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.     

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.     

Rapid Cosmic Ray Fluctuations: Evidence for Cyclic Behaviour

We study rapid cosmic-ray fluctuations using 5-min resolution data from eight neutron monitors with different cutoff rigidities as well as from the ACE satellite. We define a proxy index of rapid cosmic-ray fluctuations as the mean power of the cosmic-ray power spectrum in the frequency range 10⁻⁴ −1.67 × 10⁻³ Hz (10 min to about 3 h). A dominant 11-year periodicity in the index is found in all neutron monitors. We also report on intermittent, short-term periodicities in the power of rapid cosmic-ray fluctuations. A strong mid-term periodicity of about 1.6 – 1.8 years, possibly related to a recently found similar periodicity in IMF, appears in CR fluctuation power since the 1980s. Another strong periodicity is found at 1 year, which is likely related to the relative position of the Earth in the heliosphere. These results also provide new challenge to test the cosmic-ray modulation 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.     

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.     

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

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

Hale-cycle effects in cosmic-ray intensity during the last four cycles

Monthly cosmic-ray data from Inuvik (0.16 GV) and Climax (2.96 GV) Neutron Monitor stations has been studied with the aid of solar activity parameters for the time period 1947–1995. Systematic differences in the overall shape of successive 11-year modulation cycles and similarities in the alternate 11-year cycles seem to be related to the polarity reversals of the polar magnetic field of the Sun. This suggests a possible effectiveness of the Hale cycle during even and odd solar activity cycles. Our results can be understood in terms of open and closed models of the heliosphere. Positive north pole of the Sun leads to open heliosphere where particles reach the Earth more easily when their access route is by the heliospheric oolar regions (even cycles) than when they gain access along the current sheet (odd cycles). In this case as the route of access becomes longer due to the waviness of the neutral sheet, the hysteresis effect of cosmic-rays is also longer. This interpretation is explained in terms of different contributions of convection, diffusion and drift mechanisms to the whole modulation process influencing cosmic-ray transport in the heliosphere.     

Solar Modulation of Cosmic Rays during the Declining and Minimum Phases of Solar Cycle 23: Comparison with Past Three Solar Cycles

We study solar modulation of galactic cosmic rays (GCRs) during the deep solar minimum, including the declining phase, of solar cycle 23 and compare the results of this unusual period with the results obtained during similar phases of the previous solar cycles 20, 21, and 22. These periods consist of two epochs each of negative and positive polarities of the heliospheric magnetic field from the north polar region of the Sun. In addition to cosmic-ray data, we utilize simultaneous solar and interplanetary plasma/field data including the tilt angle of the heliospheric current sheet. We study the relation between simultaneous variations in cosmic ray intensity and solar/interplanetary parameters during the declining and the minimum phases of cycle 23. We compare these relations with those obtained for the same phases in the three previous solar cycles. We observe certain peculiar features in cosmic ray modulation during the minimum of solar cycle 23 including the record high GCR intensity. We find, during this unusual minimum, that the correlation of GCR intensity is poor with sunspot number (correlation coefficient R=?0.41), better with interplanetary magnetic field (R=?0.66), still better with solar wind velocity (R=?0.80) and much better with the tilt angle of the heliospheric current sheet (R=?0.92). In our view, it is not the diffusion or the drift alone, but the solar wind convection that is the most likely additional effect responsible for the record high GCR intensity observed during the deep minimum of solar cycle 23.     

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 secular modulation of solar rotation from 1943 to 1992 and its time-delayed correlation with the 55-year grand cycle of the 11-year solar cycle

We devised a new method, which we call the running-segment method, to achieve high-resolution time series of indices of solar rotation for determining the latitude dependence of the differential rotation by a least-squares fitting of the daily translation of positions of sunspot groups during a fixed time segment of 11 years. The segment is moved by an amount of one year to determine the differential profile of the next point of time. Time of the determined rotation data is defined by an arithmetic mean of the beginning and ending years of the segment. The rotation underwent an acceleration from 1948 to 1974 and a deceleration from 1974 to 1987. We found that the time profile of the indexM, the angular momentum surface layer density defined by integration of the angular momentum volume density over the whole surface, follows almost exactly the time profile of the 11-year running mean of the yearly mean of the sunspot relative number with a delay time of about 20 years. The acceleration (deceleration) phase corresponds to the ascending (descending) phase of amplitude of the 11-year solar cycle of cycle 16 (19) to cycle 19 (20) with a delay time of about 20 years. The cycles 15–20 correspond to the 55-year grand cycle V of the 11-year cycle. The delay time of about 20 years agrees well with the delay time predicted by a nonlinear dynamo theory of the solar cycle for driving the 55-year modulation of the 11-year solar cycle. The agreement suggests that the Lorentz force of the magnetic field of the solar cycle during grand cycle V drives the solar rotation modulation from 1948 to 1987 and that the force needed about 20 years to modify the rotation during 1943–1992.     

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.     

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.     

