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.     

Modelling of galactic Carbon in an asymmetrical heliosphere: Effects of asymmetrical modulation conditions

Observations of galactic cosmic rays (GCRs) from the two Voyager spacecraft inside the heliosheath indicate significant differences between them, suggesting that in addition to a possible global asymmetry in the north–south dimensions (meridional plane) of the heliosphere, it is also possible that different modulation (turbulence) conditions could exist between the two hemispheres of the heliosphere. We focus on illustrating the effects on GCR Carbon of asymmetrical modulation conditions combined with a heliosheath thickness that has a significant dependence on heliolatitude. To reflect different modulation conditions between the two heliospheric hemispheres in our numerical model, the enhancement of both polar and radial perpendicular diffusion off the ecliptic plane is assumed to differ from heliographic pole to pole. The computed radial GCR intensities at polar angles of 55° (approximating the Voyager 1 direction) and 125° (approximating the Voyager 2 direction) are compared at different energies and for both particle drift cycles. This is done in the context of illustrating how different values of the enhancement of both polar and radial perpendicular diffusion between the two hemispheres contribute to causing differences in radial intensities during solar minimum and moderate maximum conditions. We find that in the A > 0 cycle these differences between 55° and 125° change both quantitatively and qualitatively for the assumed asymmetrical modulation condition as reflected by polar diffusion, while in the A < 0 cycle, minute quantitative differences are obtained. However, when both polar and radial perpendicular diffusion have significant latitude dependences, major differences in radial intensities between the two polar angles are obtained in both polarity cycles. Furthermore, significant differences in radial intensity gradients obtained in the heliosheath at lower energies may suggest that the solar wind turbulence at and beyond the solar wind termination shock must have a larger latitudinal dependence.     

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.     

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.     

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.     

Numerical integration of stochastic differential equations: A parallel cosmic ray modulation implementation on Africa’s fastest computer

Three-dimensional studies of the transport and modulation of cosmic ray particles in turbulent astrospheres require large-scale simulations using specialized scientific codes. Essentially, a multi-dimensional Fokker-Planck type equation (a parabolic diffusion equation) must be integrated numerically. One such approach is to convert the relevant transport equation into a set of stochastic differential equations (SDEs), with the latter much easier to handle numerically. Due to the growing demand for high performance computing resources, research into the application of effective and suitable numerical algorithms to solve such equations is needed. We present a case study of the performance of a custom-written FORTRAN SDE numerical solver on the CHPC (Centre for High Performance Computing) Lengau cluster in South Africa for a realistic test problem with different set-ups. It is shown that SDE codes can scale very well on large parallel computing platforms. Finally, we consider an extremely computationally expensive application of the SDE approach to cosmic ray modulation, studying the behaviour of galactic cosmic ray proton latitude gradients and relative amplitudes in a physics-first manner. This is done using a modulation code that employs diffusion coefficients derived from first principles, which in turn are functions of turbulence quantities in reasonable agreement with spacecraft observations and modelled using a two-component turbulence transport model (TTM). We show that this approach leads to reduced latitude gradients qualitatively in line with spacecraft observations of the same, without making ad hoc assumptions as to anisotropic perpendicular diffusion coefficients as are often made in many cosmic ray modulation studies.     

Solar, geomagnetic and cosmic ray intensity changes, preceding the cyclone appearances around Mexico

Recently it has been suggested that there exist specific changes in the cosmic ray intensity and some solar and geomagnetic parameters during the days, preceding the hurricane appearances over the North Atlantic Ocean. To understand better these phenomena, data for all hurricanes born not only over the Atlantic but also over the Pacific waters in the last 55 years that hit the Mexican borders were elaborated. As basic hurricane parameters the maximum rotational velocity and the estimated total energy were used. To avoid any interference all hurricanes, overlapping the preceding ones with more than 20 days were not included. Then the behavior of the cosmic ray (CR) intensity, the sunspot (SS) numbers, and the geomagnetic parameters (AP) and (KP) in 35 days prior and 20 days after the cyclone start were investigated. The CR, SS, AP and KP showed much more intensive disturbances in the periods preceding and following the hurricane appearance. For SS this disturbance gradually increase with the hurricane strength. A characteristic peak in the CR intensity appears before the hurricane start. But its place varies between 5 and 20 days before that start. Specific changes were observed in the SS. For major hurricanes they begins sometimes more than 20 days in advance. The AP and the KP show series of bursts, spread over the whole period of 30 preceding days. The obtained results from the performed correlational analysis are enough interesting to motivate a further statistical analysis with more precise techniques: in particular a common periodicity of 30 years found in the number of tropical storms landing into Mexico, the averaged rotational wind velocity and the ACE must be studied in connection with the solar Hale cycle. Using coherence wavelet spectral analysis we present a comparative study between one terrestrial and one cosmophysical phenomena that presumable influence hurricanes development: African dust outbreaks versus cosmic rays for all North Atlantic tropical cyclones. It is shown that the cosmophysical influence cannot be considered as a negligible effect.     

Forbush decreases and solar events seen in the 10–20 GeV energy range by the Karlsruhe Muon Telescope

Since 1993, a muon telescope located at Forschungszentrum Karlsruhe (Karlsruhe Muon Telescope) has been recording the flux of single muons mostly originating from primary cosmic-ray protons with dominant energies in the 10–20 GeV range. The data are used to investigate the influence of solar effects on the flux of cosmic rays measured at Earth. Non-periodic events like Forbush decreases and ground level enhancements are detected in the registered muon flux. A selection of recent events will be presented and compared to data from the Jungfraujoch neutron monitor. The data of the Karlsruhe Muon Telescope help to extend the knowledge about Forbush decreases and ground level enhancements to energies beyond the neutron monitor regime.     

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.     

Solar rhythms in the characteristics of the Arctic frontal zone in the North Atlantic

Long-term changes of the Arctic frontal zone characteristics near the south-eastern coasts of Greenland were considered, the NCEP/NCAR reanalysis data being used. It was found that in the cold half of the year the temperature gradients in the layer 1000–500 hPa in the region under study reveal strong ∼10-yr and ∼22-yr periodicities that seem to be related to solar activity cycles. The results obtained suggest the influence of solar activity and cosmic ray variations on the structure of the temperature field of the troposphere resulting in the changes of the temperature contrasts in the Arctic frontal zone that, in turn, may affect the intensity of cyclogenesis at middle latitudes. The detected effects seem to indicate an important part of frontal zones in the mechanism of solar activity and cosmic ray variation influence on the development of extratropical baric systems. It is suggested that the variations of the temperature gradients revealed in the Arctic frontal zone are due to the radiative forcing of cloudiness changes which may be associated with geomagnetic activity and cosmic ray variations.     

Relativistic waves raised by explosions in space as sources of ultra-high-energy cosmic rays

The paper discusses the possibility of particle acceleration up to high energies in relativistic waves generated by various explosive processes in the interstellar medium. We propose to use the surfatron mechanism of acceleration (surfing) of charged particles trapped in the front of relativistic waves as a generator of high-energy cosmic rays (CRs). Conditions under which surfing in the waves under consideration can be made are studied thoroughly. Ultra-high-energy CRs (up to 10²⁰ eV) are shown to be obtained due to the surfing in relativistic plane and spherical waves. Surfing is supposed to take place in nonlinear Langmuir waves excited by powerful electromagnetic radiation or relativistic beams of charged particles, as well as in strong shock waves generated by relativistic jets or spherical formations that expand fast (fireballs).