On the Role of Large-Scale Solar Photospheric Motions in the Cosmic-Ray 1.68-YR Intensity Variation

Analysis of cosmic-ray intensity time evolution has led to the identification of intensity variations with several periodicities, most of them correlated with one or another phenomenon of the Sun. Recently Valdés-Galicia, Pérez-Enriquez, and Otaola (1996) reported on a newly-found 1.68-yr variation, which seems to be correlated with periodicities in X-ray long-duration events and low-latitude coronal hole area variations. As those phenomena are related with magnetic flux emergence and transport, in this paper we investigate the possible relationship of the referred cosmic-ray variation with characteristic times of different tracers of meridional circulation. Our results indicate that several of the calculated times might be related to the 1.68-yr cosmic-ray variation. A physical mechanism through which this connection may operate is discussed.     

Simulation of long-term cosmic-ray intensity variation

Selecting the most appropriate source functions among the various solar, interplanetary and terrestrial activity indices we have attempted to reproduce to a certain degree the long-term modulation of galactic cosmic-rays. For this study monthly cosmic-ray data from nine world-wide neutron monitor stations for the period 1975–1985 have been analysed. The empirical formula which has been used to compute the long-term cosmic-ray variations follows the observations fairly well.It is noteworthy that the residuals in the cosmic-ray intensity between that observed and that calculated by this empirical formula exhibits a still remaining short-term variation in all stations of 2.7 and 3.7 months. Possible interpretations of these observed periodicities related to galactic origin are given.     

On reproduction of long-term cosmic-ray modulation as seen by neutron monitor stations

The dependence of cosmic-ray intensity on 21st solar cycle phenomena has been studied using monthly cosmic-ray values from nine world wide Neutron Monitoring Stations.For this purpose the long-term cosmic-ray modulation is modelled by treating the most appropriate source functions among various solar, interplanetary and terrestrial activity indices as the input and the cosmic-ray intensity as the output of a linear system taking into account the corresponding time-lag. In this way the modulated galactic cosmic-ray intensity has been reproduced to a certain degree as the cosmic-ray variations follow the observations with a standard deviation of ~ 10%. Still remaining short-term variations in all stations with periods of 2.7 and 3.7 months can possibly be related to the galactic origin of cosmic-rays.The Simpson solar wind model improved by the spherically symmetric diffusion-convection theory can describe our proposed method.     

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.     

Cosmic-ray modulation and long-duration solar flare events

The correlation between the long-term intensity variations of cosmic rays at neutron monitor energies and the LDE index measure of solar flares with long-lasting soft X-ray emissions is reported. Three subsequent solar cycles, 20–22, are taken into account and half-monthly data are analyzed. Possible explanation of this correlation is discussed in terms of the recent concepts of cosmic-ray modulation, in particular with merged interaction regions affecting the cosmic-ray intensity.     

Simulation of the temporal variations of the galactic cosmic-ray intensity at neutron monitor energies

We show that the temporal variations of the integrated galactic cosmic-ray intensity at neutron monitor energies (approximately above 3 GeV) can be reproduced applying a semi-empirical 1-D diffusion-convection model for the cosmic-ray transport in interplanetary space. We divide the interplanetary region into `magnetic shells' and find the relative reduction that each shell causes to the cosmic-ray intensity. Then the cosmic-ray intensity at the Earth is reproduced by the successive influence of all shells between the Earth and the heliospheric termination shock. We find that the position of the termination shock does not significantly affect the cosmic-ray intensity although there are some differences between the results for a constant and a variable termination shock radius. We also reproduce the cosmic-ray intensity applying the analytical solution of the force-field approximation (Perko, 1987) and find that the results cannot fit the observed data. Our results are compared with the Climax (geomagnetic cut-off 3 GV) and Huancayo (geomagnetic cut-off 13 GV) neutron monitor measurements for almost two solar cycles (1976–1996).     

Time-evolution of cosmic-ray intensity modulation

Application of analyzing time-series into trigonometric series allows the investigation of cosmic-ray intensity variations in a wide periodicity range from a few months to 10 or even more years. By this technique, the amplitude and the phase of all observed fluctuations can be given. For this purpose, cosmic-ray data of five ground-based neutron-monitor stations for the time interval 1964–1985 have been analyzed.Two kinds of periodicities appeared in these data. The first one includes occurrences at periods greater than two years, as the ones of 10.41, 8.41, and 5.50 yr, which differ very little in amplitude from station to station but are similar in phase, and the second one includes periodicities smaller than two years (24, 12, 8, and 6 months) which are similar in all stations but appeared in variable time intervals.The possible origin of each observed variation due to a contribution either of cosmic-ray interaction in the upper atmosphere or to the solar dynamics is discussed.     

