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.     

Study of Cosmic-Ray Intensity Variations Associated with Anomalous,Long-Duration High-Speed Solar Wind Streams in 2003

High-speed solar wind streams (HSWS) were identified for solar cycles 22 and 23 (up to 2004). Preliminarily, HSWS were classified in three groups according to their continuous period of occurrence. In the declining phase of solar cycle 23, 2003 is found to be anomalous, showing a very large number of HSWS events of long duration (> ten days). We have studied the effect of HSWS on the cosmic-ray intensity as well as their relationship with geomagnetic disturbance index Ap on yearly, daily, and hourly bases. The yearly average of solar-wind speed was also found to be maximum in 2003. Being within the declining phase of solar activity, the occurrence of solar flares in 2003 is quite low. In particular during HSWS, no solar flares have been observed. Associations with cosmic-ray changes do not support the notion that the HSWS are usually effective in producing significant cosmic-ray decreases. Out of 12 HSWS events observed during the period 2002 (December) to 2003, four events of significant cosmic-ray decreases at all the stations have been selected for further analysis. The cosmic-ray intensity has been found to decrease during the first phase of the event (first five days of HSWS) at all three neutron-monitor stations situated at different latitudes with different cutoff rigidities. The rigidity spectra of observed decreases in cosmic-ray intensity for these four cases have been found to be significantly different than that of Fds (Forbush decrease). In two cases the spectra are softer, whereas in the other two they are harder than that of Fds. However, if the average of all four events is considered together then the spectra of the decrease in cosmic rays during HSWS exactly match that of Fds. Such a result implies that initially individual events should be considered, instead of combining them together, as was done earlier. The Ap index is also found to generally increase in the first phase of the event. However, the four events selected on the basis of cosmic-ray decrease are not always associated with enhanced values of the Ap index. As such, the significance of our study is that further detailed investigations for much longer periods and on an event-by-event basis is required to understand the effect of coronal-hole-associated HSWS.     

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.     

Precursor Effects in Different Cases of Forbush Decreases

Over the last few years, the pre-decreases or pre-increases of the cosmic-ray intensity observed before a Forbush decrease, called the precursor effect and registered by the worldwide neutron monitor network, have been investigated for different cases of intense events. The Forbush decreases presented in this particular study were chosen from a list of events that occurred in the time period 1967?–?2006 and were characterized by an enhanced first harmonic of cosmic-ray anisotropy prior to the interplanetary disturbance arrival. The asymptotic longitudinal cosmic-ray distribution diagrams for the events under consideration were studied using the “Ring of Stations” method, and data on solar flares, solar-wind speed, geomagnetic indices, and interplanetary magnetic field were analyzed in detail. The results revealed that the use of this method allowed the selection of a large number of events with well-defined precursors, which could be separated into at least three categories, according to duration and longitudinal zone. Finally, this analysis showed that the first harmonic of cosmic-ray anisotropy could serve as an adequate tool in the search for precursors and could also be evidence for them.     

Cosmic-Ray Modulation: An Empirical Relation with Solar and Heliospheric Parameters

Long-term variations of galactic cosmic rays were compared with the behavior of various solar activity indices and heliospheric parameters during the current solar cycle. This study continues previous works where the cosmic-ray intensity for the solar cycles 20, 21, and 22 was well simulated from the linear combination of the sunspot number, the number of grouped solar flares, and the geomagnetic index A _p. The application of this model to the current solar cycle characterized by many peculiarities and extreme solar events led us to study more empirical relations between solar-heliospheric variables, such as the interplanetary magnetic field, coronal mass ejections, and the tilt of the heliospheric current sheet, and cosmic-ray modulation. By analyzing monthly cosmic-ray data from the Neutron Monitor Stations of Oulu (cutoff rigidity 0.81 GV) and Moscow (2.42 GV) the contribution of these parameters in the ascending, maximum, and descending phases of the cycle was investigated and it is shown that a combination of these parameters reproduces the majority of the modulation potential variations during this cycle. The approach applied makes it possible to better describe the behavior of cosmic rays in the epochs of the solar maxima, which could not be done before. An extended study of the time profiles, the correlations, and the time lags of the cosmic-ray intensity against these parameters using the method of minimizing RMS over all the considered period 1996 – 2006 determines characteristic properties of this cycle as being an odd cycle. Moreover, the obtained hysteresis curves and a correlative analysis during the positive polarity (qA>0, where q is the particle charge) and during the negative polarity (qA<0) intervals of the cycle result in significantly different behavior between solar and heliospheric parameters. The time lag and the correlation coefficient of the cosmic-ray intensity are higher for the solar indices in comparison to the heliospheric ones. A similar behavior also appears in the case of the intervals with positive and negative polarity of the solar magnetic field.     

