Modulation of galactic cosmic ray anisotropy in heliomagnetosphere: Seasonal variation of sidereal daily variation

In the previous paper (Nagashima et al., 1982), we have reported the yearly averaged modulation of galactic cosmic ray anisotropy in the heliomagnetosphere. In the present paper, we analyze the seasonal (annual) dependence of the modulation, using the frequency modulation method. The seasonal variation of the sidereal daily variation produced from the anisotropy is resolved into variations with proper sideband frequencies, such as solar and anti-sidereal variations. These side-band variations are predominant in the rigidity region of 10² ～' 10³ GV and show the following characteristics.(1) Being similar to the average sidereal variation, they are strongly dependent on the polarity state (‘positive’ or ‘negative’) of the heliomagnetosphere.(2) The side-band variations with frequencies lower than the sidereal frequency (366 cycle/year) generally predominate over those with higher frequencies. The most predominant variations are produced from the component of the uni-directional anisotropy projected to the Earth's rotation axis and could be observed as the solar and anti-sidereal diurnal variations.(3) If the flat neutral sheet of the heliomagnetosphere is replaced with the wavy neutral sheet, side-band variations in the positive state tend to diminish with the increase of the heliolatitudinal extent of the wavy neutral sheet, while those in the negative state almost retain their magnitude.(4) These variations depend also on the observation periods when the Earth is located either in the “toward” field or in the “away” field. This T-A dependence changes with the transition from the positive state to the negative and increases with the increase of the heliolatitudinal extent of the wavy neutral sheet. The most remarkable T-A dependence is observed in solar diurnal variation arising from the component of the unidirectional anisotropy projected to the Earth's rotation axis and can be used for the determination of the direction of the anisotropy.     

Corrected sidereal anisotropy for underground muons

Data from underground muon telescopes in New Mexico and Bolivia are analyzed in sidereal time and anti-sidereal time to study anisotropies in the rigidity range 20 GV to a few 100s of GV. Using both vertical and North- and South-pointing telescopes in both hemispheres, a latitude range of 70°N–50°S is covered. The distribution of cosmic rays in the inner heliosphere gives rise to a diurnal variation in anti-sidereal time, and also produces a spurious contribution to the anisotropy in sidereal time. It is shown that the anti-sidereal variation is of the P₂¹ type, having opposite phase in the Northern and Southern Hemispheres, and maximum amplitude at mid latitudes. The anti-sidereal data are used to correct the sidereal data, using the Nagashima method (Nagashima, Sakakibara, Fenton and Humble, 1985); the resulting corrected sidereal vectors for Northern Hemisphere telescopes have their sidereal maxima close to 3 h sidereal time, in reasonable agreement with sidereal data at higher energies from small air showers. The Nagashima correction also appears to eliminate effects due to the reversal of the Sun's polar magnetic field which show up in the unconnected sidereal data, and which also remain in corrected data using an alternative correction.     

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.     

Modulation of galactic cosmic ray anisotropy in heliomagnetosphere: Average sidereal daily variation

We formulate the modulation of galactic anisotropy of cosmic rays caused by their orbital deflection in the heliomagnetosphere. According to the formulation, the average sidereal i-th harmonic daily variation (i = 1,2,…) produced from the anisotropy from an arbitrary direction can be expressed by a linear combination of three basic vectors for uni-directional anisotropy and five basic vectors for bi-directional anisotropy. These vectors are obtained by calculating trajectories of cosmic rays (20?10⁴GV) in a model magnetosphere having Parker's Archimedian spiral structure with a flat or a wavy neutral sheet in either of two polarity states, one is called “Positive” state (away field in the northern space of the neutral sheet and toward field in the southern space) and the other is called “Negative” state (reversed state of the above). Among general characteristics of the sidereal daily variations, the most remarkable features are: (1) The observable variations in low rigidity (? 2000 GV) can be produced even from an uni-directional anisotropy in the direction of the Earth's rotation axis. These variations are strongly dependent on the polarity state, i.e., they are greater in the Positive state than in the Negative. (2) Those produced from the anisotropy in the Equatorial plane also show the polarity dependence but contrary to the previous case they are greater in the Negative state than in the Positive. Their magnitude in the former state is not so small even in the extremely low rigidity (～ 100 GV) as compared with that in high rigidity region. (3) These general characteristics are not altered by the introduction of the wavy neutral sheet or the magnetic irregularities, but the variations are affected more or less, depending on the heliolatitudinal extent of the wavy sheet or the degree of cosmic ray scattering with the irregularities, (4) Sidereal daily variation for the wavy sheet shows a toward-away field dependence similar to that of Swinson-type of solar origin, but the dependence is predominant in intermediate rigidity region (～ 500 GV), in marked contrast to that of solar origin. (5) Finally, whichever its direction may be, the uni-directional anisotropy produces the sidereal diurnal variation common to two conjugate stations in the Northern and Southern hemisphere. If there is any difference between the observed variations at the stations, it should be interpreted as being due to higher order anisotropy such as the bi-directional anisotropy.     

