Study of the 27-day variations of the galactic cosmic ray intensity and anisotropy

We demonstrate that the general features of the radial and azimuthal components of the anisotropy of galactic cosmic rays can be studied by the harmonic analysis method using data from an individual neutron monitor with cut off rigidity <5 GV. In particular, we study the characteristics of the 27-day (solar rotation period) variations of the galactic cosmic ray intensity and anisotropy, solar wind velocity, interplanetary magnetic field strength and sunspot number. The amplitudes of the 27-day variations of the galactic cosmic ray anisotropy are greater, and the phases more clearly established, in A > 0 polarity periods than in A < 0 polarity periods at times of minimum solar activity. The phases of the 27-day variations of the galactic cosmic rays intensity and anisotropy are opposite with respect to the similar changes of the solar wind velocity in A > 0 polarity periods. No significant dependence of the amplitude of the 27-day variation of the galactic cosmic ray anisotropy on the tilt angle of the heliospheric neutral sheet is found. Daily epicyclegrams obtained by Chree’s method show that the 27-day variations of the galactic cosmic ray anisotropy during A > 0 polarity periods follow elliptical paths with the major axes oriented approximately along the interplanetary magnetic field. The paths are more irregular during A < 0 polarity periods.     

Empirical model of cosmic ray spectrum in energy interval 1 MeV–100 GeV during 11-year solar cycle

The galactic cosmic rays (GCR) are the main ionization source at altitude of ∼3–35 km in the atmosphere. For high latitude anomalous cosmic ray (ACR) component has also a significant influence on the atmospheric ionization. We propose an empirical model for differential spectra D(E) of galactic and anomalous cosmic rays in energy interval 1 MeV–100 GeV during solar cycle. In the model data are used which cover three solar cycles: 20, 22 and 23. The LEAP87, IMAX92, CAPRICE94, AMS98 and BESS experimental spectra for protons and alpha particles are fitted to the proposed empirical model. The modulated GCR differential spectra are compared with force-field approximation to the one-dimensional transport equation and with solutions of two-dimensional cosmic ray transport equation. For experimental spectra, the calculation of the model parameters is performed by Levenberg–Marquardt algorithm, applied to the special case of least squares. Algorithm that combines the rapid local convergence of Newton–Raphson method with globally convergent method for non-linear systems of equations is applied for theoretically obtained differential spectra. The described programmes are realized in algorithmic language C++. The proposed model gives practical possibility for investigation of experimental data from measurements of galactic cosmic rays and their anomalous component.     

Modelling of low-energy galactic electrons in the heliosheath

The modulation of cosmic ray electrons in the heliosphere plays an important role in improving our understanding and assessment of the processes applicable to low-energy galactic electrons. A full three-dimensional numerical model based on Parker’s transport equation is used to study the modulation of 10 MeV galactic electrons, in particular inside the heliosheath. The emphasis is placed on the role that perpendicular diffusion plays in causing the extraordinary large increase in the observed intensities of these electrons in the heliosheath. The modelling is compared with observations of 6–14 MeV electrons from the Voyager 1 mission. Results are shown for the radial intensity profiles of these electrons, as well as the modulation effects of varying the extent of the heliosheath by changing the location of the termination shock and the heliopause and the value of the local interstellar spectrum. We confirm that the heliosheath acts as a modulation ‘barrier’ for low-energy galactic electrons. The significance of this result depends on how wide the inner heliosheath is; on how high the very local interstellar spectrum is at these low energies (E < 100 MeV) and on how small perpendicular diffusion is inside the inner heliosheath.     