Long-term modulation of the Galactic cosmic-ray fluctuation spectrum

We study the temporal behavior of the power spectra for Galactic cosmic-ray fluctuations during the last two solar cycles. We use the 5-min data for 1980–2002 corrected for the barometric effect from two widely separated high-latitude cosmic-ray stations, Tixie Bay and Oulu. The cosmicray fluctuation spectrum is shown to be subjected to a regular long-term modulation with a period of about 11 years in phase with the solar cycle, in accordance with the variations in the inertial part of the turbulence spectrum for the interplanetary magnetic field. Based on independent measurements, we confirm the previously detected cosmic-ray fluctuation power enhancement at the maximum of the 11-year solar cycle and its subsequent decrease at minimum solar activity using new, more extensive data sets. We reach the conclusion about the establishment of a new cosmic-ray modulation phenomenon that has not been described previously in scientific literature.     

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.     

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.     

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.     

Unusual Cosmic Ray Variations During the Forbush Decreases of June 2015

Although the current Solar Cycle 24 is characterized by low solar activity, an intense geomagnetic storm (G4) was recorded in June 2015. It was a complex phenomenon that began on 22 June 2015 as the result of intense solar activity, accompanied by several flares and coronal mass ejections that interacted with the Earth’s magnetic field. A Forbush decrease was also recorded at the neutron monitors of the worldwide network, with an amplitude of 8.4%, and in its recovery phase, a second Forbush decrease followed, with an amplitude of 4.0% for cosmic rays of 10 GV obtained with the global survey method. The Dst index reached a minimum value of ?204 nT that was detected on 23 June 2015 at 05:00?–?06:00 UT, while the Kp index reached the value eight. For our analysis, we used hourly cosmic-ray intensity data recorded by polar, mid-, and high-latitude neutron monitor stations obtained from the High Resolution Neutron Monitor Database. The cosmic-ray anisotropy variation at the ecliptic plane was also estimated and was found to be highly complex. We study and discuss the unusual and complex cosmic-ray and geomagnetic response to these solar events.     

Inversion of the Cosmic-Ray Solar Diurnal Variations

We have bounded the upper cut-off rigidity (R_c) of the cosmic-ray diurnal anisotropy during the period 1968–1995. This period covers almost three solar cycles and includes three epochs of the solar polar field reversals. The diurnal variation observed by two detectors characterized by linearly independent kernels has been inverted in order to estimate the greatest lower bound (GLB) of R_c. We obtain a step function solution for the cosmic-ray anisotropy in free space which vanishes at the GLB of R_c. The greatest lower bound shows a magnetic cycle variation. The highest value of the amplitude of the anisotropy in free space at the GLB have been estimated as well.     

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 anisotropies observed late in the decay phase of solar flare events

Concurrent interplanetary magnetic field and 0.7–7.6 MeV proton cosmic-ray anisotropy data obtained from instrumentation on Explorers 34 and 41 are examined for five cosmic-ray events in which we observe a persistent eastern-anisotropy phase late in the event (t ? 4 days). The direction of the anisotropy at such times shows remarkable invariance with respect to the direction of the magnetic field (which generally varies throughout the event) and it is also independent of particle species (electrons and protons) and particle speed over the range 0.06 ? β ? 0.56. The anisotropy is from the direction 38.3° ± 2.4° E of the solar radius vector, and is inferred to be orthogonal to the long term, mean interplanetary field direction. Both the amplitude of the anisotropy and the decay time constant show a strong dependence on the magnetic field azimuth. Detailed comparison of the anisotropy and the magnetic field data shows that the simple model of convection plus diffusion parallel to the magnetic field is applicable for this phase of the flare effect. It is demonstrated that contemporary theories do not predict the invariance of the direction as observed, even when the magnetic field is steady; these theories need extension to take into account the magnetic field direction ψ varying from its mean direction ψ _o. It is shown that the late phase anisotropy vector is not expected to be everywhere perpendicular to the mean magnetic field. The suggestion that we are observing kinks in the magnetic field moving radially outwards from the Sun leads to the conclusion that the parallel diffusion coefficient varies as 1/cos² (ψ ? ψ _o). Density gradients in the late decay phase are estimated to be ≈ 700%∣AU for 0.7–7.6 MeV protons. A simple theory reproduces the dependence of the decay time constant on anisotropy; it also leads to a radial density gradient of about 1000%∣AU and diffusion coefficient of 1.3 × 10²⁰ cm² s^?1.     

