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.     

North-south asymmetry in solar, interplanetary, and geomagnetic indices

Data of hourly interplanetary plasma (field magnitude, solar wind speed, and ion density), solar (sunspot number, solar radio flux), and geomagnetic indices (Kp, Ap) over the period 1970-2010, have been used to examine the asymmetry between the solar field north and south of the heliospheric current sheet (HCS). A persistent yearly north-south asymmetry of the field magnitude is clear over the considered period, and there is no magnetic solar cycle dependence. There is a weak N-S asymmetry in the averaged solar wind speed, exhibited well at times of maximum solar activities. The solar plasma is more dense north of the current sheet than south of it during the second negative solar polarity epoch (qA < 0). Moreover, the N - S asymmetry in solar activity (Rz) can be statistically highly significant. The sign of the average N - S asymmetry depends upon the solar magnetic polarity. The annual magnitudes of N - S asymmetry depend positively on the solar magnetic cycle. Most of the solar radio flux asymmetries occurred during the period of positive IMF polarity.     

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.     

Twenty-Seven-Day Variation of Galactic Cosmic Rays

Neutron monitor data observed at Climax (CL) and Huancayo/Haleakala (HU/HAL) have been used to calculate the amplitude A of the 27-day variation of galactic cosmic rays (CRs). The median primary rigidity of response, R _m, for these detectors encompasses the range 18 ≤R _m≤46 GV and the threshold rigidity R ₀ covers the range 2.97≤R ₀≤12.9 GV. The daily average values of CR counts have been harmonically analyzed for each Bartels solar rotation (SR) during the period 1953 – 2001. The amplitude of the 27-day CR variation is cross-correlated to solar activity as measured by the sunspot number R, the interplanetary magnetic field (IMF) strength B, the z-component B _z of the IMF vector, and the tilt angle ψ of the heliospheric current sheet (HCS). It is anticorrelated to the solar coronal hole area (CHA) index as well as to the solar wind speed V. The wind speed V leads the amplitude by 24 SRs. The amplitude of the 27-day CR variation is better correlated to each of the these parameters during positive solar polarity (A>0) than during negative solar polarity (A<0) periods. The CR modulation differs during A>0 from that during A<0 owing to the contribution of the z-component of the IMF. It differs during A ₁>0 (1971 – 1980) from that during A ₂>0 (1992 – 2001) owing to solar wind speed.     

Galactic Cosmic Ray Modulation and the Last Solar Minimum

In this work the galactic cosmic ray modulation in relation to solar activity indices and heliospheric parameters during the years 1996??C?2010 covering solar cycle 23 and the solar minimum between cycles 23 and 24 is studied. A new perspective of this contribution is that cosmic ray data with a rigidity of 10 GV at the top of the atmosphere obtained from many ground-based neutron monitors were used. The proposed empirical relation gave much better results than those in previous works concerning the hysteresis effect. The proposed models obtained from a combination of solar activity indices and heliospheric parameters give a standard deviation <?10?% for all the cases. The correlation coefficient between the cosmic ray variations of 10?GV and the sunspot number reached a value of r=?0.89 with a time lag of 13.6±0.4 months. The best reproduction of the cosmic ray intensity is obtained by taking into account solar and interplanetary indices such as sunspot number, interplanetary magnetic field, CME index, and heliospheric current sheet tilt. The standard deviation between the observed and calculated values is about 7.15?% for all of solar cycle 23; it also works very well during the different phases of the cycle. Moreover, the use of the cosmic ray intensity of 10?GV during the long minimum period between cycles 23 and 24 is of special interest and is discussed in terms of cosmic ray intensity modulation.     

Global Heliospheric Parameters and Cosmic-Ray Modulation: An Empirical Relation for the Last Decades

We study empirical relations between the modulation of galactic cosmic rays quantified in terms of the modulation potential and the following global heliospheric parameters: the open solar magnetic flux, the tilt angle of the heliospheric current sheet, and the polarity of the heliospheric magnetic field. We show that a combination of these parameters explains the majority of the modulation potential variations during the neutron monitor era 1951 – 2005. Two empirical models are discussed: a quasi-linear model and a model assuming a power-law relation between the modulation potential and the magnetic flux. Both models describe the data fairly well. These empirical models provide a simple tool for evaluating various cosmic-ray related effects on different time scales. The models can be extended backwards in time or used for predictions, if the corresponding global heliospheric variables can be independently estimated.     