The heliospheric modulation of cosmic rays: Effects of a latitude dependent solar wind termination shock

Observations made with the two Voyager spacecraft confirmed that the solar wind decelerates to form the heliospheric termination shock and that it has begun its merger with the local interstellar medium. The compression ratio of this shock affects galactic cosmic rays when they enter the heliosphere. Hydrodynamic (HD) models show that the compression ratio can have a significant latitude dependence; with the largest value in the nose direction of the heliosphere, becoming significantly less towards the polar regions. The modulation effects of such large latitude dependence are studied, using a well-established numerical drift and shock modulation model. We focus on computing the modulated spectra for galactic protons with emphasis on the radial and polar gradients in the equatorial plane and at a polar angle of θ = 55°, corresponding to the heliolatitude of Voyager 1. Two sets of solutions are computed and compared each time; with and without a latitude dependence for the compression ratio. All computations are done for the two magnetic field polarity cycles assuming solar minimum conditions. Including the termination shock in the model allows the study of the re-acceleration of galactic protons in the outer heliosphere. We find that for the A < 0 polarity cycle the intensity between ∼200 MeV and ∼1 GeV in the vicinity of the shock in the heliospheric equatorial plane may exceed the local interstellar value specified at the heliopause. Unfortunately, at θ = 55°, the effect is reduced. This seems not possible during an A > 0 cycle because significant modulation is then predicted between the heliopause and the termination shock, depending on how strong global gradient and curvature drifts are in the heliosheath. The overall effect of the shock on galactic protons in the equatorial plane is to reduce the total modulation as a function of radial distance with respect to the interstellar spectrum. Making the compression ratio latitude dependent enhances these effects at energies E < 200 MeV in the equatorial plane. At larger heliolatitudes these effects are even more significant. The differences in the modulation between the two drift cycles are compelling when the compression ratio is made latitude dependent but at Earth this effect is insignificant. A general result is that the computed radial gradient changes for galactic protons at and close to the TS and that these changes are polarity dependent. In line with previous work, large polarity dependent effects are predicted for the inner heliosphere and also close to the shock’s position in the equatorial plane. In contrast, at θ = 55°, the largest polarity effect occurs in the middle heliosphere (50 AU), enhanced by the latitude dependence of the compression ratio. At this latitude, the amount of proton modulation between the heliopause and the termination shock is much reduced. If galactic cosmic rays were to experience some diffusive shock acceleration over the 100–1000 MeV range at the shock, the radial gradient should change its sign in the vicinity of the shock, how large, depends on the compression ratio and the amount of drifts taking place in the outer heliosphere. The effective polar gradient shows a strong polarity dependence at Earth but this dissipates at θ = 55°, especially with increasing radial distance. This tendency is enhanced by making the compression ratio latitude dependent.     

Effects of solar modulation on the cosmic ray positron fraction

We implemented a 2D Monte Carlo model to simulate the solar modulation of galactic cosmic rays. The model is based on the Parker’s transport equation which contains diffusion, convection, particle drift and energy loss. Following the evolution in time of the solar activity, we are able to modulate a local interstellar spectrum (LIS), that we assumed isotropic beyond the termination shock, down to the Earth position inside the heliosphere. In this work we focused our attention to the cosmic ray positron fraction at energy below ∼10 GeV, showing how the particle drift processes could explain different results for AMS-01 and PAMELA. We compare our modulated spectra with observations at Earth, and then make a prediction of the cosmic ray positron fraction for the AMS-02 experiment.     

Rigidity spectrum of the 27-day variation of the galactic cosmic ray intensity in different epochs of solar activity

We study the temporal evolution of the power rigidity spectrum of the first (27 days) and the second (14 days) harmonics of the 27-day variation of the galactic cosmic ray intensity measured by neutron monitors in the period of 1965–2002. The rigidity spectrum of these variations can be approximated by a power law. We show the rigidity spectra of the first and the second harmonics of the 27-day variation of the galactic cosmic ray intensity have similar time profiles. These spectra are hard (γ ≈ 0.5 ± 0.1) and soft (γ ≈ 1.1 ± 0.2) during solar maximum and minimum activity, respectively. We ascribe this to the alternation of the sizes of the modulation regions responsible for the 27-day variation of the galactic cosmic ray intensity in different epochs of solar activity. Especially, the average radial sizes of the modulation regions of the 27-day variation and the heliolatitudinal extension of the heliolongitudinal asymmetry are smaller during solar minimum than during solar maximum. We show also, that the temporal changes of the power rigidity spectra of the first and the second harmonics of the 27-day variation of the galactic cosmic ray intensity are in a negative correlation with the changes of the rigidity spectrum of the corresponding 11-year variation.     

