Magnetic Cycle Dependence of the Cosmic-Ray Diurnal Anisotropy

The two components of the solar diurnal variation observed with two detectors characterized by linearly independent coupling functions have been used to estimate the free space anisotropy vector during the period 1968–1995 using the least-squares method (LSM). The values of R_cshow 20-year magnetic cycle with the lowest values at solar activity minima for positive polarity (qA>0). A good correlation is obtained between R_cand the IMF magnitude. The amplitude of the radial anisotropy (A_R) shows 20-year magnetic cycle with the highest values around solar activity minima for qA>0 (1975–1976 and 1995), whereas that of the east-west (A) is minimum. This results in shifting the anisotropy vector to the earliest hours. The amplitude of the anisotropy is high around solar maxima and low around solar minima. It is also enhanced during the declining phase of solar activity (1971, 1984–1985, and 1991). Our results of the anisotropy have been used to calculate the cosmic-ray radial and transverse gradients. The value of the radial gradient exhibits a magnetic polarity dependence as well, with larger value during qA<0 than during qA>0.     

Study of the Cosmic Ray Diurnal Anisotropy During Different Solar and Magnetic Conditions

The pressure-corrected hourly counting rate data of four neutron monitor stations have been employed to study the variation of cosmic ray diurnal anisotropy for a period of about 50 years (1955–2003). These neutron monitors, at Oulu ( R _c = 0.78 GV), Deep River ( R _c = 1.07 GV), Climax ( R _c = 2.99 GV), and Huancayo ( R _c = 12.91 GV) are well distributed on the earth over different latitudes and their data have been analyzed. The amplitude of the diurnal anisotropy varies with a period of one solar cycle (∼11 years), while the phase varies with a period of two solar cycles (∼22 years). In addition to its variation on year-to-year basis, the average diurnal amplitude and phase has also been calculated by grouping the days for each solar cycle, viz. 19, 20, 21, 22, and 23. As a result of these groupings over solar cycles, no significant change in the diurnal vectors (amplitude as well as phase) from one cycle to other has been observed. Data were analyzed by arranging them into groups on the basis of the polarity of the solar polar magnetic field and consequently on the basis of polarity states of the heliosphere ( A > 0 and A < 0). Difference in time of maximum of diurnal anisotropy (shift to earlier hours) is observed during A < 0 (1970s, 1990s) polarity states as compared to anisotropy observed during A > 0 (1960s, 1980s). This shift in phase of diurnal anisotropy appears to be related to change in preferential entry of cosmic ray particles (via the helioequatorial plane or via solar poles) into the heliosphere due to switch of the heliosphere from one physical/magnetic state to another following the solar polar field reversal.     

Application of diffusion — Convection model to diurnal anisotropy data

The diurnal anisotropy of cosmic-ray intensity observed over the period 1970–1977 has been analysed using neutron-monitor data of the Athens and Deep River stations. Our results indicate that the time of the maximum of diurnal variation shows a remarkable systematic shift towards earlier hours than normally beginning in 1971. This phase shift continued until 1976, the solar activity minimum, except for a sudden shift to a later hour for one year, in 1974, the secondary maximum of solar activity.This behavior of the diurnal time of maximum has been shown to be consistent with the convective- diffusive mechanism which relates the solar diurnal anisotropy of cosmic-rays to the dynamics of the solar wind and of the interplanetary magnetic field. Once again we have confirmed the field-aligned direction of the diffusive vector independently of the interplanetary magnetic field polarity. It is also noteworthy that the diurnal phase may follow in time the variations of the size of the polar coronal holes. All these are in agreement with the drift motions of cosmic-ray particles in the interplanetarty magnetic field during this time period.     

Secular changes in the upper cut-off rigidity of the solar diurnal anisotropy of cosmic rays

We have calculated the upper cut-off rigidities applicable to the solar diurnal anisotropy of cosmic rays, for the period 1965–1979. Our results are consistent with those reported by others. We note that the mean values of the upper cut-off rigidities during 1975–1977 are less than 50 GV. This explains why no diurnal variation is observed by the muon detectors at Socorro (NM) at a depth of 80 m of water equivalent (MWE) for this period. The threshold (R_o) and the median primary rigidities (R_m) of response applicable to the underground vertical telescope at Socorro are 45 and 300 GV, respectively.     