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 10-year time delay of the solar cycle luminosity modulation of the Sun behind the solar cycle magnetic oscillation

We found an evidence that the solar cycle luminosity modulation of the Sun deduced from the total irradiance modulation which was measured by the Earth Radiation Budget (ERB) experiment on board of Nimbus 7 from November 16, 1978 to December 13, 1993 was not in phase with the solar cycle magnetic oscillation when we used the sunspot relative number as its index. The modulation was delayed in time behind the solar cycle magnetic oscillation by an amount of about 10.3 years on the order of length of one solar cycle. In order to quantitatively evaluate the correlation between the two quantities, we devised a method to extract characteristics which were proper to a particular solar cycle by defining a new index of the correlation called multiplied correlation index (MCI). We found that the characteristics of the ERB data time profile between solar cycles 21 and 22 were more similar to those of the solar cycle magnetic oscillation between solar cycles 20 and 21 than those between solar cycles 21 and 22 and thus the time profile of the luminosity modulation from the maximum phase of solar cycle 21 to the declining phase of the solar cycle 22 corresponded to the solar cycle magnetic oscillation from the maximum phase of solar cycle 20 to the declining phase of solar cycle 21. We interpret this phenomenon as an evidence that main features of the modulation is not caused by dark sunspots and bright faculae and plages on the surface of the Sun that should instantaneously affect the luminosity modulation but is caused by time-delayed modulation of global convection by the Lorentz force of the magnetic field of the solar cycle. The delay time of about 10.3 years is the time needed for the force to modify the flows of the convection and to modulate heat flow. Thus the delay time is a function of the strength of the magnetic field oscillation of the solar cycle which is represented by amplitude of the solar cycle. Accordingly, the delay time for other time intervals of the solar cycle magnetic oscillation with different amplitudes can be different from 10.3 years for the interval of the present analysis.     

Short-term variations of cosmic-ray intensity and flare related data in 1981–1983

A statistical analysis of the cosmic-ray intensity (CR) daily means, registered at three Neutron Monitor stations with different cut-off rigidities (Deep River, Climax and Alma-Ata), as well as, of the solar hard X-ray flares fluence recorded by Venera-13, -14 space-probes, has been performed for the time interval 1981–1983. Various methods of time series spectrum analysis, such as Fast Fourier Analysis (FFT) and Maximum Entropy (MESA), accompanied by appropriate statistical tests, have been employed to detect periodicities, while the method of Successive Approximations (SA) is used independently in order to define the amplitude and the phase of each fluctuation. New short-term periodicities of 100, 70, 50 and 32 days, in addition to the known ones of 152, 27 and 14 days, appeared in cosmic ray data. During this particular time interval, similar spectral behaviour has been reported in the solar hard X-ray flares data. The influence of the solar hard X-ray flares variability in the energy range 50–500 keV, expressed by their fluence values, upon the cosmic-ray modulation, is discussed.     

Cosmic-Ray Decreases and Interplanetary Disturbances During the Solar Magnetic Polarity Reversal in Solar Cycle 20

Using the cosmic-ray intensity data recorded with ground-based monitors at Mt. Washington and Deep River, and with cosmic-ray telescopes on Pioneer 8 and 9 spacecraft as well as the 2-hour averages of the IMF (magnitude and direction) and the solar wind bulk speed and density at 1 AU, the cosmic-ray decreases and interplanetary disturbances, that occurred during the period of solar magnetic polarity reversal in solar cycle 20, were investigated.We observed a two-step Forbush decrease on 22–23 November 1969, and a Forbush decrease on 26 November 1969, which are respectively consistent with the model of Barnden (1973), and of Parker (1963) and Barnden (1973). Only one Forbush decrease event was observed in December 1969, a period during which there was a solar magnetic polarity reversal; the Forbush decrease was attributed to a long-lived corotating high-speed solar wind stream. This is indicative that at heliolongitudes from 43° E to 70° W of S–E radial, covered by the observations, the solar magnetic polarity reversal in solar cycle 20 was not carried by, nor related to, individual transient structures, and that the reversal most probably evolved gradually.     

Aspects of the long-term cosmic-ray modulation

To investigate the long-term modulation of galactic cosmic rays at the ground-based detector energies, the monthly values of the neutron monitor (Climax, Mt. Washington, Deep River, and Huancayo) and ionization chamber (Cheltenham/Fredericksburg, Huancayo, and Yakutsk) intensities have been correlated with the sunspot numbers (used as a proxy index for transient solar activity) for each phase of sunspot cycles 18 to 22. Systematic differences are found for results concerning odd and even sunspot cycles. During odd cycles (19 and 21) the onset time of cosmic-ray modulation is delayed when compared with the onset time of the sunspot cycle, while they are more similar during even (18, 20, and 22) cycles. Checking the green corona data, on a half-year basis, we found typical heliolatitudinal differences during ascending phases of consecutive sunspot cycles. This finding suggests a significant role of the latitudinal coronal behaviour in the heliospherical dynamics during a Hale cycle. Such effectiveness concerns not only the transient interplanetary perturbations but also the recurrent ones. In fact, when lag between cosmic-ray data and sunspot numbers is considered, the anticorrelation between both parameters is very high (correlation coefficient |r| > 0.9) for all the phases considered, except for the declining ones of cycles 20 and 21, when high-speed solar wind streams coming from coronal holes affect the cosmic-ray propagation, and theRz parameter is no longer the right proxy index for solar-induced effects in the interplanetary medium.     

Short and long-term variations in the cosmic ray intensity and their connection with the 5303 Å coronal line intensity in solar cycle No. 20

The cosmic ray modulation in the period 1965–70 is investigated by the comparison of the intensity data of groundbased stations with different response to primaries. The socalled step-like modulation, already observed by other authors, is found to be produced by the overlapping between the quasi-stationary solar cycle modulation and the Forbush decrease events. Moreover a good correlation between the cosmic-ray variance (Forbush decrease index) and the 5303 coronal intensity at middle heliolatitudes (17.5°–42.5°) is found, while the quasi-stationary solar cycle modulation is well correlated with the 5303 intensity near the solar equator (0°–17.5°). The different time behaviour of the solar activity at different heliolatitudes causes the step-like modulation.     

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.     

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.