Cosmic ray anisotropies in the outer heliosphere

The observation of the directional distribution of energetic and cosmic ray particles has been done with the Voyager spacecraft over a long period. Since 2002, when the first flux enhancements of charged particles associated with the approach of Voyager 1 to the solar wind termination shock were observed, these anisotropy measurements have become of special interest. They play an important role to understand the magnetic field and shock structure and the basics of the modulation of cosmic ray and anomalous particles at and beyond the termination shock. They also serve as motivation to study the spatial behavior of galactic and anomalous cosmic ray anisotropies with numerical modulation models in order to illustrate how the radial anisotropy, at different energies, change from upstream to downstream of the termination shock. Observations made by Voyager 1 indicate that the termination shock is a complicated region than previously thought, hence the effects of the latitude dependence of the termination shock’s compression ratio and injection efficiency on the radial anisotropies of galactic and anomalous protons will be illustrated. We find that the magnitude and direction of the radial anisotropy strongly depends on the position in the heliosphere and the energy of particles. The effect of the TS on the radial anisotropy is to abruptly increase its value in the heliosheath especially in the A > 0 cycle for galactic protons and in both polarity cycles for anomalous protons. Furthermore, the global effect of the latitude dependence of the shock’s compression ratio is to increase the radial anisotropy for galactic protons throughout the heliosphere, while when combined with the latitude dependence of the injection efficiency this increase depends on modulation factors for anomalous protons and can even alter the direction of the radial anisotropy.     

Where does the heliospheric modulation of galactic cosmic rays start?

The long outstanding question of where the heliospheric (solar) modulation of galactic cosmic rays actually begins, in terms of spatial position, as well as at what high kinetic energy, can now be answered. Both answers are possible by using the results of an advanced numerical model, together with appropriate observations. Voyager 1 has been exploring the outskirts of the heliosphere and is presently entering what can be called the very local interstellar medium. It has been generally expected, and accepted, that once the heliopause is crossed, the local interstellar spectrum (LIS) should be measured in situ by the Voyager spacecraft. However, we show that this may not be the case and that modulation effects on galactic cosmic rays can persist well beyond the heliopause. For example, proton observations at 100 MeV close to the heliopause can be lower by ∼$\sim$25% to 40% than the LIS, depending on solar modulation conditions. It is also illustrated quantitatively that significant solar modulation diminishes above ∼$\sim$50 GeV at Earth. It is found that cosmic ray observations above this energy contain less that 5%$5\%$ solar modulation effects and should therefore reflect the LIS for galactic cosmic rays. Input spectra, in other words the very LIS, for solar modulation models are now constrained by in situ observations and can therefore not any longer be treated arbitrarily. It is also possible for the first time to determine the lower limit of the very LIS from a few MeV/nuc to very high energies.     

Challenges to cosmic ray modeling: From beyond the solar wind termination shock

Voyager 1 crossed the solar wind termination shock on December 16, 2004 at a distance of 94 AU from the Sun, to become the first spacecraft to explore the termination shock region and to enter the heliosheath, the final heliospheric frontier. By the end of 2006, Voyager 1 will be at ∼101 AU, with Voyager 2 at ∼81 AU and still approaching the termination shock. Both spacecraft have been observing the modulation of galactic and anomalous cosmic rays since their launch in 1977. The recent observations close to or inside the heliosheath have provided several interesting ‘surprises’ with subsequent theoretical and modeling challenges. Examples are: what does the modulation of galactic cosmic rays amount to in this region?; how do the anomalous cosmic rays get accelerated and modulated?; why are there ‘breaks’ in the power-law slopes of the spectra of accelerated particles? Several numerical models have been applied to most of these topics over the years and comprehensive global predictions have been made the past decade, thought to be based on reasonable assumptions about the termination shock and the heliosheath. Examples of these predictions and assumptions are concisely discussed within the context of the main observed features of cosmic rays in the vicinity of the termination shock, ending with a discussion of some of the issues and challenges to cosmic ray modeling in particular.     

