Solar Modulation Of Cosmic Rays Research Articles

The charge-sign dependent effect in the solar modulation of cosmic rays

The centennial anniversary of the discovery of cosmic rays was in 2012. Since this discovery considerable progress has been made on several aspects related to galactic cosmic rays in the heliosphere. It is known that they encounter a turbulent solar wind with an imbedded heliospheric magnetic field when entering the Sun’s domain. This leads to significant global and temporal changes in their intensity inside the heliosphere, a process known as the solar modulation of cosmic rays. The prediction of a charge-sign dependent effect in solar modulation in the late 1970s and the confirmatory observational discoveries can also be considered as a milestone. A short review is given of these predictions based on theoretical and numerical modelling work, the observational confirmation and related issues.

Solar Modulation of Cosmic Rays

This is an overview of the solar modulation of cosmic rays in the heliosphere. It is a broad topic with numerous intriguing aspects so that a research framework has to be chosen to concentrate on. The review focuses on the basic paradigms and departure points without presenting advanced theoretical or observational details for which there exists a large number of comprehensive reviews. Instead, emphasis is placed on numerical modeling which has played an increasingly significant role as computational resources have become more abundant. A main theme is the progress that has been made over the years. The emphasis is on the global features of CR modulation and on the causes of the observed 11-year and 22-year cycles and charge-sign dependent modulation. Illustrative examples of some of the theoretical and observational milestones are presented, without attempting to review all details or every contribution made in this field of research. Controversial aspects are discussed where appro- priate, with accompanying challenges and future prospects. The year 2012 was the centennial celebration of the discovery of cosmic rays so that several general reviews were dedicated to historical aspects so that such developments are brie y presented only in a few cases.

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 (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 is the most likely additional effect responsible for the record high GCR intensity observed during the deep minimum of solar cycle 23.

THREE-DIMENSIONAL WAVY HELIOSPHERIC CURRENT SHEET DRIFTS

We present an analytic method to determine the directions of the three-dimensional (3D) heliospheric current sheet (HCS) drift for any tilt angle based on Parker's heliospheric magnetic field and compare it with published two-dimensional and quasi-3D methods. We also present a new approach to determine the magnitude of the 3D HCS drift numerically. Implications of these new methods for the solar modulation of Galactic cosmic rays are considered and compared with results from prior methods reported in the literature. Our results support the concept that HCS drift plays an important role in the solar modulation of cosmic rays.

A new empirical relation to estimate atmospheric electrical columnar resistance, effect of changing aerosol concentration and cosmic ray ionization on it: A quantitative study

A new empirical relation is found among atmospheric electrical columnar resistance, aerosol concentration, and eddy diffusion coefficient. The methodology is reported for the first time. This empirical relation can be used regularly for estimating columnar resistance. As solar modulation of cosmic rays and consequent changes in columnar resistance of global atmospheric electric circuit convey solar influence on lower atmospheric meteorological phenomena, a quantitative comparison of percent change in columnar resistance due to change in cosmic ray ionization and that due to change in aerosol concentration is made, which shows that 20% change in cosmic ray ionization causes more (about two times) change in columnar resistance over ocean but less (about 1/3) change over land as compared to that caused by 20% change in aerosol concentration. This confirms that over ocean, ionization due to cosmic rays and over land, atmospheric aerosol concentration mainly determine columnar resistance. This land‐ocean contrast gets reduced with atmospheric turbulence. It is found that, for small heights of the boundary layer (low eddy diffusivity), columnar resistance changes more with respect to change in aerosol concentration, and change in eddy diffusivity has negligible effect on it, but for large values of heights (large eddy diffusivity), there is substantial increase in columnar resistance. Furthermore, exceeding a certain critical value of conductivity, columnar resistance becomes independent of conductivity. The estimated values of columnar resistance using this method are very well consistent with the previous studies. Also, calculated percent change in global atmospheric electrical parameters agrees well with the previous results.

