Modeling ground and space based cosmic ray observations

After entering our local astrosphere (called the heliosphere), galactic cosmic rays, as charged particles, are affected by the Sun’s turbulent magnetic field. This causes their intensities to decrease towards the inner heliosphere, a process referred to as modulation. Over the years, cosmic ray modulation has been studied extensively at Earth, utilizing both ground and space based observations. Moreover, modelling cosmic ray modulation and comparing results with observations, insight can be gained into the transport of these particles, as well as offering explanations for observed features. We review some of the most prominent cosmic ray observations made near Earth, how these observations can be modelled and what main insights are gained from this modelling approach. Furthermore, a discussion on drifts, as one of the main modulation processes, are given as well as how drift effects manifest in near Earth observations. We conclude by discussing the contemporary challenges, fuelled by observations, which are presently being investigated. A main challenge is explaining observations made during the past unusual solar minimum.     

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.     

Cosmic ray modulation in the outer heliosphere: Predictions for cosmic ray intensities up to the heliopause along Voyager 1 and 2 trajectories

Time dependent cosmic ray modulation in the outer heliosphere is calculated and results are compared to Voyager 1 and 2 observations using a two-dimensional time-dependent cosmic ray transport model. We predict possible future 133–242 MeV proton observations along the Voyager 1 and 2 spacecraft trajectories. Recent theoretical advances in cosmic ray transport parameters are introduced in order to provide a time-dependence for the assumed transport parameters used in the model. This leads to results that are in general compatible with the spacecraft observations in the inner and outer heliosphere over multiple solar cycles. However, for the outer heliosphere, we find that the Voyager 1 and 2 spacecraft observations cannot be fitted with an identical set of parameters along both trajectories. This indicates a possible asymmetric heliosphere or a symmetric heliosphere but with different diffusion parameters in the northern and southern hemispheres, respectively. Furthermore, results indicate that Voyager 2 observations are still under the influence of solar cycle related changes because of the large modulation volume between the heliopause and spacecraft location in contrast to Voyager 1 which shows a steady increase in cosmic ray intensities.     

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.     

Modeling the acceleration and modulation of anomalous cosmic ray oxygen

After the solar wind termination shock crossings of the Voyager spacecraft, the acceleration of anomalous cosmic rays has become a very contentious subject. In this paper we examine several topics pertinent to anomalous cosmic ray oxygen acceleration and transport using a numerical cosmic ray modulation model. These include the effects of drifts on a purely Fermi I accelerated spectra, the effects of introducing higher charge states of oxygen into the modulation model, examining the viability of momentum diffusion as a re-acceleration process in the heliosheath and examining energy spectra, and intensity gradients, in the inner heliosphere during consecutive drift cycles.     

Propagation modes of energetic charged particles in the heliosphere

Several years ago, the anisotropic diffusion and convective transport accompanied by adiabatic deceleration were considered as the principal means for cosmic ray propagation. Particles of relatively small energies (～ 1 MeV) can propagate along the force lines of the magnetic field without scattering at distances of several astronomical units in the quiet heliosphere. The theory describing the 11-year variation of galactic cosmic ray intensity and the propagation of solar cosmic rays was founded on this basis. However, the anomalies of the 11-year variation of galactic cosmic ray intensity in 1969–1971 revealed the necessity to take into account the influence of the general electromagnetic field of the heliosphere giving rise to a rapid magnetic drift of particles. The particles drift either from the magnetic axis to the ecliptic plane (in the cycle of 1969–1980) or in the opposite direction depending on the sign of the general magnetic field of the sun. The neutral layers along which the drift velocity is comparable to the particle velocity is of great significance. However, in the presence of sector structure, the time of particle propagation along the neutral layer from the boundary of the modulation region to the earth orbit is substantially increased. Thus a marked adiabatic deceleration is here possible. The time delay observed in the recovery of proton intensities at various energies can be explained in terms of a transient phase of the interplanetary field following the polarity reversal.     

The transport of galactic and jovian cosmic ray electrons in the heliosphere

An overview is given on what we know about the cosmic ray diffusion process from the modelling of low-energy (MeV) electron transport in the heliosphere. For energies below ∼300 MeV, these electrons give a direct indication of the average mean free paths because they do not experience large adiabatic energy changes and their modulation is largely unaffected by global gradient and curvature drifts. Apart from galactic cosmic ray electrons, the jovian magnetosphere at ∼5 AU in the ecliptic plane is also a relatively strong source of MeV electrons, with energies up to ∼30 MeV. Therefore, when modelling the transport of these particles in the inner heliosphere, a three-dimensional treatment is essential. By comparing these models to observations from the Ulysses, Pioneer and Voyager missions, important conclusions can be made on e.g., the relative contributions of the galactic and jovian electrons to the total electron intensity, the magnitude of the parallel and perpendicular transport coefficients, and the time dependant treatment thereof.     

Temporal variations of the cosmic ray intensity and the magnetic configurations of the heliosphere

Data from worldwide network of neutron and muon detectors are used to study 11-year variations of cosmic rays, over four solar activity cycles. We find that the recovery of the cosmic ray intensity follows one of the two distinct modes. During odd cycles recovery is completed in 6 to 8 years, but during even cycles complete recovery occurs in 2 to 3 years. Two model magnetic configurations of the heliosphere are proposed to understand these recovery modes. Implications of these models are also discussed.     

