Fluctuations of energetic particle flux during solar cycle based on measurements in the solar wind,in the magnetosphere,and at Earth

We present the results of our studies of the cosmic-ray fluctuations in the frequency range 10⁻⁴−1.67 × 10⁻³ Hz based on energetic particle flux measurements on spacecraft in the solar wind, in the magnetosphere, and at Earth in the 11-year solar cycle. The cosmic-ray fluctuation spectrum is shown to have an 11-year modulation related to the solar cycle. A different behavior of the level of energetic particle fluctuations measured in different regions of space is observed for cosmic rays of different origins. We conclude that the new, previously unknown phenomenon of 11-year modulation of the cosmic-ray fluctuation spectrum has been established. A possible explanation of this phenomenon is given.     

TWO COMPONENTS OF COSMIC-RAY MODULATION

The long-term modulation of galactic cosmic rays is investigated from 1957 up to 1992 analysing the dynamic and the quasi-stationary components, separately. It has been found that the dynamic component is characterized by the presence of two peaks at the maximum phase of each solar activity cycle. We infer that the time interval between the two peaks corresponds to a period (well-related to the polar heliomagnetic reversal) in which somewhat decreased activity occurs for intense and long-lasting solar events. In fact, a contemporary dip in the magnetic energy released from the Sun was observed, in agreement with the suggested double maximum displayed by the basic features of the 11-year solar-activity cycle (Gnevyshev, 1977, and references therein). Moreover, the dynamic component of cosmic-ray modulation often shows a multi-structured profile in both peaks of activity, fairly well-connected with the pattern of the green corona brightness. On the other hand, analysing the quasi-stationary long-term trend of cosmic-ray intensity we pick out a good relationship between periods of enhanced cosmic-ray modulation and the area expansion of coronal intensity levels. The relevance of our results for solar-terrestrial forecasting is underlined.     

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.     

The 22-Year Hale Cycle in Cosmic Ray Flux – Evidence for Direct Heliospheric Modulation

The ability to predict times of greater galactic cosmic ray (GCR) fluxes is important for reducing the hazards caused by these particles to satellite communications, aviation, or astronauts. The 11-year solar-cycle variation in cosmic rays is highly correlated with the strength of the heliospheric magnetic field. Differences in GCR flux during alternate solar cycles yield a 22-year cycle, known as the Hale Cycle, which is thought to be due to different particle drift patterns when the northern solar pole has predominantly positive (denoted as qA>0 cycle) or negative (qA<0) polarities. This results in the onset of the peak cosmic-ray flux at Earth occurring earlier during qA>0 cycles than for qA<0 cycles, which in turn causes the peak to be more dome-shaped for qA>0 and more sharply peaked for qA<0. In this study, we demonstrate that properties of the large-scale heliospheric magnetic field are different during the declining phase of the qA<0 and qA>0 solar cycles, when the difference in GCR flux is most apparent. This suggests that particle drifts may not be the sole mechanism responsible for the Hale Cycle in GCR flux at Earth. However, we also demonstrate that these polarity-dependent heliospheric differences are evident during the space-age but are much less clear in earlier data: using geomagnetic reconstructions, we show that for the period of 1905?–?1965, alternate polarities do not give as significant a difference during the declining phase of the solar cycle. Thus we suggest that the 22-year cycle in cosmic-ray flux is at least partly the result of direct modulation by the heliospheric magnetic field and that this effect may be primarily limited to the grand solar maximum of the space-age.     

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.     

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.     

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).     

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.     

The physical significance of the unusual worldwide fluctuations of cosmic-ray intensity on July 14–15, 1961

We have examined the characteristics of the unusual worldwide fluctuations of cosmic-ray intensity on July 14–15, 1961, using corrected hourly data from global network of neutron and meson detectors. A careful study of the associated solar, interplanetary and geophysical phenomena has also been made. These investigations lead us to recognise the dominant role played by the Interplanetary Magnetic Field Inhomogeneities (IMFI) in modulating galactic cosmic-ray flux received at earth during recovery from Forbush decreases. When approaching the earth from the sunward side the IMFI's scatter galactic cosmic rays diffusing towards solar equatorial plane from higher heliolatitudes on to the interplanetary magnetic-field lines which connect to earth. When propagating past the orbit of the earth, the IMFI's set up a flow of scattered galactic cosmic-ray flux in the general direction of the earth. Most of these cosmic rays probably sink in the sun. Transient Spatial Anisotropies are thus set up in the vicinity of the earth in cosmic-ray intensity as viewed by ground-based detectors. Depending upon the relative position of the region abounding in IMFI's and the earth, these short-lived anisotropies appear either from sunward or antisun directions. Sometimes the configuration is such as to set up bidirectional anisotropies. Implications of this broad picture are discussed qualitatively.Our analysis also enables us to place constraint on the mechanism responsible for heating the solar corona over active regions, which we feel must be taken into account by all theoretical models on the subject.This research is supported in part by U.S. Air Force Office of Scientific Research under grant AF-AFOSR-319-66. The paper was presented at the Tenth International Conference on Cosmic Rays, Calgary, June 18–29, 1967.Now at the Dept. of Physics and Astronomy, University of New Mexico, Albuquerque, N.M., U.S.A.     

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.     

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.     