A wavelet based analysis of cosmic rays modulation

In this work we present estimated results of the Morlet wavelet analysis from the modulation of relative cosmic ray intensities, sunspot numbers, modulation potentials variabilities registered by Moscow and worldwide neutron monitors (NM). Unlike the conventional spectral analysis the wavelet transform are suitable tool for description of non-stationary processes containing multiscale features detection of singularities and analysis of transient phenomena [P. Kumar, E. Foufoula-Georgiou, Reviews of Geophysics 35 (4) (1977) 385–412]. Methods such as wavelets should be very suitable, thus it can be applied to the problem under consideration. On the other hand this approach is not frequently used for cosmic ray time series. Solar modulation of cosmic rays and their possible effect on cloud cover is the most complex candidate and remains hardest to test. However the yearly averages of cosmic ray intensities registered by Moscow NM from 1958 to 2007 are investigated to verify and explore 11-year cycles and other structures. Besides Time series of solar activity indicators such as sunspot number have been studied over the period 1810–2000 with Morlet wavelet method. The modulation potential ϕ often parametrising differential energy spectrum of galactic cosmic rays (GCR) is also used in this work to characterise solar modulation of GCRs. We have investigated the series of yearly values of the modulation potential ϕ of [I.G. Usoskin, K. Alanko-Huotari, G.A. Kovaltsov, K. Mursula, Heliospheric modulation of cosmic rays monthly reconstruction for 1951–2004, Journal of Geophysical Research 110 (2005) A12108] since 1951–2004 using the data of worldwide NM. Main results of the wavelet analysis and reconstruction suggest that the maximum of Morlet decomposition coefficients was found around the main 11–12 year cycle. However we have found for both solar activity indicator: the sunspot number and modulation potential a dominating period around 12–15 years. Magnitude of cycles is not absolutely the same but vary from cycle to cycle. The attempt of extrapolation has shown other periods of about 20–22, 27–30 years after the year 2007.

Variations on Sun’s role in climate change

In their Opinion piece “Is Climate Sensitive to Solar Variability?” (Physics Today, Physics Today 0031-9228 61 3 2008 50 https://doi.org/10.1063/1.2897951. March 2008, page 50 ), Nicola Scafetta and Bruce West draw attention to a “phenomenological solar signature” they find in preindustrial records of global temperature. Correlations between temperature proxies and solar activity have been reported since the 18th century; see, for example, reference 11. J. Eddy, Science 192, 1189 (1976). https://doi.org/10.1126/science.192.4245.1189 . However, their significance cannot be judged without considering volcanism, which may account for much of the apparent correlation with solar activity over the past millennium. 2 2. G. Hegerl et al. , J. Climate 20, 650 (2007). https://doi.org/10.1175/JCLI4011.1 Scafetta and West assume that the only secular influence on preindustrial climate is the Sun.Scafetta and West also state that anthropogenic influence on global warming is overestimated if climate is as sensitive to solar activity as their studies suggest. But in their referenced work, they admit that such a high sensitivity requires more powerful couplings between solar activity and climate than have been identified so far. That is hardly news; for more than a decade, the big question has been whether such powerful Sun–climate coupling mechanisms exist. For reasons we reviewed recently, 3 3. P. Foukal et al. , Nature 443, 161 (2006). https://doi.org/10.1038/nature05072 variation in total solar irradiance (TSI) seems to lack the required power, and the solar UV flux variation—another candidate mentioned by the authors—seems to account for less than 10% of the variance in the 20th-century global temperature. Solar modulation of cosmic rays and their possible effect on cloud cover is the most complex candidate and remains hardest to test.Additionally, Scafetta and West use solar flare statistics as a proxy for TSI variations to derive a similarity in the power law indices of solar fluctuations and Earth temperature variations. Their claim is puzzling since solar flares make a negligible contribution to TSI variation. Why not just analyze the widely available TSI record itself?In summary, a solar effect on global temperature may well exist, and incisive correlation studies can play a role in its investigation. However, it is increasingly clear that deployment of improved radiometric and photometric instruments will be required to discriminate between suggested Sun–climate coupling mechanisms.REFERENCESSection:ChooseTop of pageREFERENCES <<CITING ARTICLES1. J. Eddy, Science 192, 1189 (1976). https://doi.org/10.1126/science.192.4245.1189 , Google ScholarCrossref, ISI2. G. Hegerl et al. , J. Climate 20, 650 (2007). https://doi.org/10.1175/JCLI4011.1 , Google ScholarCrossref, ISI3. P. Foukal et al. , Nature 443, 161 (2006). https://doi.org/10.1038/nature05072 , Google ScholarCrossref, ISI© 2008 American Institute of Physics.

Design concept and modeling of a new Positron Identification by Coincident Annihilation Photons (PICAP) system

The Positron Identification by Coincident Annihilation Photons (PICAP) system is a new design concept to measure moderate energy (∼few MeV) positrons and negatrons in space. Positron measurements in this energy range would open a window on cosmic ray propagation in the Galaxy, Solar modulation of cosmic rays (particularly charge-sign effects) and Solar energetic particles. Electrons of both charge signs are first identified by the conventional d E/d x versus residual energy technique. Coincident 511 keV annihilation photons are used to identify stopping positrons. This technique is far simpler than magnet spectrometers, which require elaborate tracking systems and associated electronics. We present a baseline design and Monte-Carlo modeling results using EGS4. We estimate the baseline instrument would mass ∼4 kg and use ∼3 W of power making such an instrument highly attractive for resource-constrained space missions.