PHASE EVOLUTION OF SOLAR ACTIVITY AND COSMIC-RAY VARIATION CYCLES

Cycles of phase evolution of solar activity and cosmic-ray variations are reconstructed by means of the delay component method, which allows us to study the temporal behaviour of time lag between solar activity and cosmic-ray cycle phases. It is shown that the period of the late 20th cycle was very unusual. We have found a delay in the phase of the solar activity cycle with respect to that of cosmic rays and discuss the heliospheric conditions responsible for this delay.     

Solar activity and the 11-year modulation of cosmic rays

The cosmic-ray intensity during the 18th and 19th solar cycles is examined in the light of Gnevyshev's suggestion of the presence of two maxima in each solar cycle. The 18th solar cycle (1944–54) has two prominent and widely separated cosmic-ray minima corresponding in phase with the two maxima in Bartel's A_p index. For the 19th solar cycle the existence of two minima is less prominent than for the 18th solar cycle. The maximum at higher solar latitudes is more effective in reducing cosmic-ray intensity than the maximum at the lower latitudes. A_p, however, has a larger maximum during the lower latitude solar maximum. A relation between A_p and cosmic-ray intensity is obtained. This relationship is shown to be consistent with Parker's solar-wind theory of the modulation of cosmic rays.     

On the magnitude and direction of the anisotropy of galactic cosmic rays

The results of measuring the diurnal cosmic-ray intensity variations in the energy range 1–100 TeV are discussed. Whereas the phase of the first harmonic of the sidereal daily wave directly determines the phase (right ascension) of the cosmic-ray anisotropy vector, the amplitude and declination of the true anisotropy cannot be reconstructed directly from the amplitude of the first harmonic. However, they can be determined by invoking data on the zero harmonic. The results of some recent experiments purporting to measure the cosmic-ray anisotropy with a particularly high accuracy are shown to be interpreted erroneously.     

Sector structure of the interplanetary magnetic field and anisotropy of 50–1000 GV cosmic rays

It is demonstrated that, at high rigidities (50 GV and beyond), all the main features of cosmic-ray anisotropy of solar origin can be explained in terms of regular particle motion —without diffusion being involved — in the large-scale interplanetary magnetic field (IMF). A simple model of the IMF is adopted with a corotating warped neutral sheet separating the regions of alternative polarities; the warped shape is indispensable for obtaining any form of anisotropy. Energy losses occurring along various computed trajectories are calculated to give the sidereal, solar and antisidereal intensity waves. The reliability of the variations obtained are checked by changing the parameters of the IMF model. Both the sense and amplitude of the polarity-dependent sidereal vector are compatible with those established experimentally. Also reproduced are the predictions of corotation in addition to the 3-hour phase of the semi-diurnal wave. The corotation is found to be near perfect at 50 GV, while it reduces at 100 GV. The model presented accounts for the change of solar daily vector that was observed in 1969.     

Intensity of Cosmic Rays at the Initial Stage of a Solar Flare

The propagation of solar cosmic rays in the interplanetary space is analyzed by solving the Fokker–Planck equation in the small-angle approximation. The particle source is assumed to be instantaneous and point-like. The spatiotemporal distribution of density of energetic particles in the anisotropic phase of a solar cosmic-ray enhancement is examined. Prolonged particle injection into the interplanetary medium is also discussed.     

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.     

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.