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.     

Diurnal anisotropy of cosmic rays during intensive solar activity for the period 2001–2014

The diurnal variation of cosmic ray intensity, based on the records of two neutron monitor stations at Athens (Greece) and Oulu (Finland) for the time period 2001 to 2014, is studied. This period covers the maximum and the descending phase of the solar cycle 23, the minimum of the solar cycles 23/24 and the ascending phase of the solar cycle 24.These two stations differ in their geographic latitude and magnetic threshold rigidity. The amplitude and phase of the diurnal anisotropy vectors have been calculated on annual and monthly basis.From our analysis it is resulted that there is a different behaviour in the characteristics of the diurnal anisotropy during the different phases of the solar cycle, depended on the solar magnetic field polarity, but also during extreme events of solar activity, such as Ground Level Enhancements and cosmic ray events, such as Forbush decreases and magnetospheric events. These results may be useful to Space Weather forecasting and especially to Biomagnetic studies.     

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.     

Solar magnetic cycle dependence in corotating modulation of galactic cosmic rays

We study the temporal evolution of cosmic ray intensity during ～27-day Carrington rotation periods applying the method of superposed epoch analysis. We discuss about the average oscillations in the galactic cosmic ray intensity, as observed by ground based neutron monitors, during the course of Carrington rotation in low solar activity conditions and in different polarity states of the heliosphere (A<0 and A>0). During minimum and decreasing phases in low solar activity conditions, we compare the oscillation in one polarity state with that observed in other polarity state in similar phases of solar activity. We find difference in the evolution and amplitude of ～27-day variation during A<0 and A>0 epoch. We also compare the average variations in cosmic ray intensity with the simultaneous variations of solar wind parameters such as solar wind speed and interplanetary magnetic field strength. From the correlation analysis between the cosmic ray intensity and the solar wind speed during the course of Carrington rotation, we find that the correlation is stronger for A>0 than A<0.     

Harmonics of exceptionaly low amplitude anisotropic wave train events in cosmic ray intensity

The unusually low amplitude anisotropic wave train events (LAEs) in cosmic ray intensity using the ground based Deep River neutron monitor data has been studied during the period 1991–94. It has been observed that the phase of the diurnal anisotropy for the majority of the LAE events remains in the co-rotational direction. However, for some of the LAE events the phase of the diurnal anisotropy shifts towards earlier hours as compared to the annual average values. On the other hand, the amplitude of the semi-diurnal anisotropy remains statistically the same, whereas phase shift-towards later hours; a similar trend has also been found in case of tri-diurnal anisotropy. The high-speed solar wind streams do not play a significant role in causing the LAE events. The occurrence of LAE is independent of the nature of the Bz component of IMF polarity. Published in Astrofizika, Vol. 50, No. 2, pp. 313–324 (May 2007).     

On the Analysis of the Complex Forbush Decreases of January 2005

In this work an analysis of a series of complex cosmic ray events that occurred between 17 January 2005 and 23 January 2005 using solar, interplanetary and ground based cosmic ray data is being performed. The investigated period was characterized both by significant galactic cosmic ray (GCR) and solar cosmic ray (SCR) variations with highlighted cases such as the noticeable series of Forbush effects (FEs) from 17 January 2005 to 20 January 2005, the Forbush decrease (FD) on 21 January 2005 and the ground level enhancement (GLE) of the cosmic ray counter measurements on 20 January 2005. The analysis is focusing on the aforementioned FE cases, with special attention drawn on the 21 January 2005, FD event, which demonstrated several exceptional features testifying its uniqueness. Data from the ACE spacecraft, together with GOES X-ray recordings and LASCO CME coronagraph images were used in conjunction to the ground based recordings of the Worldwide Neutron Monitor Network, the interplanetary data of OMNI database and the geomagnetic activity manifestations denoted by K _p and D _st indices. More than that, cosmic ray characteristics as density, anisotropy and density gradients were also calculated. The results illustrate the state of the interplanetary space that cosmic rays crossed and their corresponding modulation with respect to the multiple extreme solar events of this period. In addition, the western location of the 21 January 2005 solar source indicates a new cosmic ray feature, which connects the position of the solar source to the cosmic ray anisotropy variations. In the future, this feature could serve as an indicator of the solar source and can prove to be a valuable asset, especially when satellite data are unavailable.     