Cosmic ray detector response to transient solar modulation: Forbush decreases

The observed modulation of galactic cosmic ray (GCR) intensity, on time and spatial scales, contains information regarding their transport in the heliosphere. One way to extract crucial information from the data is to study the rigidity dependence of modulation. A methodology is described to study the rigidity dependence of the short‐term variations in galactic cosmic ray intensity Earth, in terms of the median rigidity of detector response (Rm) to cosmic ray spectrum. We define Rm as the rigidity below which lies 50% of detector counting rate. For neutron monitors (NMs), it is easily calculated from the latitude survey obtained at sea level and higher elevations. We compute Rm values for some NM sites; solar cycle dependence for them is shown to be small. Their practical utility is demonstrated in a study of transient cosmic ray solar modulation (Forbush decreases (FDs)), using data published in the literature. We plot the rigidity dependence of the amplitudes of three large Forbush decreases that occurred during the declining phase of three solar cycles (19, 20, and 21). We show that the Forbush decrease amplitude varies inversely with Rm over a large range (1 to 300 GV) of GCR rigidities. Thereby, we rule out the existence of a “transition rigidity” suggested by Jokipii even for a short‐term modulation (large Forbush decreases). We speculate that the force field model may be applicable to large Forbush decreases.

Cosmic Ray Intensity Variations in Relation with Solar Flare Index and Sunspot Numbers

From the monthly data of cosmic ray intensity (CRI), sunspot numbers (SSN) and solar flare index (SFI), an attempt has been made to study the relationship between CRI and solar activity (SA) parameters SSN and SFI. The correlation between SA parameters and CRI for different neutron monitoring stations having low, middle and high cut-off rigidity has been investigated. The anti-correlation between SA and CRI is found to exist with some time lag. Based on the method of minimizing correlation coefficient and time-delayed component method, the observed time-lag between SA parameters (SSN and SFI) and CRI has been found to be large for odd solar cycles in comparison to even solar cycles. The results of time-lag analysis between CRI and SSN and between CRI-SFI have also been compared. The findings of correlative study between CRI and SSN are in agreement with earlier results, while the CRI-SFI relationship provides new insights to understand the solar modulation of cosmic rays.

Cycle 20 solar wind modulation of galactic cosmic rays: Understanding the challenge

It is well known that time variations of galactic cosmic rays for cycle 20 (1964–1976) challenge our understanding of the heliospheric dynamics and the physical processes involved in causing observed modulations. Several interesting questions have been raised over the years. We attempt to provide some plausible answers based on analyses of cosmic ray data obtained with detectors on the ground, on balloons, and on satellites; median rigidity of response of these detectors to the cosmic ray spectrum covers a range of rigidities (R) from 1 to 70 GV. In particular, we explore the observed correlation between hourly rates of neutron monitors and the time series of the product of solar wind velocity (V) and interplanetary magnetic field intensity (B) at Earth's orbit. Local convection is identified as a contributor to “steps” in cosmic ray time variations near Earth and in the outer heliosphere. The amplitude of 11‐year modulation varies as 1/R; data do not support the concept of “transition” rigidity for modulation. We argue that heliosheath‐related modulation effects are minimal at Earth's orbit at R &gt; 3 GV. Heuristic considerations suggest that the space‐dependent part of the diffusion coefficient should vary as 1/B (not 1/B2). We relate modulation function to the product BV, suggesting it plays a significant role in the solar modulation of cosmic rays.

The Global Atmospheric Electrical Circuit and Climate

Evidence is emerging for physical links among clouds, global temperatures, the global atmospheric electrical circuit and cosmic ray ionisation. The global circuit extends throughout the atmosphere from the planetary surface to the lower layers of the ionosphere. Cosmic rays are the principal source of atmospheric ions away from the continental boundary layer: the ions formed permit a vertical conduction current to flow in the fair weather part of the global circuit. Through the (inverse) solar modulation of cosmic rays, the resulting columnar ionisation changes may allow the global circuit to convey a solar influence to meteorological phenomena of the lower atmosphere. Electrical effects on non-thunderstorm clouds have been proposed to occur via the ion-assisted formation of ultra-fine aerosol, which can grow to sizes able to act as cloud condensation nuclei, or through the increased ice nucleation capability of charged aerosols. Even small atmospheric electrical modulations on the aerosol size distribution can affect cloud properties and modify the radiative balance of the atmosphere, through changes communicated globally by the atmospheric electrical circuit. Despite a long history of work in related areas of geophysics, the direct and inverse relationships between the global circuit and global climate remain largely quantitatively unexplored. From reviewing atmospheric electrical measurements made over two centuries and possible paleoclimate proxies, global atmospheric electrical circuit variability should be expected on many timescales.