Two intense Forbush decreases of solar activity cycle 22

We study two intense Forbush decreases that occurred during two adjacent SOLTIP (Solar connection of Transient Interplanetary Processes) intervals; namely SOLTIP 1 (22–27 March 1991) and SOLTIP 2 (1–17 June 1991); galactic cosmic ray intensity at the depth of the second Forbush decrease was the lowest ever recorded since continuous monitoring by Climax neutron monitor began in 1951 (58% below the solar minimum value of 1954), indicating extreme conditions in the heliosphere that prevented galactic cosmic rays from reaching the Earth. These decreases were seen propagating in outer heliosphere by the deep space missions Voyagers 1, 2 and Pioneer 10, 11, with suitable time delays. We analyze hourly, pressure corrected, neutron monitor data from the global sites in both hemispheres, and muon telescopes located underground; they respond to 10–300 GV range of the galactic cosmic ray spectrum. This circumstance provides us an ideal opportunity to study the rigidity dependence of the amplitudes of the two Forbush decreases. In both cases the amplitude is found to be a power law in rigidity, with negative exponents.     

Research by the Tasmanian cosmic ray group during the International Geophysical Year

Systematic recording of the cosmic radiation commenced in Hobart in 1946 and at Mawson in Antarctica in 1955, making these two of the longest running cosmic ray observatories in the world. For the IGY, observations were also made at a sub-Antarctic island and near the equator, and an airborne survey of the nucleonic component was made from Geomagnetic Latitude −60°, south of Australia, to Japan and back. At Hobart there were neutron monitors, vertical and inclined muon telescopes, an ionization chamber, and two muon telescopes at ∼40 m of water equivalent underground. The research based on these and other observations determined the energy dependence of the Forbush and 11-year variations and concentrated, in particular, on understanding the anisotropic nature of galactic cosmic rays up to 150 GeV; the anisotropies in the onset phase of Forbush decreases; and the anisotropies in solar cosmic ray events. An investigation was initiated to calculate the trajectories and cutoff rigidities of cosmic rays in a high order simulation of the geomagnetic field. This was completed in 1959–60.     

The scaler mode in the Pierre Auger Observatory to study heliospheric modulation of cosmic rays

The impact of the solar activity on the heliosphere has a strong influence on the modulation of the flux of low energy galactic cosmic rays arriving at Earth. Different instruments, such as neutron monitors or muon detectors, have been recording the variability of the cosmic ray flux at ground level for several decades. Although the Pierre Auger Observatory was designed to observe cosmic rays at the highest energies, it also records the count rates of low energy secondary particles (the scaler mode) for the self-calibration of its surface detector array. From observations using the scaler mode at the Pierre Auger Observatory, modulation of galactic cosmic rays due to solar transient activity has been observed (e.g., Forbush decreases). Due to the high total count rate coming from the combined area of its detectors, the Pierre Auger Observatory (its detectors have a total area greater than 16,000 m²) detects a flux of secondary particles of the order of ∼10⁸ counts per minute. Time variations of the cosmic ray flux related to the activity of the heliosphere can be determined with high accuracy. In this paper we briefly describe the scaler mode and analyze a Forbush decrease together with the interplanetary coronal mass ejection that originated it. The Auger scaler data are now publicly available.     

Observation of enhanced sub-iron (Sc---Cr) to iron ration in low energy cosmic rays of 50–100 MeV/N in spacelab-3

Relative abundances of sub-iron (Sc-Cr) to iron nuclei in low energy (50–100 MeV/N) galactic cosmic rays have been determined from an analysis of about 100 events of heavy ions (Z = 10−28) recorded in a detector assembly flown in the Anuradha cosmic ray experiment in the Spacelab-3 on a six day mission in April–May 1985. The measured abundance ratio of (Sc-Cr)/Fe nuclei in 50–100 MeV/N energy range is 1.1 ± 0.3, and the present result of enhanced ratio of sub-iron to iron nuclei is in agreement with other experimental results in 200–800 MeV/N range. The over-abundance of iron secondaries at these low energies cannot be explained in the conventional models for propagation of cosmic rays. Available experimental data indicate a very different time history for the low energy iron-group, as compared to those of lighter nuclei in galactic cosmic rays.     