Heliospheric modulation of cosmic rays in solar cycles 19–23

The previously developed basic theory of the heliospheric modulation of high-energy cosmic rays is generalized to lower energies. Comparison of the theory with the results of long-term observations of cosmic rays in the stratosphere carried out by the group from the Lebedev Institute of Physics inMoscow andMurmansk shows satisfactory agreement. The cosmic rays are shown to behave quite differently when even and odd solar cycles alternate. Possible causes of the anomalously high cosmic-ray intensity recorded during the last solar activity minimum are discussed.     

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.     

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.     

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.     

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 Polarity Dependence of Cosmic Ray Power Spectra Observed with Mawson Underground Muon Telescopes

Power spectral density (PSD) of cosmic rays has been calculated from hourly averaged counts observed by underground muon telescopes located at Mawson over the low-frequency range 2.7×10⁻⁷ – 1.4×10⁻⁴ Hz. The first two harmonics of the solar daily variation are well defined for even cycles (20 and 22) whereas only the first harmonic is defined in cycle 21. The amplitude of the diurnal variation is lower for even cycles than for the odd cycle. The spectral power of the odd cycle exceeds those of the even cycles. The spectra are flatter and have lower power when the interplanetary magnetic field (IMF) is directed away from the Sun above the current sheet (A>0) than when the IMF is directed toward the Sun above the current sheet (A<0). The spectra imply that heliospheric magnetic turbulence may be more variable on time scales of several years than previously suspected.     

On the Relationship of the 27-day Variations of the Solar Wind Velocity and Galactic Cosmic Ray Intensity in Minimum Epoch of Solar Activity

We study the relationship of the 27-day variations of the galactic cosmic ray intensity with similar variations of the solar wind velocity and the interplanetary magnetic field based on observational data for the Bartels rotation period # 2379 of 23 November 2007 – 19 December 2007. We develop a three-dimensional (3-D) model of the 27-day variation of galactic cosmic ray intensity based on the heliolongitudinally dependent solar wind velocity. A consistent, divergence-free interplanetary magnetic field is derived by solving Maxwell’s equations with a heliolongitudinally dependent 27-day variation of the solar wind velocity reproducing in situ observations. We consider two types of 3-D models of the 27-day variation of galactic cosmic ray intensity, i) with a plane heliospheric neutral sheet, and ii) with the sector structure of the interplanetary magnetic field. The theoretical calculations show that the sector structure does not significantly influence the 27-day variation of galactic cosmic ray intensity, as had been shown before, based on observational data. Furthermore, good agreement is found between the time profiles of the theoretically expected and experimentally obtained first harmonic waves of the 27-day variation of the galactic cosmic ray intensity (with a correlation coefficient of 0.98±0.02). The expected 27-day variation of the galactic cosmic ray intensity is inversely correlated with the modulation parameter ζ (with a correlation coefficient of −0.91±0.05), which is proportional to the product of the solar wind velocity V and the strength of the interplanetary magnetic field B (ζ∼VB). The high anticorrelation between these quantities indicates that the predicted 27-day variation of the galactic cosmic ray intensity mainly is caused by this basic modulation effect.     

Study of the Cosmic Ray Diurnal Anisotropy During Different Solar and Magnetic Conditions

The pressure-corrected hourly counting rate data of four neutron monitor stations have been employed to study the variation of cosmic ray diurnal anisotropy for a period of about 50 years (1955–2003). These neutron monitors, at Oulu ( R _c = 0.78 GV), Deep River ( R _c = 1.07 GV), Climax ( R _c = 2.99 GV), and Huancayo ( R _c = 12.91 GV) are well distributed on the earth over different latitudes and their data have been analyzed. The amplitude of the diurnal anisotropy varies with a period of one solar cycle (∼11 years), while the phase varies with a period of two solar cycles (∼22 years). In addition to its variation on year-to-year basis, the average diurnal amplitude and phase has also been calculated by grouping the days for each solar cycle, viz. 19, 20, 21, 22, and 23. As a result of these groupings over solar cycles, no significant change in the diurnal vectors (amplitude as well as phase) from one cycle to other has been observed. Data were analyzed by arranging them into groups on the basis of the polarity of the solar polar magnetic field and consequently on the basis of polarity states of the heliosphere ( A > 0 and A < 0). Difference in time of maximum of diurnal anisotropy (shift to earlier hours) is observed during A < 0 (1970s, 1990s) polarity states as compared to anisotropy observed during A > 0 (1960s, 1980s). This shift in phase of diurnal anisotropy appears to be related to change in preferential entry of cosmic ray particles (via the helioequatorial plane or via solar poles) into the heliosphere due to switch of the heliosphere from one physical/magnetic state to another following the solar polar field reversal.     

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.     

