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.     

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.     

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.     

Modulation of cosmic rays: Perpendicular diffusion and drifts in a heliosphere with a solar wind termination shock

In this study the roles of polar perpendicular diffusion and drifts are illustrated in a model containing a heliosheath and diffusive shock acceleration as applied to the solar wind termination shock. Of particular interest is the relation of polar perpendicular diffusion to particle drifts and how the effectiveness of the termination shock acceleration of galactic and anomalous protons is influenced by this relation. We found that drifts have a more prominent effect than the polar enhancement of perpendicular diffusion so that its omission from termination shock models would produce unrealistically large shock acceleration and consequently also larger modulation effects throughout the heliosphere. The computed spectra at a heliolatitude of 35° are almost similar for the two polarity epochs indicating that the two Voyager spacecraft might not observe differences between the two cycles in future.     

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.     

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.     

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.     

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.     

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.     

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.     

Spatial variation of the supersonic thermal plasma flow downstream of the termination shock

In this paper we start from the most recently observed fact that the solar wind plasma after passage over the termination shock is still supersonic with a Mach number of about 2. To explain this unexpected phenomenon and to predict the evolution of properties of the downstream plasma flow we here consider a two-fluid proton plasma with pick-up protons as a separate suprathermal, second proton fluid. We then formulate a self-consistent system of hydrodynamical conservation equations coupling the two fluids by dynamical and thermodynamical coupling terms and taking into account the effects of newly incorporated protons due to charge exchange with the H-atoms in the heliosheath. This then allows us to predict that in the most probable case the solar wind protons will become subsonic over a distance of about 30 AU downstream of the shock. As we can also show, it may, however, happen that the plasma mixture later again reconverts to a supersonic signature and has to undergo a second shock before meeting the heliopause.     

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.     

Acceleration of interplanetary pick-up ions and anomalous cosmic rays

It may not be doubted anymore that anomalous cosmic rays (ACRs) are produced in the heliosphere from interplanetary pick-up ions through their acceleration at the solar wind termination shock. However, there is no general agreement in the community of heliospheric researchers concerning the mechanism of injection of the pick-up ions into the shock acceleration. We discuss here three possible ways for pick-up ions to be involved into the acceleration process at the termination shock: (1) preacceleration of pick-up ions in the whole region from the Sun up to the termination shock by solar wind turbulences and interplanetary shock waves, (2) local preacceleration of pick-up ions in a vicinity of the termination shock by shock surfing, and (3) formation of high-velocity tails in pick-up ion spectra consisting of secondary pick-up ions which are produced in the supersonic solar wind due to ionization of energetic neutral atoms entering from the inner heliosheath.     

Heliospheric asymmetries due to the action of the interstellar magnetic field

We discuss the asymmetry of the heliospheric discontinuities obtained from the analysis of 3D modeling of the solar wind (SW) interaction with local interstellar medium (LISM). The flow of charged particles is governed by the ideal MHD equations and the flow of neutral particles is described by the Boltzmann equation. The emphasis is made on the asymmetries of the termination shock (TS) and the heliopause under the combined action of the interstellar and interplanetary magnetic fields (ISMF and IMF) in the presence of neutral hydrogen atoms whose transport through the heliosphere is modeled kinetically, using a Monte Carlo approach. We show that the deflection of neutral hydrogen flow from its original direction in the unperturbed LISM is highly anisotropic and evaluate a possible angle between the hydrogen deflection plane measured in the SOHO SWAN experiment and the plane containing the ISMF and LISM velocity vectors for different ISMF strengths. It is shown that the ISMF of a strength greater than 4 μG can account for the 10 AU difference in the TS heliocentric difference observed during its crossing by the Voyager 1 and Voyager 2 spacecraft, which however results in a larger discrepancy between the calculated and observed velocity distributions. The effect of a strong ISMF on the distribution of plasma quantities in the inner heliosheath and on 2–3 kHz radio emission is 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.     

The role of radial perpendicular diffusion and latitude dependent acceleration along the solar wind termination shock

A numerical model, based on Parker’s transport equation, describing the modulation of anomalous cosmic rays and containing diffusive shock acceleration is applied. The role of radial perpendicular diffusion at the solar wind termination shock, and as the dominant diffusion coefficient in the outer heliosphere, is studied, in particular the role it plays in the effectiveness of the acceleration of anomalous protons and helium when its latitude dependence is changed. It is found that the latitudinal enhancement of radial perpendicular diffusion towards the heliospheric poles and along the termination shock has a prominent effect on the acceleration of these particles. It results in a ‘break’ in the energy spectrum for anomalous protons at ∼6.0 MeV, causing the spectral index to change from E^−1.38 to E^−2.23, but for anomalous helium at ∼3.0 MeV, changing the spectral index from E^−1.38 to E^−2.30. When approaching the simulated TS, the changes in the modulated spectra as they unfold to a ‘steady’ power law shape at energies below 50 MeV are much less prominent as a function of radial distances when radial perpendicular diffusion is increased with heliolatitude.     

The dynamic heliosphere,solar activity,and cosmic rays

This brief review addresses the relation between solar activity, cosmic ray variations and the dynamics of the heliosphere. The global features of the heliosphere influence what happens inside its boundaries on a variety of time-scales. Galactic and anomalous cosmic rays are the messengers that convey vital information on global heliospheric changes in the manner that they respond to these changes. By observing cosmic rays over a large range of energies at Earth, and with various space detectors, a better understanding is gained about space weather and climate. The causes of the cosmic ray variability are reviewed, with emphasis on the 11-year and 22-year cycles, step modulation, charge-sign dependent modulation and particle drifts. Advances in this field are selectively discussed in the context of what still are some of the important uncertainties and outstanding issues.     

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.