Characteristics of Enhanced and Low Amplitude Anisotropic Wave Trains and Interplanetary Transients

The occurrence of a large number of high and low amplitude anisotropic wave train events over the years 1981–1994 has been examined along with the different solar features. The results indicate that the time of maximum of diurnal variation significantly remains in the 18-h direction for majority of the high and low amplitude wave trains. The amplitude of diurnal anisotropy remains significantly high and phase shifts towards earlier hours as compared to the quite day annual average values for majority of the HAEs. The diurnal amplitude remains significantly low and phase shifts towards earlier hours as compared to the quiet day annual average values for majority of the LAEs. The occurrence of these enhanced/low amplitude events is found to be dominant during the positive polarity of the Bz component of the interplanetary magnetic field. The amplitude of the diurnal anisotropy of these events is found to increase on the days of magnetic cloud as compared to the days prior to the event and it 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. The interplanetary disturbances (magnetic clouds) are also effective in producing cosmic ray decreases.     

Harmonics of Low Amplitude Anisotropic Wave Train Events in Cosmic Ray Intensity

The unusually low amplitude anisotropic wave train events (LAWEs) in cosmic ray intensity using the ground based Deep River neutron monitor data has been studied during the period 1991–1994. It has been observed that the amplitude of the diurnal anisotropy for LAWE events significantly remains quite low and statistically constant as compared to the quiet day annual average amplitude for majority of the events. The time of maximum of the diurnal anisotropy of LAWE significantly shifts towards earlier hours as compared to the co-rotational direction and remains in the direction of quiet day annual average anisotropy for majority of the events. On the other hand, the amplitude of the semi/tri-diurnal anisotropy remains statistically the same and high whereas, phase shift towards later hours as compared to the quiet day annual average values for majority of the LAWEs. The diurnal anisotropy vectors are found to shifts towards earlier hours for 50% of the events; whereas they are found to shifts towards later hours for rest of the events (50%) relative to the average vector for the entire period. It is also noted that the amplitude of these vectors are found to increase significantly with the shift of the diurnal anisotropy vectors towards later hours. The high-speed solar wind streams do not play a significant role in causing the LAWE events on short-term basis, however it may be responsible in causing these events on long-term basis (Mishra and Mishra 2007). Occurrence of LAWE is dominant, when the polarity of Bx and Bz remains positive and polarity of By remains negative, which is never been reported earlier. The amplitude of first harmonic shows good anti-correlation and direction of first and third harmonic shows nearly good anti-correlation with solar wind velocity, whereas the direction of second harmonic shows nearly good anti-correlation with interplanetary magnetic field strength.     

Transient perturbations and their effects in the heliosphere, the geo-magnetosphere, and the Earth’s atmosphere: Space weather perspective

We discuss the effects of certain dynamic features of space environment in the heliosphere, the geo-magnetosphere, and the earth’s atmosphere. In particular, transient perturbations in solar wind plasma, interplanetary magnetic field, and energetic charged particle (cosmic ray) fluxes near 1 AU in the heliosphere have been discussed. Transient variations in magnetic activity in geo-magnetosphere and solar modulation effects in the heliosphere have also been studied. Emphasis is on certain features of transient perturbations related to space weather effects. Relationships between geomagnetic storms and transient modulations in cosmic ray intensity (Forbush decreases), especially those caused by shock-associated interplanetary disturbances, have been studied in detail. We have analysed the cosmic ray, geomagnetic and interplanetary plasma/field data to understand the physical mechanisms of two phenomena namely, Forbush decrease and geomagnetic storms, and to search for precursors to Forbush decrease (and geomagnetic storms) that can be used as a signature to forecast space weather. It is shown that the use of cosmic ray records has practical application for space weather predictions. Enhanced diurnal anisotropy and intensity deficit of cosmic rays have been identified as precursors to Forbush decreases in cosmic ray intensity. It is found that precursor to smaller (less than 5%) amplitude Forbush decrease due to weaker interplanetary shock is enhanced diurnal anisotropy. However, larger amplitude (greater than 5%) Forbush decrease due to stronger interplanetary shock shows loss cone type intensity deficit as precursor in ground based intensity record. These precursors can be used as inputs for space weather forecast.     