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.     

The Global Survey Method Applied to Ground-level Cosmic Ray Measurements

The global survey method (GSM) technique unites simultaneous ground-level observations of cosmic rays in different locations and allows us to obtain the main characteristics of cosmic-ray variations outside of the atmosphere and magnetosphere of Earth. This technique has been developed and applied in numerous studies over many years by the Institute of Terrestrial Magnetism, Ionosphere and Radiowave Propagation (IZMIRAN). We here describe the IZMIRAN version of the GSM in detail. With this technique, the hourly data of the world-wide neutron-monitor network from July 1957 until December 2016 were processed, and further processing is enabled upon the receipt of new data. The result is a database of homogeneous and continuous hourly characteristics of the density variations (an isotropic part of the intensity) and the 3D vector of the cosmic-ray anisotropy. It includes all of the effects that could be identified in galactic cosmic-ray variations that were caused by large-scale disturbances of the interplanetary medium in more than 50 years. These results in turn became the basis for a database on Forbush effects and interplanetary disturbances. This database allows correlating various space-environment parameters (the characteristics of the Sun, the solar wind, et cetera) with cosmic-ray parameters and studying their interrelations. We also present features of the coupling coefficients for different neutron monitors that enable us to make a connection from ground-level measurements to primary cosmic-ray variations outside the atmosphere and the magnetosphere. We discuss the strengths and weaknesses of the current version of the GSM as well as further possible developments and improvements. The method developed allows us to minimize the problems of the neutron-monitor network, which are typical for experimental physics, and to considerably enhance its advantages.     

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.     

Variations of cosmic-ray energy in interplanetary space

A consistent theory of energy exchange between high-energy charged cosmic-ray particles and the random inhomogeneities of a magnetic field frozen in the moving solar wind plasma is developed. It is shown that the mode of the particle energy variations at a given law of plasma velocity variation in space is determined by the specific form of the particle distribution function. The equation for the density of cosmic-ray energy is obtained. Consideration is given to the generation of a charged particle energy spectrum in the course of multiple scatterings by the random inhomogeneities of the magnetic field.     

Variations of the interplanetary magnetic field and the electron and cosmic-ray intensities under the influence of Jupiter

Analysis of experimental data on the variations in the intensities of 2–12 MeV electrons and cosmic rays and the interplanetary magnetic field (IMF) magnitude has revealed “responses” to the influence of Jupiter in these parameters. Their amplitudes, in instrumental count units, are the following: 0.15 (71%) in the electron intensity, 48 (0.8%) in the cosmic-ray intensity, and 0.19 (2.8%) in the IMF magnitude. The maximum of the response in the electron intensity and the minimum of the response in the IMF magnitude coincide and lie near the magnetic field line that runs along the Sun-Earth-Jupiter axis. The minimum of the response in the cosmic-ray intensity is shifted against the solar rotation by 75 days from the magnetic field line connecting Jupiter and the Earth. Jupiter has the strongest influence on the intensity of high-energy electrons (71% of their total intensity).     

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.     

An Analysis of Polar Coronal Hole Evolution: Relations to Other Solar Phenomena and Heliospheric Consequences

We use observations of the green corona low-brightness regions to construct a time series of a polar coronal hole area from 1939 to 1996, covering 5 solar cycles. We then perform a power-spectral analysis of the monthly data time series. Several persistent significant periodicities appear in the spectra, which are related with those found in solar magnetic flux emergence, geomagnetic storm sudden commencements and cosmic-ray flux at Earth. Of particular importance are the peak at around 1.6–1.8 yr recently found in cosmic-ray intensity fluctuations, and the peak at around 1 yr, also identified in coronal hole magnetic flux variations. Additional interesting features are the peaks close to 5 yr, 3 yr and the possible peak at around 30 yr, that were also found in other solar and interplanetary phenomena. Our results stress the physical connection between the solar magnetic flux emergence and the interplanetary medium dynamics, in particular the importance of coronal hole evolution in the structuring of the heliosphere.     

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.     

An empirical model for the 11-year cosmic-ray modulation

An analysis of monthly data from nine world-wide neutron monitoring stations over the period 1965–1975 is carried out for the study of the long-term cosmic-ray modulation. In an attempt to gain insight into the relationships which exist between solar activity, high-speed solar wind streams and various terrestrial phenomena an empirical relation for the cosmic-ray modulation has been found. Accordingly the modulated cosmic-ray intensity is equal to the galactic cosmic-ray intensity corrected by a few appropriate solar, interplanetary and terrestrial activity indices which causes the disturbances in interplanetary space, multiplying with the corresponding time-lag of cosmic-ray intensity from each of these indices. This relation is well explained by a generalization of the Simpson solar wind model which has been proved by the spherically symmetric diffusion-convection theory.     