Characteristics of Two-Way Cosmic-Ray Diurnal Anisotropy

We examine the deviation of the solar diurnal anisotropy vector from the 18 LT direction during the positive state of the solar cycle by assuming two anisotropies in free space. We use two detectors characterized by two linearly independent coupling functions. The median primary rigidity of response of these detectors covers the range 16 GV R _m 331 GV. Amplitude, direction, spectrum exponent, and the upper cut-off rigidity of each anisotropy have been calculated using the least-squares method over the time interval 1968–1988. This period covers a complete solar magnetic cycle. Only one anisotropy is dominant during each magnetic state of the solar cycle. The upper cut-off rigidity at which the dominant anisotropy vanishes varies between 50–250 GV. The direction of the dominant anisotropy vector points toward the 18 LT direction during the negative state of the solar cycle and toward earlier hours than 18 LT during the positive state. The non-dominant anisotropy is characterized by very high upper cut-off rigidity and sharper energy spectral.     

Study of the Diurnal Variation of Cosmic Rays during Different Phases of Solar Activity

The pressure-corrected hourly counting rate data of ground-based super neutron monitor stations, situated in different latitudes, have been employed to study the characteristics of the long-term variation of cosmic-ray diurnal anisotropy for a long (44-year) period (1965?–?2008). Some of these super neutron monitors are situated in low latitudes with high cutoff rigidity. Annual averages of the diurnal amplitudes and phases have been obtained for each station. It is found that the amplitude of the diurnal anisotropy varies with a period of one solar activity cycle (11 years), whereas the diurnal phase varies with a period of 22 years (one solar magnetic cycle). The average diurnal amplitudes and phases have also been calculated by grouping the days on the basis of ascending and descending periods of each solar cycle (Cycles 20, 21, 22, and 23). Systematic and significant differences are observed in the characteristics of the diurnal variation between the descending periods of the odd and even solar cycles. The overall vector averages of the descending periods of the even solar cycles (20 and 22) show significantly smaller diurnal amplitudes compared to the vector averages of the descending periods of the odd solar cycles (21 and 23). In contrast, we find a large diurnal phase shift to earlier hours only during the descending periods of even solar cycles (20 and 22), as compared to almost no shift in the diurnal phase during the descending periods of odd solar cycles. Further, the overall vector average diurnal amplitudes of the ascending period of odd and even solar cycles remain invariant from one ascending period to the other, or even between the even and odd solar cycles. However, we do find a significant diurnal phase shift to earlier hours during the ascending periods of odd solar cycles (21 and 23) in comparison to the diurnal phase in the ascending periods of even solar cycles (20 and 22).     

Interplanetary Transients and Cosmic-Ray Anisotropy

Cosmic-ray intensity data recorded with the ground-based neutron monitor at Deep River have been investigated taking into account the associated interplanetary magnetic field and solar-wind plasma data during 1981 – 1994. A large number of days having abnormally high or low amplitudes for five or more successive days as compared to the annual average amplitude of diurnal anisotropy have been taken as high- or low-amplitude anisotropic wave-train events. The amplitude of the diurnal anisotropy of these events is found to increase on days with a magnetic cloud as compared to the days prior to the event, and it is found to decrease during the later period of the event as the cloud passes the Earth. The high-speed solar-wind streams do not play any significant role in causing these types of events. However, corotating solar-wind streams produce significant deviations in cosmic-ray intensity during high- and low-amplitude events. The interplanetary disturbances (magnetic clouds) are also effective in producing cosmic-ray decreases. Hα solar flares have a good positive correlation with both the amplitude and direction of the anisotropy for high-amplitude events, while the principal magnetic storms have a good positive correlation with both amplitude and direction of the anisotropy for low-amplitude events. The source responsible for these unusual anisotropic wave trains in cosmic rays has been proposed.     

