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.     

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.     

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.     

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-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.     

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.     

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.     

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 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.     

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.     

Long-Term Modulation of Cosmic-Ray Intensity and Correlation Analysis Using Solar and Heliospheric Parameters

Based on the monthly sunspot numbers (SSNs), the solar-flare index (SFI), grouped solar flares (GSFs), the tilt angle of heliospheric current sheet (HCS), and cosmic-ray intensity (CRI) for Solar Cycles 21?–?24, a detailed correlation study has been performed using the cycle-wise average correlation (with and without time lag) method as well as by the “running cross-correlation” method. It is found that the slope of regression lines between SSN and SFI, as well as between SSN and GSF, is continuously decreasing from Solar Cycle 21 to 24. The length of regression lines has significantly decreased during Cycles 23 and 24 in comparison to Cycles 21 and 22. The cross-correlation coefficient (without time lag) between SSN–CRI, SFI–CRI, and GSF–CRI has been found to be almost the same during Cycles 21 and 22, while during Cycles 23 and 24 it is significantly higher between SSN–CRI and HCS–CRI than for SFI–CRI and GSF–CRI. Considering time lags of 1 to 20 months, the maximum correlation coefficient (negative) amongst all of the sets of solar parameters is observed with almost the same time lags during Cycles 21?–?23, whereas exceptional behaviour of the time lag has been observed during Cycle 24, as the correlation coefficient attains its maximum value with two time lags (four and ten months) in the case of the SSN–CRI relationship. A remarkably large time lag (22 months) between HCS and CRI has been observed during the odd-numbered Cycle 21, whereas during another odd cycle, Cycle 23, the lag is small (nine months) in comparison to that for other solar/flare parameters (13?–?15 months). On the other hand, the time lag between SSN–CRI and HCS–CRI has been found to be almost the same during even-numbered Solar Cycles 22 and 24. A similar analysis has been performed between SFI and CRI, and it is found that the correlation coefficient is maximum at zero time lag during the present solar cycle. The GSFs have shown better maximum correlation with CRI as compared to SFI during Cycles 21 to 23, indicating that GSF could also be used as a significant solar parameter to study the cosmic-ray modulation. Furthermore, the running cross-correlation coefficient between SSN–CRI and HCS–CRI, as well as between solar-flare activity parameters (SFI and GSF) and CRI is observed to be strong during the ascending and descending phases of solar cycles. The level of cosmic-ray modulation during the period of investigation shows the appropriateness of different parameters in different cycles, and even during the different phases of a particular solar cycle. We have also studied the galactic cosmic-ray modulation in relation to combined solar and heliospheric parameters using the empirical model suggested by Paouris et al. (Solar Phys.280, 255, 2012). The proposed model for the calculation of the modulated cosmic-ray intensity obtained from the combination of solar and heliospheric parameter gives a very satisfactory value of standard deviation as well as \(R^{2}\) (the coefficient of determination) for Solar Cycles 21?–?24.     

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.     

Multi-parametric effect of solar activity on cosmic rays

The long-term modulation of cosmic ray intensity (CRI) by different solar activity (SA) parameters and an inverse correlation between individual SA parameter and CRI is well known. Earlier, it has been suggested that the concept of multi-parametric modulation of CRI may play an important role in the study of long-term modulation of CRI. In the present study, we have tried to investigate the combined effect of a set of two SA parameters in the long-term modulation of CRI. For this purpose, we have used a new statistical technique called “Running multiple correlation method”, based on the “Running cross correlation method”. The running multiple correlation functions among different sets of two SA parameters (e.g., sunspot numbers and solar flux, sunspot numbers and coronal index, sunspot numbers and grouped solar flares, etc.) and CRI have been correlated separately. It is found that the strength of multiple correlation (among two SA parameters and CRI) and cross correlation (between individual SA parameter and CRI) is almost similar throughout the period of investigation (1955–2005). It is also found that the multiple correlations among various SA parameters and CRI is stronger during ascending and descending phases of the solar cycles and it becomes weaker during maxima and minima of the solar cycles, which is in accordance with the linear relationship between SA parameters and CRI. The values of multiple correlation functions among different sets of SA parameters and CRI fall well within the 95% confidence interval. In the view of odd-even hypothesis of solar cycles, the strange behaviour of present cycle 23 (odd cycle), as this is characterized by many peculiarities with double peaks and many quiet periods (Gnevyshev gaps) interrupted the solar activity (for example April 2001, October–November 2003 and January 2005), leads us to speculate that the solar cycle 24 (even cycle) might be of exceptional nature.     

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.     