Twenty-two year modulation of cosmic rays associated with polarity reversal of polar magnetic field of the sun

The existence of the 22-year modulation of cosmic ray intensity is pointed out, using data of the ion chamber at Huancayo and the neutron monitors at Ottawa and Deep River for about four solar cycles. The modulation consists of two discrete states (high and low intensities), corresponding respectively to those of the polarity of the polar magnetic field of the Sun. This can be interpreted on the basis of the following hypothesis; when the polar magnetic field of the Sun is nearly parallel to the galactic magnetic field, they could easily connect with each other, so that galactic cosmic rays could intrude more easily into the heliomagnetosphere along the magnetic line of force, as compared with those in the anti-parallel state of the magnetic fields. The observed intensity difference between two states is about 4.3 ± 0.2% for neutron monitor (P_c = 1.5GV). The abnormal increase in proton (0.28–0.42 GV) and electron (0.41-3.24 GV) fluxes in the 20th solar cycle and the sudden appearance of anomalous components (He⁺, etc.) since 1972 can be also explained on the basis of the present hypothesis. The transition between the two states has a time lag behind the polarity reversal, depending on the cosmic ray rigidity, such as about 1 year for the neutron monitor (P_c = 1.5 GV) and about 3.5 years for low rigidity components (P < 1 GV). These time lags could be explained on the basis of the generalized Simpson's coasting solar wind model and the general diffusion-convection theory on some assumptions.     

A search of cosmic-ray variations generated by pulsations of the heliosphere

Application of new statistical techniques to time series allow the investigation of cosmic-ray intensity variation in the periodicity range of 1 to 10 years. We can put significant levels to the existence of these oscillations and define their character as quasi-periodic and/or recurrent. Correlations between cosmic-ray intensity variations and solar activity changes during 1944–1979 are investigated. The two-year variation in cosmic rays is observed to be variable both in amplitude and phase, and not correlated with sunspot cyclic variations; but seems to depend on the magnetic polarity of the interplanetary medium. No significant evidence for the existence of longer period variations is obtained.     

Is the Highest Cosmic-Ray Flux Yet to Come?

The recent 2009 solar-minimum period was characterized by a record-setting high Galactic cosmic-ray flux observed at Earth. This, along with the unexpected low heliospheric magnetic-field magnitude, caused this period to be characterized as unusual compared with previous minimum epochs. In this work, selected solar-activity proxies and corresponding cosmic-ray observations for the past five solar cycles are compared with each other, and we identify those that showed unusual behaviour during the 2009 solar-minimum modulation period. Using a state-of-the-art numerical-modulation model, the proton-intensity spectra for the past solar minima are reproduced to establish which of the transport processes might be considered the main cause of this unusually high cosmic-ray flux. It is found that diffusion was more prominent during 2009 so that drift effects on the modulation of cosmic rays in the heliosphere were less evident than during previous solar-polarity epochs. However, particle drifts still occurred and because of these drift effects, the proton spectrum is predicted to be even higher during the coming A>0 solar-minimum period.     

Similarities and Distinctions in Cosmic-Ray Modulation During Different Phases of Solar and Magnetic Activity Cycles

We study the solar-activity and solar-polarity dependence of galactic cosmic-ray intensity (CRI) on the solar and heliospheric parameters playing a significant role in solar modulation. We utilize the data for cosmic-ray intensity as measured by neutron monitors, solar activity as measured by sunspot number (SSN), interplanetary plasma/field parameters, solar-wind velocity [V] and magnetic field [B], as well as the tilt of the heliospheric current sheet [Λ], and we analyze these data for Solar Cycles 20?–?24 (1965?–?2011). We divide individual solar cycles into four phases, i.e. low, high, increasing, and decreasing solar activity. We perform regression analysis to calculate and compare the CRI-response to changes in different solar/interplanetary parameters during

1. different phases of solar activity and
2. similar activity phases but different polarity states.

We find that the CRI-response is different during negative (A<0) as compared to positive (A>0) polarity states not only with SSN and Λ but also with B and V. The relative CRI-response to changes in various parameters, in negative (A<0) as compared to positive (A>0) state, is solar-activity dependent; it is ≈?2 to 3 times higher in low solar activity, ≈?1.5 to 2 times higher in moderate (increasing/decreasing) activity, and it is nearly equal in high solar-activity conditions. Although our results can be ascribed to the preferential entry of charged particles via the equatorial/polar regions of the heliosphere as predicted by drift models, these results also suggest that we should look for any polarity-dependent response of solar-wind and transport parameters in modulating CRI in the heliosphere.     

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.