisotropies with these directions can be identified respectively with the heliotail-in anisotropy from α = 06 h and δ = −24° (cf. Nagashima et al., 1998) and the helionose-in anisotropy from α = 18 h and δ > 0° (cf. Nagashima and Fujii, 2006). Therefore, it is concluded that the departure of the yearly average of the observed solar diurnal variation of cosmic rays from that predicted by the diffusion-convection theory is due to the excess flux from 0 h LT produced by the seasonal variations of the heliotail-in and helionose-in anisotropies, with their maximum and minimum at the times when the Earth is closest to and farthest, respectively, from their sources.
It is noted further that the agreement of the directions of the anisotropies with those derived from the previous observations of the sidereal diurnal variations mentioned above support the previous conclusion (Nagashima et al., 1998; Nagashima and Fujii, 2006) that the major axis of the HMS in the noseward direction expected from the sidereal cosmic-ray anisotropies FT and FH is in the direction of α ∼ 18 h and δ ∼ 24° and does not coincide with that (αN = 16.8h, δ = −15° ∼ −17°) inferred from the relative motion of the solar system to the neutral gas (cf. Ajello et al., 1978; McClintock et al., 1978).
The authors express their sincere appreciation to the staffs at all the neutron monitor stations in the world and also to the staffs at the muon telescope station, the Cosmic-Ray Research Section, Solar-Terrestrial Environment Laboratory, Nagoya Unversity, who have been responsible for the continuous long-term observations of cosmic rays.
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