The influence of the anomalous cosmic-ray component on the dynamics of the solar wind

It is well known that both the galactic and anomalous cosmic rays show positive intensity gradients in the outer heliosphere which are connected with corresponding pressure gradients. Due to an efficient dynamical coupling between the solar wind plasma and these highly energetic media by means of convected MHD turbulences, there exists a mutual interaction between these media. As one consequence of this scenario the enforced pressure gradients influence the distant solar wind expansion. Here we concentrate in our theoretical study on the interaction of the solar wind only with the anomalous cosmic-ray component. We use the standard two-fluid model in which the cosmic-ray fluid modifies the solar wind flow via the cosmic-ray pressure gradient. Then we derive numerical solutions in the following steps: first we calculate an aspherical pressure distribution for the anomalous cosmic rays, describing their diffusion in an unperturbed radial solar wind. Second, we then consider the perturbation of the solar wind flow due to these induced anomalous cosmic-ray pressure gradients. Within this context we especially take account of the action of a non-spherical geometry of the heliospheric shock which may lead to pronounced upwinddownwind asymmetries in the pressures and thereby in the resulting solar wind flows. As we can show in our model, which fits the available observational data, radial decelerations of the distant solar wind by between 5 to 11% are to be expected, however, the deviations of the bulk solar wind flow from the radialdirections are only slightly pronounced.     

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.     

Possible origin of the radio emission from SS433 jets

It is shown that radio emission from the jet of the galactic source SS433 as well as the variability of its flux density could be accounted for by the inelastic collision model. Variability in the jet flux is attributed mainly to the variability in the thermal proton number density available in the jet regions.     

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.     

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 proposed associations of solar neutrino flux with solar particles,cosmic rays,and the solar activity cycle

It has been proposed that the observed solar neutrino flux exhibits important correlations with solar particles, galactic cosmic rays, and the sunspot cycle, with the latter correlation being opposite in phase and lagging behind the sunspot cycle by about one year. Re-examination of the data-available interval 1971–1981, employing various tests of statistical significance, however, suggests that such a claim is, at present, unwarrantable. For example, on the associations of solar neutrino flux and cosmic-ray flux with the Ap geomagnetic index, neither were found to be statistically significant (at the 95% level of confidence), regardless of the choice of lag (-1, 0, or +1 yr). Presuming linear fits, all correlations with Ap had coefficients of determination (r ², where r is the linear correlation coefficient) less than 16%, meaning that 16% of the variation in the selected test parameters could be explained by the variation in Ap. Similarly, on the associations of solar neutrino flux and cosmic ray flux with sunspot number, only the latter association proved to be of statistical importance. Using the best linear fits, the correlation between yearly averages of solar neutrino flux and sunspot number had r ² 19%, the correlation between weighted moving averages (of order 5) of solar neutrino flux and sunspot number had r ² 45%, and the correlation between cosmic-ray flux and sunspot number had r ² 76%, all correlations being inverse associations. Solar neutrino flux was found not to correlate strongly with cosmic-ray flux, and the Ap geomagnetic index was found not to correlate strongly with sunspot number.     

Modeling the Relationship Between Neutron Counting Rates and Sunspot Numbers Using the Hysteresis Effect

Several studies show that temporal variations in the Galactic cosmic ray (GCR) intensity display a distinct 11-year periodicity due to solar modulation of the galactic cosmic rays in the heliosphere. The 11-year periodicity of GCRs is inversely proportional to, but out of phase with, the 11-year solar cycle, implying that there is a time lag between actual solar cycle and the GCR intensity, which is known as the hysteresis effect. In this study, we use the hysteresis effect to model the relationship between neutron counting rates (NCRs), an indicator of the GCR intensity, and sunspot numbers (SSNs) over the period that covers the last four solar cycles (20, 21, 22, and 23). Both linear and ellipse models were applied to SSNs during odd and even cycles in order to calculate temporal variations of NCRs. We find that ellipse modeling provides higher correlation coefficients for odd cycles compared to linear models, e.g. 0.97, 0.97, 0.92, and 0.97 compared to 0.69, 0.72, 0.53, and 0.68 for data from McMurdo, Swarthmore, South Pole, and Thule neutron monitors, respectively, during solar cycle 21 with overall improvement of 31 % for odd cycles. When combined to a continuous model, the better correlation observed for the odd cycles increases the overall correlation between observed and modeled NCRs. The new empirical model therefore provides a better representation of the relationship between NCRs and SSNs. A major goal of the ongoing research is to use the new non-linear empirical model to reconstruct SSNs on annual time scales prior to 1610, where we do not have observational records of SSNs, based on changes in NCRs reconstructed from ¹⁰Be in ice cores.     

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.     

Long-Term Modulation of Cosmic Rays in the Heliosphere and its Influence at Earth

The temporal variation of the cosmic-ray flux at Earth directly influences the production rate of cosmogenic isotopes in the Earth’s atmosphere. Here we put the emphasis on problems of the modulation of cosmic rays in the heliosphere. The physics of the modulation region, e.g., the heliosphere, is described and also the transport theory of the cosmic rays through the heliosphere is presented. The discussion includes more recent ideas of the modulation in the heliosheath. In the light of these ideas the cosmic-ray fluxes during the Maunder minimum are discussed. It is also discussed, that the 22-year cycle observed in the cosmogenic isotopes is a modulation effect of the cosmic rays, and hence directly connected with the physics of the outer heliosphere.