Time-dependent cosmic ray modulation

Time-dependent cosmic ray modulation is calculated over multiple solar cycles using our well established two-dimensional time-dependent modulation model. Results are compared to Voyager 1, Ulysses and IMP cosmic ray observations to establish compatibility. A time-dependence in the diffusion and drift coefficients, implicitly contained in recent expressions derived by , ,  and , is incorporated into the cosmic ray modulation model. This results in calculations which are compatible with spacecraft observations on a global scale over consecutive solar cycles. This approach compares well to the successful compound approach of Ferreira and Potgieter (2004). For both these approaches the magnetic field magnitude, variance of the field and current sheet tilt angle values observed at Earth are transported time-dependently into the outer heliosphere. However, when results are compared to observations for extreme solar maximum, the computed step-like modulation is not as pronounced as observed. This indicates that some additional merging of these structures into more pronounced modulation barriers along the way is needed.     

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.     

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.     

Effects of the position of the solar wind termination shock and the heliopause on the heliospheric modulation of cosmic rays

The effects of changing the position of the solar wind termination shock and the position of the heliopause, and therefore the extent of the heliosheath, on the modulation of cosmic ray protons are illustrated. An improved numerical model with diffusive termination shock acceleration, a heliosheath and drifts is used. The modulation is computed in the equatorial plane and at 35 heliolatitude using recently derived diffusion coefficients applicable to a number of cosmic ray species during both magnetic polarity cycles of the Sun. It was found that qualitatively the modulation results for the different heliopause positions are similar although they differ quantitatively, e.g., clearly different radial gradients are predicted for the regions beyond the termination shock compared to inside the shock. The difference between the modulation for the two solar polarity cycles are less significant at a heliolatitude of 35° than in the equatorial plane. We found that moving the termination shock from 90 to 100 AU, with the heliopause fixed at 120 AU, caused only quantitative differences so that the exact position of the TS in the outer heliosphere seems not crucially important to global modulation. Moving the heliopause outwards, to represent the modulation in the tail region of the heliosphere, causes overall decreases in the cosmic ray intensities but not linearly as a function of energy, e.g., at 1 GeV the effect is insignificant. We conclude from this modelling that the modulation of protons in the heliospheric nose and tail regions are qualitatively similar although, clear quantitative and interesting differences occur.     

Radial distribution of galactic cosmic rays at solar maximum

In this paper we analyze the spatial distribution of galactic cosmic rays during periods of maximum solar activity of the cycles 21, 22 and 23. We have used a two dimensional model to solve the cosmic ray transport equation. This model includes all relevant physical processes: diffusion, convection, drift and shock effects on cosmic ray propagation inside the heliosphere. We focused on the study of the radial distribution of galactic cosmic rays, and compare our results with the spacecraft observations for two energies (175 MeV H and 265 MeV/n He). Although the radial intensities of galactic cosmic rays can be explained qualitatively with all three local interstellar spectra (LISs) used in this work, we applied a reduced chi-squared analysis to investigate the best LIS that could fit the data.     

Cosmic ray flux at the Earth in a variable heliosphere

In recent years the variability of the cosmic ray flux has become one of the main issues not only for the interpretation of the abundances of cosmogenic isotopes in cosmochronic archives like, e.g., ice cores, but also for its potential impact on the terrestrial climate. It has been re-emphasized that the cosmic ray flux is not only varying due to the solar activity-induced changes of the solar wind but also in response to the changing state of the interstellar medium surrounding the heliosphere. We demonstrate the significance of these external boundary condition changes along the galactic orbit of the Sun for the flux as well as spectra of cosmic rays. Such interstellar–terrestrial relations are a major topic of the International Heliophysical Year 2007.     

Cosmic rays in the dynamic heliosheath

Cosmic ray modulation in the outer heliosphere is discussed from a modeling perspective. Emphasis is on the transport and acceleration of these particles at and beyond the solar wind termination shock in the inner heliosheath region and how this changes over a solar cycle. We will show that by using numerical models, and by comparing results to spacecraft observations, much can be learned about the dependence of cosmic ray modulation on solar cycle changes in the solar wind and heliospheric magnetic field. While the first determines the heliospheric geometry and shock structure, the latter results in a time-dependence of the transport coefficients. Depending on energy, both these effects contribute to cosmic ray intensities in the inner heliosheath changing over a solar cycle.     

Galactic cosmic ray composition and energy spectra.

Galactic cosmic ray nuclei represent a significant risk to long-duration spaceflight outside the magnetosphere. We review briefly existing measurements of the composition and energy spectra of heavy cosmic ray nuclei, pointing out which species and energy ranges are most critical to assessing cosmic ray risks for spaceflight. Key data sets are identified and a table of cosmic ray abundances is presented for elements from H to Ni (Z = 1 to 28). Because of the 22-year nature of the solar modulation cycle, data from the approaching 1998 solar minimum is especially important to reducing uncertainties in the cosmic ray radiation hazard. It is recommended that efforts to model this hazard take advantage of approaches that have been developed to model the astrophysical aspects of cosmic rays.     

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.     

Observed solar cycle modulation of galactic cosmic rays over a range of rigidities

We have studied the long-term, steady-state, solar cycle modulation of galactic cosmic ray intensity for seven cycles (17–23). Our analysis is based on the data obtained with a variety of detectors on earth (neutron monitors of the global network and muon detectors) as well as telescopes flown on high altitude balloons and on-board near-earth satellites. The median rigidity of response for these detectors to galactic cosmic ray spectrum lies in the range 1–70 GV. We correlate cosmic ray data to sunspot numbers, Ap, solar wind bulk speed (V), magnetic field (B), as well as to the cycle maximum (M), minimum (m), and the epochs of the solar polar field reversals. This enables us to derive the rigidity dependence of observations, and helps us to define the characteristics of the modulation function in the heliosphere.