Effect of Interplanetary Turbulences Causing High/low Amplitude Anisotropic Wave Trains in Cr Intensity

The high/low-amplitude anisotropic wave train events (HAE/LAE) in CR intensity have been investigated during the period 1981–1990, using the neutron monitoring data for different latitudes. In all, 21 HAE and 15 LAE cases have been studied. It has been observed that the phase of the diurnal anisotropy remains in the same co-rotational direction for the majority of the HAE/LAE cases. However, it has also been observed that the phase of the diurnal anisotropy changes to later hours in some of the HAE cases, whereas it changes to early hours in some of the LAE cases. Further, the amplitude of the semi-diurnal anisotropy for HAE/LAE cases remains statistically the same; however, the phase of the semi-diurnal anisotropy for HAE has been found to shift to later hours for all events. Furthermore, the HAE occur dominantly during the declining phase of solar activity, whereas LAE occur dominantly during the minimum solar activity period. The geomagnetic activity index-A_p has been observed to remain low during the period of each HAE/LAE. The possible phenomenon to cause the enhanced/low-amplitude daily variation has been proposed to appear on the back side of the Sun.     

Heliolatitudinal dependence of cosmic-ray anisotropy

We analyze the heliolatitudinal dependence of the cosmic-ray anisotropy using data from the Yakutsk complex of muon telescopes on the ground and underground at depths of 7, 20, and 60 m w. e. for 1972–2002. The radial cosmic-ray anisotropy component during this period at all recording levels is shown to have been systematically enhanced southward from the helioequator irrespective of the polarity of the general solar magnetic field. The azimuthal anisotropy component depends on heliolatitude only at negative polarity of the general solar magnetic field; it increases northward from the helioequator. Such a situation can take place in the case of interaction of the fast solar wind from coronal holes with the slow wind in the northern part of the heliosphere and continuous particle removal in its southern part.     

Cosmic-ray anisotropy in interplanetary space

The kinetic equation describing cosmic-ray propagation in interplanetary space has been used to construct a consistent theory of cosmic-ray anisotropy including the second spherical harmonic of particle angular distribution. The amplitude and phase of semi-diurnal cosmic-ray variation have been calculated. Expressions describing the relationships of the semi-diurnal variation parameters to helio-latitude distribution of cosmic rays have been derived. The results obtained are compared with observational data.     

Long-term variations in north-south asymmetry of solar activity

We present a new set of data on relative sunspot number (total, northern hemisphere, and southern hemisphere), taken for the 37-yr period 1947 to 1983; this constitutes a particularly coherent and consistent set of data, taken by the same observer (Hisako Koyama) using the same observing instrument. These data are combined with earlier data (White and Trotter, 1977) on the variation of sunspot areas for both solar hemispheres from 1874 to 1971. The combined data, covering 110 years and 10 solar cycles, are examined for periodicity in solar activity north-south asymmetry. We show that, in general, northern hemisphere activity, displayed as either An/(An + As) or Rn/(Rn + Rs), peaks about two years after sunspot minimum. This peak is greater during even cycles, pointing to a 22-yr periodicity in north-south asymmetry in solar activity, suggesting that the asymmetry is related to the 22-yr solar magnetic cycle. We demonstrate that the largest and most protracted period of northern-hemisphere activity excess in the last 110 years has occurred from 1959 to 1970; we show that there is a strong correlation between northern activity excess and a cosmic-ray density gradient perpendicular to the ecliptic plane, pointing southward, which is evident in cosmic-ray diurnal variation data from the Embudo underground cosmic-ray telescope.     

Tridiurnal variations in cosmic-ray intensity

The tridiurnal wave in cosmic-ray intensity expected from a free space anisotropy is theoretically calculated for different cosmic-ray stations which are characterized by different shapes of asymptotic cones of acceptance. The amplitude A and the time of maximum Tmax are given for latitude dependence of the form cosⁿ λ and rigidity dependence of the form $\text{R}{}^{\mathrm{\beta }}\text{exp (?(R?}\text{1}\text{R}{}_0\text{))}$, where λ and R are the latitude and rigidity respectively and n, β, R₀ are constants. The values of A and Tmax, are calculated for different values of n, β and R₀ for each station. The dependence of A and Tmax on the anisotropy parameters is studied for the proper selection of cosmic-ray stations whose data may be used in determining these parameters.Available experimental data were used to find the observed amplitudes of the tridiurnal variations at five stations using power spectrum analysis with hanning applied on the averaged trains. Minimum variance analysis of the theoretical and experimental amplitudes showed that β has a value between 1 and 2, R₀ greater than 100 GV and n smaller than 3.     