Modulation of galactic cosmic rays in a north–south asymmetrical heliosphere

Observations made with the two Voyager spacecraft confirmed that the solar wind decelerates to form the heliospheric termination shock. Voyager 1 crossed this termination shock at ∼94 AU in 2004, while Voyager 2 crossed it in 2007 at a different heliolatitude, about 10 AU closer to the Sun. These different positions of the termination shock confirm the dynamic and cyclic nature of the shock’s position. Observations from the two Voyager spacecraft inside the heliosheath indicate significant differences between them, suggesting that apart from the dynamic nature caused by changing solar activity there also may exist a global asymmetry in the north–south (polar) dimensions of the heliosphere, in addition to the expected nose–tail asymmetry. This relates to the direction in which the heliosphere is moving in interstellar space and its orientation with respect to the interstellar magnetic field. In this paper we focus on illustrating the effects of this north–south asymmetry on modulation of galactic cosmic ray Carbon, between polar angles of 55° and 125°, using a numerical model which includes all four major modulation processes, the termination shock and the heliosheath. This asymmetry is incorporated in the model by assuming a significant dependence on heliolatitude of the thickness of the heliosheath. When comparing the computed spectra between the two polar angles, we find that at energies E < ∼1.0 GeV the effects of the assumed asymmetry on the modulated spectra are insignificant up to 60 AU from the Sun but become increasingly more significant with larger radial distances to reach a maximum inside the heliosheath. In contrast, with E > ∼1.0 GeV, these effects remain insignificant throughout the heliosphere even very close to the heliopause. Furthermore, we find that a higher local interstellar spectrum for Carbon enhances the effects of asymmetric modulation between the two polar angles at lower energies (E < ∼300 MeV). In conclusion, it is found that north–south asymmetrical effects on the modulation of cosmic ray Carbon depend strongly on the extent of the geometrical asymmetry of the heliosheath together with the assumed value of the local interstellar spectrum.     

Evolution of Dst index,cosmic rays and global temperature during solar cycles 20–23

We have studied conditions in interplanetary space, which can have an influence on galactic cosmic ray (CR) and climate change. In this connection the solar wind and interplanetary magnetic field parameters and cosmic ray variations have been compared with geomagnetic activity represented by the equatorial Dst index from the beginning 1965 to the end of 2012. Dst index is commonly used as the solar wind–magnetosphere–ionosphere interaction characteristic. The important drivers in interplanetary medium which have effect on cosmic rays as CMEs (coronal mass ejections) and CIRs (corotating interaction regions) undergo very strong changes during their propagation to the Earth. Because of this CMEs, coronal holes and the solar spot numbers (SSN) do not adequately reflect peculiarities concerned with the solar wind arrival to 1 AU. Therefore, the geomagnetic indices have some inestimable advantage as continuous series other the irregular solar wind measurements. We have compared the yearly average variations of Dst index and the solar wind parameters with cosmic ray data from Moscow, Climax, and Haleakala neutron monitors during the solar cycles 20–23. The descending phases of these solar cycles (CSs) had the long-lasting solar wind high speed streams occurred frequently and were the primary contributors to the recurrent Dst variations. They also had effects on cosmic rays variations. We show that long-term Dst variations in these solar cycles were correlated with the cosmic ray count rate and can be used for study of CR variations. Global temperature variations in connection with evolution of Dst index and CR variations is discussed.     

Modeling and data analysis of a Forbush decrease

We study the Forbush decrease of the galactic cosmic ray intensity observed in 9–25 September 2005 using the experimental data and a newly developed time-dependent three dimensional modeling. We analyze neutron monitors and muon telescopes, and the interplanetary magnetic field data. We demonstrate a clear relationship between the rigidity (R) spectrum exponent (γ) of the Forbush decrease and the exponent (ν) of the power spectral density of the components of the interplanetary magnetic field in the frequency range of ∼ 10⁻⁶–10 ⁻⁵ Hz. We confirm that an inclusion of the time-dependent changes of the exponent ν makes the newly developed nonstationary three dimensional model of the Forbush decrease compatible with the experimental data. Also, we show that the changes of the rigidity spectrum exponent γ does not depend on the level of convection of the galactic cosmic rays stream by solar wind; depending on the changes of the exponent ν, i.e. on the state of the turbulence of the interplanetary magnetic field.     