On radial evolution of stochastic acceleration in a dissipative solar wind turbulence with spatially distributed sources

The spatial behavior of stochastic acceleration of particles in the expanding solar wind plasma is considered. For this, a standard model is used representing a radially evolving, driven solar wind turbulence. On the basis of a turbulence correlation timescale approach, an analytical model is developed describing the radial dependence of the correlation length of the turbulence driven by stream interactions and the production of pickup ions. This analytical model, which might also be beneficial for other interesting problems such as solar modulation of cosmic rays, is used to consider the radial variation of Fermi‐II acceleration of pickup ions in a dissipative, fully driven solar wind turbulence on their way to the heliospheric termination shock. This might be of particular interest for the injection of pickup ions into the process of diffusive shock acceleration and their subsequent conversion to anomalous cosmic rays.

Spatial and temporal variability of the gamma radiation from Earth's atmosphere during a solar cycle

The Solar Maximum Mission satellite's Gamma Ray Spectrometer spent much of its 1980–1989 mission pointed at Earth, accumulating spectra of atmospheric albedo γ‐rays. Its 28° orbit ensured that a range of geomagnetic latitudes was sampled. We measured the variation with time and cutoff rigidity of some key γ‐ray lines which are diagnostic of the intensity of the Galactic cosmic radiation penetrating the geomagnetic cutoff and of the secondary neutrons produced in the atmosphere. We found that the intensities of nuclear lines at 1.6 MeV, 2.3 MeV and 4.4 MeV varied inversely with solar activity in cycles 21–22 as expected from the theory of solar modulation of cosmic rays. They were found to be strongly anticorrelated with cutoff rigidity, as expected from the theory of the cutoff, falling by a factor ∼3.6 between the lowest (&lt;7 GV) and highest (&gt;13 GV) rigidities sampled. The solar cycle modulation was particularly marked at the lowest rigidities, reaching an amplitude of 16%. The ratios of the intensities of the lines produced by nuclear de‐excitation (1.6 MeV, 2.3 MeV) and those from nuclear spallation (4.4 MeV) did not vary with either solar activity or cutoff rigidity, indicating that the shape of the secondary neutron spectrum in the atmosphere above 5 MeV was approximately constant over the times and regions sampled. If it is approximated by a power law in energy, we derive constraints on the absolute value of the power law index ∼−1.15–−1.45 and better constraints on its variability, ≤5% over a solar cycle, and ≤6% over SMM's range of sampled cutoff rigidities. We also measured the intensity of the electron‐positron annihilation line at 0.511 MeV. This line also varies with the solar cycle, but its variation with cutoff rigidity is weaker than that of the nuclear lines, falling by a factor 2 (rather than 3.6) over SMM's range of sampled cutoff rigidities. This can be understood in terms of the energy dependences of the cross sections for positron production and for the hadronic interactions which produce secondary neutrons.

Production of cosmogenic Be nuclei in the Earth's atmosphere by cosmic rays: Its dependence on solar modulation and the interstellar cosmic ray spectrum

Recent work by McCracken [2001] shows that 10Be production rates by cosmic rays on the polar plateau are little affected by geomagnetic field changes in the last few hundred years. Also, the 10Be observed in ice cores on the polar plateau probably originated at high latitudes and precipitated to the Earth in about 1 year, according to McCracken. As a result of this assumption, ice core records of 10Be concentration extending back several hundred years, including the Maunder minimum, have the potential to study the solar modulation of cosmic rays on a time scale extending back several hundred years. These ice core records indicate that the 10Be concentration at the time of the Maunder minimum was ∼2.0 times what it was during recent sunspot minima in 1965 and 1976. We have examined 10Be production in the atmosphere using new data related to the interstellar cosmic ray spectrum and the effects of solar modulation as determined from Voyager spacecraft data in the outer heliosphere. We have used the FLUKA Monte Carlo program along with new cross‐section data to calculate the production of nucleons and 10Be nuclei in the atmosphere. These calculations show that 10Be temporal variations are sensitive indicators of low‐energy solar modulation. Our calculations of 10Be production are able to reproduce well the factor ∼1.5–2.0 change in 10Be observed in the ice core data as a result of the 11‐year solar modulation. We are also able to show that starting as recently as the sunspot minimum of 1954, the cosmic ray intensity at the Earth was higher than it was during more recent minima. The cosmic ray intensity during these minima time periods represents the residual modulation between the Earth and interstellar space. The 10Be measurements are consistant with the fact that given the interstellar cosmic ray spectrum used in this analysis, this residual modulation was small or zero at the time of the Maunder minimum.