Cosmic-ray intensity related to solar and terrestrial activity indices in solar cycle No. 20

The 11-year modulation of cosmic-ray intensity is studied using the data from nine world-wide neutron monitoring station over the period 1965–1975. From this analysis the following relation among the modulated cosmic-ray intensityI, the relative sunspot numberR, the number of proton eventsN _p and the geomagnetic indexA _p has been derived which describes the long-term modulation of cosmic rays $$I = C - 10^{ - 3} (KR + 4N_P + 12A_P ),$$ whereC is a constant which depends on the rigidity of each station, andK is a coefficient related to the diffusion coefficient of cosmic rays and its transition in space. The standard deviation between the observed and calculated values of cosmic-ray intensity is about 5–9%. This relation has been explained by a generalization of the Simpson solar wind model which has been proved by the spherically symmetric diffusion-convection theory.     

Unusual anisotropic wave trains in cosmic rays

Several workers have attempted to find out the possible origin of the “high amplitude wave trains” of enhanced diurnal variation of cosmic rays and to develop a suitable realistic theoretical model that can explain the different harmonics in individual days. The various observed harmonics of the cosmic-ray variation may be understood on a unified basis if the free-space cosmic-ray anisotropy is non-sinusoidal in form. The major objective of this paper is to study the first three harmonics of high-amplitude wave trains of cosmic-ray intensity over the period 1981–1994 for Deep River neutron monitoring station. The main characteristic of these events is that the high-amplitude wave trains show a maximum intensity of diurnal component in a direction earlier than 18:00 h/co-rotational direction. It is noteworthy that the amplitude significantly enhanced and the phase remains in the co-rotational direction during the years close to solar-activity maximum for first harmonic. Significant deviations have been observed in the semi-diurnal amplitude after the onset of solar-activity maximum. This leads us to conclude that the amplitude as well as direction of the first harmonic and the amplitude of second harmonic are correlated with solar-activity cycle during these HAEs. The amplitude and phase of all the three harmonics (diurnal/semi-diurnal/tri-diurnal) are not found to depend on the polarity of Bz component of interplanetary magnetic field for long-term variation. The occurrence of high-amplitude events is dominant for the positive polarity of Bz component of IMF. The occurrence of HAEs is dominant during the period of average solar-wind velocity, but their occurrence during HSSWSs cannot be denied. The possibility of occurrence of these events is more during the periods of co-rotating streams. The occurrence of HAE is dominant when Dst-index remains negative and this point is not reported earlier in the litterature. All the high amplitude events occurred, when geomagnetic activity index, Ap, remains ⩽20.     

Cosmic ray sidereal diurnal variation of galactic origin observed by neutron monitors

We have analyzed the sidereal diurnal variation of cosmic rays, using 620 station-years of neutron monitor data during the period 1958–1979. The sidereal variation averaged over the period for all the stations in the Northern Hemisphere is different from the corresponding variation in the Southern Hemisphere. The difference is statistically significant and can be identified with the spurious sidereal variation produced from the stationary anisotropy of solar origin, responsible for the solar semi-diurnal variation. The variation common to both hemispheres is also exceptionally significant from the statistical point of view and could be regarded as being due to a uni-directional galactic anisotropy. This variation has an amplitude of 0.0204 ± 0.0015% and a phase of 6.8 ± 0.3 h and is clearly different from that ( ～ 0.05%, 0 ～ 3 h) observed in the high rigidity region (500 ～ 10⁴ GV). The physical meaning of the variation is discussed from the standpoint of the heliomagnetospheric modulation of galactic anisotropy.     