Long-term changes in the cosmic-ray diurnal anisotropy

A detailed study has been conducted on the long-term changes in diurnal anisotropy of cosmic rays for the two solar cycles (20 and 21) during the period 1965–1990; this shows that the amplitude of the anisotropy is related to the characteristics of high and low amplitude days. The occurrence of high amplitude days are found to be positively correlated with the sunspot cycle while the low amplitude days are correlated negatively with the sunspot cycle. Further, the variability of the time of maximum of the aniotropy indicates that it essentially is composed of two components; one in the 1800 hours (corotation) direction and the other, an additional component in the 1500 hours direction (45° east of the S-N line) apparently caused by the reversal of the solar polar magnetic field. Our observations also suggest that the direction of the anisotropy of high- and low-amplitude days contribute significantly to the long-term behaviour of the diurnal anisotropy as it produces an additional component of cosmic rays in the radial (1200 hours) direction.     

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.     

Diurnal variations of cosmic rays during a solar magnetic cycle

We have used data from five neutron monitor stations with primary rigidity (Rm) ranging from 16 GeV to 33 GeV to study the diurnal variations of cosmic rays over the period: 1965–1986 covering one 22-year solar magnetic cycle. The heliosphere interplanetary magnetic field (IMF) and plasma hourly measurements taken near Earth orbit, by a variety of spacecraft, are also used to compare with the results of solar diurnal variation. The local time of maximum of solar diurnal diurnal variations displays a 22-year cycle due to the solar polar magnetic field polarities. In general, the annual mean of solar diurnal amplitudes, magnitude of IMF and plasma parameters are found to show separte solar cycle variations. Moreover, during the declining period of the twenty and twenty-ne solar cycles, large solar diurnal amplitudes are observed which associated with high values of solar wind speed, plasma temperature and interplanetary magnetic field magnitude B3.     

Average anisotropy characteristics of high energy cosmic ray particles and geomagnetic disturbance index Ap

The average characteristics of the diurnal and semi-diurnal anisotropy of cosmic ray intensity at relativistic energies have been obtained by using data from the worldwide grid of neutron monitor for the period 1989 to 1996. The complex behaviour of the diurnal amplitudes and time of maxima (phase) and its association with the Ap index on a long-term and day-to-day basis have been studied. Even though the general characteristics, on a yearly average basis, have not changed significantly during this period, both the diurnal and semi-diurnal amplitudes and phases vary significantly, besides significant changes being observed for different interplanetary conditions on a short-term basis. It is found that the relationship between the Ap index and the diurnal vector is out of phase during the period 1991 to 1995. On a long-term basis, the correlation of diurnal variation with Ap index has been found to vary during the solar cycle. On a short-term basis, it has been observed that the high Ap days are usually associated with higher amplitudes with phase shifted to earlier hours.     

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.     

Harmonics of high-amplitude wave trains in cosmic ray intensity

Using the ground based neutron monitor data of Deep River, the high-amplitude anisotropic wave train events (HAE) in cosmic ray intensity have been investigated during the period 1991-1994. It has been observed that the phase of diurnal anisotropy for majority of HAE shifts towards later hours; whereas it remains in the corotational/18-h direction for some of the HAE cases. Further, for majority of HAE cases the amplitude of diurnal and semi-diurnal anisotropy significantly deviates from the annual average values. The phase of semi-diurnal and tri-diurnal anisotropy for all HAE cases has shifted to later hours. Furthermore, for tri-diurnal anisotropy the amplitude remains statistically the same. The occurrence of HAE is unaffected by the nature of the B_z component of IMF polarity.     

IMF-sense-dependent cosmic ray anisotropy produced from diffusion-convection in heliosphere

An IMF-sense-dependent first order (or unidirectional) anisotropy of cosmic rays, which is produced perpendicularly to the ecliptic from the radial density gradient in solar system, has been confirmed by Swinson. In the present paper, we point out the existence of IMF-sense-dependent higher order anisotropies, based on the simulation of cosmic ray diffusion-convection in the heliomagnetosphere. In order to confirm their existence, we demonstrate some examples of the observed cosmic ray daily variation which is supposed to be due to these anisotropies.