Effect of pick-up ions on the magnetic field correlation length: Implications for solar modulation of galactic cosmic rays

In this study the solar modulation of cosmic rays is modeled by direct numerical simulation of Parker's transport equation. We use our ab initio modulation model where the diffusion tensor is specified by particle scattering theory based on observed properties of the turbulence, and the spatial variation is determined by turbulence transport models that specify how turbulence properties vary throughout the heliosphere. We discuss the effect of pick-up ions on the spatial dependence of the magnetic field correlation length which is not well understood. If the effect is negligible, turbulence models suggest that the correlation length should increase almost monotonically with radial distance. If not, it should at some point (determined by the size of the ionization cavity) start to decrease. We model such a two-stage behavior by assuming two power laws for the radial dependence of the correlation length. We show that varying the position of the breakpoint between the two power laws by as little as 10 AU has large effects on the radial intensity profiles and provides better agreement with observation than when a single power law is used (Parhi et al. 2002, 2003).

Perpendicular Transport of Charged Particles in Composite Model Turbulence: Recovery of Diffusion

The computation of charged particle orbits in model turbulent magnetic fields is used to investigate the properties of particle transport in the directions perpendicular to the large-scale magnetic field. Recent results by Qin, Matthaeus, & Bieber demonstrate that parallel scattering suppresses perpendicular diffusion to a subdiffusive level when the turbulence lacks transverse structure. Here numerical computations are used to show that in turbulence in which there is substantial transverse structure, a second regime of diffusive transport can be established. In both the subdiffusion regime and this "second diffusion" regime, perpendicular transport is intrinsically nonlinear. The regime of second diffusion persists for long times and may therefore be of interest in astrophysical transport problems such as the scattering and solar modulation of cosmic rays.

Sensitivity of a neutron monitor to galactic cosmic rays

Abstract We studied the sensitivity of a neutron monitor to Galactic cosmic rays depending on energy of cosmic ray particles in the interstellar medium. This is important for studying of the interstellar spectrum of cosmic rays and details of solar modulation by means of the world neutron monitor network. We calculated the expected response of a standard sea-level neutron monitor vs. energy of cosmic ray particles. First, we studied modulation of a monoenergetic flux of cosmic rays. Then the specific atmospheric yield function of a neutron monitor was applied to the calculated flux of cosmic rays at the Earth's orbit. The obtained response function, being convoluted with the model interstellar spectrum of cosmic rays, gives a maximum of neutron monitor sensitivity at around several GV of rigidity of cosmic ray particles. We performed calculations for weak (φ = 350 MV) and medium (φ = 750 MV) modulation strength. A normalisation of neutron monitor count rate is suggested which can give an experimental measure of the overall solar modulation of cosmic rays.

Large Scale Modulation: View from the Earth

The current knowledge and ideas, obtained from groundlevel observations and concerning the solar modulation of cosmic rays, are reviewed. The following topics are discussed: observations of the cosmic ray modulation at the Earth and main characteristics of the accumulated experimental data; manifestations of the solar magnetic cycle in cosmic rays; the effect of hysteresis and its relation to the size of the heliosphere; the rigidity spectrum of long-term cosmic ray variations; the influence of the sporadic effects on long-term modulation; long-term variations of cosmic ray anisotropy and gradients; the place of groundlevel observations in current studies of cosmic ray modulation and their future prospects. Particular consideration is given to the correlation of long-term cosmic ray variations with different solar-heliospheric parameters, and to empirical models of cosmic ray modulation.

A stochastic view of the solar modulation phenomena of cosmic rays

We report on a numerical method for solving the Fokker‐Planck equation (FPE) which describes the solar modulation of cosmic rays using Itô's stochastic differential equations (SDEs) and discuss on it's power and profound implications not easily attainable by standard methods. It is shown how easily the modulated energy spectrum of cosmic rays is calculated from the interstellar spectrum utilizing the momentum distribution function obtained by SDE method for particles with a fixed momentum of various values at 1 AU. The resultant modulated spectra are compared with the results by the standard numerical technique using the Crank‐Nicholson method to demonstrate the validity of our method.