Solar-cycle evolution of the coronal general magnetic field of 1959–1974 and the synchronous variation of high-speed solar wind streams and galactic cosmic rays

The simultaneous enhancement or subsidence of both the high-speed solar wind streams and the galactic cosmic rays in the minimum or the maximum phase of the solar cycle are interpreted in a unified manner by the concept of geometrical evolution of the general magnetic field of the corona-heliomagnetosphere system. The coronal general magnetic field evolves from an open dipole-like configuration in the minimum phase to a closed configuration with many loop-like formations in the maximum phase of the solar cycle. This concept, developed in a theoretical solar-cycle model driven by the dynamo action of the global convection, is examined and found to be valid by studying the evolution of the coronal general magnetic field calculated from the observed surface general magnetic field of 1959–1974. It is also found that the energy density of the poloidal component of the general surface field, from which the coronal field originates, attained a maximum in the maximum phase and showed a evolution with virtually no phase delay with respect to that of the toroidal component of the field, to which the sunspot activity is related. The subsidence of the high-speed solar wind in the maximum phase is understood as a braking of the solar wind streams by the tightly closed and strong coronal field lines in the lower corona in the maximum phase. The field lines of the heliomagnetosphere, which originate from the coronal field lines drawn by the solar wind, are inferred to be also more tightly closed at the heliopause in the maximum phase than in the minimum phase. The decrease of the galactic cosmic rays in the maximum phase (known as the Forbush's negative correlation between the galactic cosmic ray intensity and the solar activity or the Forbush solar-cycle modulation of the galactic cosmic rays) is interpreted as a braking of the cosmic rays by the closed magnetic field lines at the heliopause. The observed phase lag (approximately one year) of the galactic cosmic ray modulation with respect to the evolution of the solar cycle, and the observed absence of the gradient of the total cosmic ray intensity between 1 AU and 8 AU, are discussed to support this view of the cosmic ray modulation at the remote heliopause, and reject other hypotheses to explain the phenomenon in terms of the magnetic irregularities of various kinds carried by the solar wind: The short-term Forbush decrease at a time of a flare shows that the magnetic irregularities can react on the cosmic rays relatively near the Sun if they even played a dominant role in the long-term modulation. The concept of the general magnetic field of the corona and the surface is also used to understand the basic nature of the surface field itself, by comparing the geometry of the calculated coronal field lines with the eclipse photographs of the corona, and by discussing, in the context of the coronal general magnetic field associated with the solar cycle, the process of the emergence of the coronal field lines from the interior and the formation of the transequatorial arches and loops connecting the two hemispheres in the corona.     

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.     

Evidence for Planetary Forcing of the Cosmic Ray Intensity and Solar Activity Throughout the Past 9400 Years

Paleo-cosmic-ray (PCR) records based on cosmogenic ¹⁰Be and ¹⁴C data are used to study the variations in cosmic-ray intensity and solar activity over the past 9400 years. There are four strong correlations with the motion of the Jovian planets; the probability of occurring by chance being <?10^?5. They are i) the PCR periodicities at 87, 350, 510, and 710 years, which closely approximate integer multiples of half the Uranus–Neptune synodic period; ii) eight periodicities in the torques calculated to be exerted by the planets on an asymmetric tachocline that approximate the periods observed in the PCR; iii) the maxima of the long-term PCR variations are coincident with syzygy (alignment) of the four Jovian planets in 5272 and 644 BP; and iv) in the time domain, the PCR intensity decreases during the first 60 years of the ≈?172 year Jose cycle (Jose, Astron. J. 70, 193, 1965) and increases in the remaining ≈?112 years in association with barycentric anomalies in the distance between the Sun and the center of mass of the solar system. Furthermore, sunspot and neutron-monitor data show that three anomalous sunspot cycles (4th, 7th, and 20th) and the long sunspot minimum of 2006 – 2009 CE coincided with the first and second barycentric anomalies of the 58th and 59th Jose cycles. Phase lags between the planetary and heliospheric effects are ≤?five years. The 20 largest Grand Minima during the past 9400 years coincided with the latter half of the Jose cycle in which they occurred. These correlations are not of terrestrial origin, nor are they due to the planets’ contributing directly to the cosmic-ray modulation process in the heliosphere. Low cosmic-ray intensity (higher solar activity) occurred when Uranus and Neptune were in superior conjunction (mutual cancellation), while high intensities occurred when Uranus–Neptune were in inferior conjunction (additive effects). Many of the prominent peaks in the PCR Fourier spectrum can be explained in terms of the Jose cycle, and the occurrence of barycentric anomalies.     

Cosmic-ray intensity versus solar soft X-ray background in cross-correlation analysis

The relationship between the galactic cosmic ray modulation (CR) and the non-flare coronal level, as given by the solar soft X-ray background (XBG), is investigated from 1 July 1968 to 30 June 1980 on a daily basis. The stationarity problem of a multivariate time series, as well as the role of the short- and medium-term corona variability are faced. From them it is found that the CR/XBG relation is variable during the considered heliomagnetic semicycle, while CR and XBG are highly anticorrelated on a long-time scale (12-month averages). The CR/XBG relationship during the declining phase of solar activity shows a moderately strong anticorrelation, on short- and medium-term time scales (coefficient up to –0.77 for 27-day running averages), went towards insignificant values in the minimum phase and is only partially reconstructed during the rise of the following solar cycle. During the solar activity maximum of cycle 20 the cosmic-ray modulation is only related to the short-term coronal fluctuations (no other time scales are significant, supporting the reliability of the so-called `Gnevyshev gap' in solar parameters).     

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.     

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.