Power Spectrum of Cosmic-ray Fluctuations During Consecutive Solar Minimum and Maximum Periods

Power spectral analysis of cosmic-ray intensity recorded by eight stations was carried out over a wide range of frequencies from 2.3 × 10^–8 Hz to 5.8 × 10^–6 Hz (2–500 days) during the period 1964–1995. Spectrum results of large-scale fluctuations have revealed the existence of a broad peak near 250–285 days and a narrower peak at 45–50 days during the studied epochs as a stable feature in all neutron monitors covering a wide rigidity range. The cosmic-ray power spectrum displayed significant peaks of varying amplitude with the solar rotation period (changed inversely with the particle rigidities) and its harmonics. The amplitudes of 27-day and 13.5-day fluctuations are greater during the positive-polarity epochs of the interplanetary magnetic field (qA>0) than during the qA<0 epochs. The comparison of cosmic-ray power spectra during the four successive solar activity minima have indicated that at the low-rigidity particles the spectrum differences between the qA>0 and qA<0 epochs are significantly large. Furthermore, the spectrum for even solar maximum years are higher and much harder than the odd years. There are significant differences in the individual spectra of solar maxima for different cycles.     

Time-lag of cosmic-ray intensity

The best correlation coefficient between the monthly cosmic-ray intensity of the Inuvik Station and various kinds of solar, interplanetary, and geophysical parameters has been found. It is calculated for different time-lags of cosmic-ray intensity with respect to these parameters. The maximum of these coefficients lead us to a useful empirical model for the 11-year cosmic-ray modulation.     

Galactic cosmic-ray anisotropy and its heliospheric modulation, inferred from the sidereal semidiurnal variations observed in the rigidity range 300–600 GV with multidirectional muon telescope at Sakashita underground station

The existence of sidereal semidiurnal variation of cosmic-ray intensity in a rigidity region 10²-10³ GV has been reported by many researchers, but there is no consensus of opinion on its origin. In this paper, using the observed semidiurnal variations in a rigidity range (300–600 GV) with 10 directional muon telescopes at Sakashita underground station (geog. lat. = 36°, long. = 138°E, DEPTH = 80 m.w.e.), the authors determine the magnitudes (η₁, η₂) and directions (a₁, a₂) of the first- and second-order anisotropies in the following galactic cosmic-ray intensity distribution (j)

jdp = j₀{1 + η₁P₁(cos χ₁) + η₂P₂(cos χ₂)}dp

, where P_nis the nth order spherical function and χ_n is the pitch angle of cosmic rays with respect to a_n. For the determination, the influence of cosmic-ray's heliomagnetospheric modulation, geomagnetic deflection and nuclear interaction with the terrestrial material and also of the geometric configuration of the telescopes are taken into account. Usually, the semidiurnal variation is produced by the second-order anisotropy. The present observation, however, requires also the first-order anisotropy which usually produces only the diurnal variation, but can produce also the semidiurnal variation as a result of the heliospheric modulation. The first- and second-order anisotropies are characterized with η₁) > 0 and η₂ < 0 have almost the same direction (a₁ a₂) specified by the right ascension ( 0.75 h) and declination (δ 50°S) and, therefore, they can be expressed, as a whole, by an axis-symmetric anisotropy of loss-cone type (i.e. deficit intensities in a cone). It is noteworthy that this anisotropy approximately coincides with that inferred from the air shower observation at Mt Norikura in the rigidity region 10⁴ GV.     

Solar-cycle phenomena in cosmic-ray intensity: Differences between even and odd cycles

Cosmic-ray intensity data for the period 1964–1985 covering two solar cycles are used to investigate the solar activity behaviour in relation to cosmic-ray modulation. A detailed statistical analysis of them shows a large time-lag of about one and half years between cosmic-ray intensity and solar activity (as indicated by sunspot number, solar flares and high-speed solar-wind streams) during the 21st solar cycle appearing for a first time. This lag indicates the very high activity level of this solar cycle estimating the size of the modulating region to the unambiguous value of 180 AU. The account of the solar-wind speed in the 11-year variation significantly decreases the modulation region of cosmic-rays to the value of 40 AU.A comparison with the behaviour of the previous solar cycle establishes a distinction between even and odd solar cycles. This is explained in terms of different contributions of drift, convection and diffusion to the whole modulation mechanism during even and odd solar cycles.