Interplanetary turbulences causing unusual anisotropic wave trains in cosmic rays

The various observed harmonics of the cosmic ray variation may be understood on a unified basis if the free space cosmic ray anisotropy is non-sinusoidal in form. The major objective of this paper is to study the first three harmonics of high amplitude wave trains of cosmic ray intensity over the period 1991–1994 for Deep River Neutron Monitoring Station. The main characteristic of these events is that the high amplitude wave trains shows a maximum intensity of diurnal component in a direction earlier than 1800 Hr/co-rotational direction. It is noticed that these events are not caused either by the high-speed solar wind streams or by the sources on the Sun responsible for producing these streams such as polar coronal holes. The direction of semi-diurnal anisotropy shows negative correlation with Bz. The occurrence of high amplitude events is dominant for the positive polarity of Bz component of IMF. The diurnal amplitude of these events shows a negative and the time of maximum shows a weak correlation with disturbance storm time index Dst. The direction of tri-diurnal anisotropy of these events is found to significantly correlate with geomagnetic activity index Ap.     

Measurement of the solar diurnal anisotropy of the cosmic-ray albedo neutron flux

The solar diurnal anisotropy of the cosmic-ray albedo neutron flux has been measured by a neutron detector on board the OGO-6 satellite. On the average the diurnal amplitudes and phases of the cosmic ray albedo neutron flux (10 MeV) were respectively 0.18 (±0.02)% and 15(±1) hr LT though there were substantial fluctuations of a few days duration which did not depend on the solar sector structure polarity and a 27-day periodicity in the diurnal amplitudes which was associated with the Sun's rotation.     

Cosmic-ray streaming and anisotropies

The principal result of this paper is the demonstration that in interplanetary space the electric-field drifts and convective flow parallel to the magnetic field of cosmic-ray particles combine as a simple convective flow with the solar wind. In addition there are diffusive currents and transverse gradient drift currents. With this interpretation direct reference to the interplanetary electric-field drifts is eliminated and the study of steady-state and transient cosmic-ray anisotropies is both more systematic and simpler. Following a discussion of our present knowledge of the diffusion coefficient in the interplanetary medium, the theory is applied to steady-state anisotropies near Earth in the kinetic energy (T) range 7.5 MeV<T<20 GeV. First the theory of the diurnal variation atT>-2 GeV is examined and it is suggested that the azimuthal streaming associated with the observations be regarded simply as proof that there is no significant net radial flow of cosmic rays at these energies. Second, it is predicted that, near Earth, the radial anisotropy will have a (+?+) variation with energy and this prediction is very insensitive to the precise values of the parameters used: intensity spectrum, solar wind speed, radial density gradient, and diffusion coefficient. Then, third, the small and radial steady-state anisotropies reported by Raoet al. (1967) in the intervals 7.5<T<45 MeV and 45<T<90 MeV are re-examined and it is found that the gradients and diffusion coefficients required to produce the reported anisotropies in 7.5<T<45 MeV are inconsistent with those expected from other data.     

Large amplitude wave-trains of cosmic-ray intensity

The large amplitude wave-trains of cosmic-ray intensity observed during June, July and August, 1973, were analysed. These events exhibit the same characteristics as the event of May, 1973. During these days the phase of the enhanced diurnal anisotropy is shifted to a point earlier than either the corotation direction or the anti-garden-hose direction. For this analysis we used data from high- and middle-latitude neutron monitors and from the satellites HEOS-2, IMP-7 and IMP-8. The diurnal variation of these days is well understood in terms of a radially outward convective vector and a field-aligned inward diffusive vector yielding a diurnal anisotropy vector along about 1600 h in space.     

The insensitivity of the cosmic ray galactic anisotropy to heliomagnetic polarity reversals

Using the cosmic ray sidereal and anti-sidereal diurnal variations observed underground in London and Hobart during the period 1958–1983, it is demonstrated that: (1) the phase changes of the apparent sidereal diurnal variation observed only in the Northern Hemisphere cannot be attributed to the change of the heliomagnetospheric modulation of galactic cosmic ray anisotropy caused by the polarity reversal of the solar magnetic field, but that they are due to the fluctuation of the spurious sidereal variation produced from the anisotropy responsible for the solar semi-diurnal variation; (2) the spurious sidereal variation can be eliminated from the apparent variation by using the observed anti-sidereal diurnal variation; and (3) after the elimination, the sidereal diurnal variations in the Northern and Southern Hemispheres almost coincide with each other and are stationary throughout the period, regardless of the polarity reversal of the heliomagnetosphere. The origin of the corrected sidereal variation is discussed.