The role of drift and convection–diffusion mechanisms in small energy global cosmic ray modulation: Application to the hysteresis phenomenon of proton and alpha particle satellite data

The hysteresis effect for small energies of galactic cosmic rays is due to two effects. The first is the same as for neutron monitor energies – the delay of the interplanetary processes responsible for cosmic ray modulation with respect to the initiating solar processes, according to the effective velocity of solar wind and shock waves propagation. Then, the observed cosmic ray intensity is connected to the solar activity variations during many months before the time of cosmic ray measurement. The second is caused by the time delay of small energy cosmic ray diffusion from the boundary of modulation region to the Earth’s orbit. The model describing the connection between solar activity variation and cosmic ray convection–diffusion global modulation for neutron monitor energies is here developed by taking into account also the time-lag of the small energy particle diffusion in the Heliosphere. We use theoretical results on drifts and analytically approximate the dependences of drifts from tilt angle, and take into account the dependence from the sign of primary particles, and from the sign of polar magnetic field (A > 0 or A < 0). The obtained results are applied on proton and alpha-particle satellite data. We analyze satellite 5-min data of proton fluxes with energies >1 MeV, >2 MeV, >5 MeV, >10 MeV, >30 MeV, >50 MeV, >60 MeV, >100 MeV, and in intervals 10–30 MeV, 30–60 MeV, and 60–100 MeV during January 1986–December 1999. We exclude periods with great cosmic ray increases caused by particle acceleration in solar flare events. Then, we determine monthly averaged fluxes, as well as 5-month and 11-month smoothed data. We analyze also satellite 5-min data on alpha-particle fluxes in the energy intervals 60-160 MeV, 160–260 MeV and 330–500 MeV during January 1986–May 2000. We correct observation data for drifts and then compare with what is expected according to the convection–diffusion mechanism. We assume different dimensions of the modulation region (by the time propagation X₀ of solar wind from the Sun to the boundary of modulation region), for X₀ values from 1 to 60 average months, by one-month steps. For each value of X₀ we determine the correlation coefficient between variations of expected and observed cosmic ray intensities (the estimation of cosmic ray intensities values is given in Section 3 by Eq. (9), and the determination of correlation and regression coefficients in Section 3 by Eq. (8)). The dimension of modulation region is determined by the value of X_0 max, for which the correlation coefficient reaches the maximum value. Then the effective radial diffusion coefficient and residual modulation in small energy region can be estimated.     

Detection of the high energy component of Jovian electrons in Low Earth Orbit with the PAMELA experiment

The PAMELA experiment is devoted to the study of cosmic rays in Low Earth Orbit with an apparatus optimized to perform a precise determination of the galactic antimatter component of c.r. It is constituted by a number of detectors built around a permanent magnet spectrometer. PAMELA was launched in space on June 15th 2006 on board the Russian Resurs-DK1 satellite for a mission duration of 3 years. The characteristics of the detectors, the long lifetime and the orbit of the satellite, will allow to address several aspects of cosmic-ray physics. In this work we discuss the observational capabilities of PAMELA to detect the electron component above 50 MeV. The magnetic spectrometer allows a detailed measurement of the energy spectrum of electrons of galactic and Jovian origin. Long term measurements and correlations with Earth–Jupiter 13 months synodic period will allow to separate these two contributions and to measure the primary electron Jovian component, dominant in the 50–70 MeV energy range. With this technique it will also be possible to study the contribution to the electron spectrum of Jovian e⁻ reaccelerated up to 2 GeV at the Solar Wind Termination Shock.     

Cosmic ray reacceleration on the galactic wind termination shock

Reacceleration of cosmic rays produced by galactic sources on the galactic wind termination shock is considered. The problem of the cosmic ray spectrum continuity is investigated. Numeric results are presented and discussed. We found that a smooth spectral transition from the galactic cosmic rays to the cosmic rays reaccelerated at the galactic wind termination shock is difficult to produce, if the maximum energy of accelerated particles is the same throughout the surface of the termination shock. The possible solution of this problem is the non-spherical termination shock with different maximum energies at different places of the shock.