Galactic Cosmic Rays in the Outer Heliosphere: Theory and Models

We review recent advances in the field of galactic cosmic ray transport in the distant heliosphere. The advent of global MHD models brought about a better understanding of the three-dimensional structure of the interface between the solar system and the surrounding interstellar space, and of the magnetic field topology in the outer heliosphere. These results stimulated a development of galactic cosmic ray transport models taking the advantage of the available detailed plasma backgrounds and of the new Voyager results from the heliosheath. It emerges that the heliosheath plays a prominent role in the process of modulation and filtration of low-energy galactic ions and electrons. The heliosheath stores particles for a duration of several years thus acting as a large reservoir of galactic cosmic rays. Cosmic-ray trajectories, transit times, and entry locations across the heliopause are discussed. When compared to observations model calculations of low energy electrons show almost no radial gradient up to the termination shock, irrespective of solar activity, but a large gradient in the inner heliosheath. Intensities are however sensitive to heliospheric conditions such as the location of the heliopause and shock. In contrast, high energy proton observations by both the Voyager spacecraft show a clear solar cycle dependence with intensities also increasing with increasing distance. By comparing these observations to model calculations we can establish whether our current understanding of long-term modulation result in computed intensities compatible to observations.     

Cosmic Ray Modulation over the Poles at Solar Maximum: Observations

Our knowledge of how galactic and anomalous cosmic rays are modulated in the inner heliosphere has been dramatically enlarged as a result of measurements from several missions launched in the past ten years. Among them, Ulysses explored the polar regions of the inner heliosphere during the last solar minimum period and is now revisiting southern polar latitudes under solar maximum conditions. This gives us for the first time the possibility to compare modulation of cosmic rays at high heliographic latitudes during such different time periods. We present data from different instruments on board the Ulysses spacecraft together with 1 AU measurements in the ecliptic. In this paper we focus on measurements that have direct implications for our understanding of modulation of cosmic rays in the inner heliosphere. This revised version was published online in August 2006 with corrections to the Cover Date.     

The Onset of Long Term Modulation in the Heliosphere in Cycle 23

The combination of Voyager 1 (77.9 AU, 34.4° N) and Voyager 2 (61.2 AU, 24.5° S) at moderate heliolatitudes in the distant heliosphere and Ulysses with its unique latitudinal surveys in the inner heliosphere along with IMP 8 and other satellites at 1 AU constitutes a network of observatories that are ideally suited to study cosmic rays over the solar minimum of cycle 22 and the onset of solar activity and the long term cosmic ray modulation of cycle 23. Through 2000.7 there have been three well-defined step decreases in the cosmic ray intensity at 1 AU with the cumulative effect being in good agreement with the net decrease in cycle 21 at a comparable time in the solar cycle. Over this period the intensity changes at Ulysses are similar to those at 1 AU. In the distant heliosphere the initial decreases appear to be smaller than those at 1 AU. However the full effects of the interplanetary disturbances producing the most recent and largest step decrease in the inner heliosphere have not yet reached V-2. This revised version was published online in August 2006 with corrections to the Cover Date.     

Modulation of Galactic Cosmic Rays at Solar Minimum

Cosmic ray particles respond to the heliospheric magnetic field in the expanding solar wind and its turbulence and therefore provide a unique probe for conditions in the changing heliosphere. During the last four years, concentrated around the solar minimum period of solar cycle 22, the exploration of the solar polar regions by the joint ESA/NASA mission Ulysses revealed the three-dimensional behavior of cosmic rays in the inner and middle heliosphere. Also during the last decades, the Pioneer and Voyager missions have greatly expanded our understanding of the structure and extent of the outer heliosphere. Simultaneously, numerical models describing the propagation of galactic cosmic rays are becoming sophisticated tools for interpreting and understanding these observations. We give an introduction to the subject of the modulation of galactic cosmic rays in the heliosphere during solar minimum. The modulation effects on cosmic rays of corotating interaction regions and their successors in the outer heliosphere are discussed in more detail by Gazis, McDonald et al. (1999) and McKibben, Jokipii et al. (1999) in this volume. Cosmic-ray observations from the Ulysses spacecraft at high heliographic latitudes are also described extensively in this volume by Kunow, Lee et al. (1999). This revised version was published online in August 2006 with corrections to the Cover Date.     

ICMEs at High Latitudes and in the Outer Heliosphere

Interplanetary coronal mass ejections (ICMEs) propagate into the outer heliosphere, where they can have a significant effect on the structure, evolution, and morphology of the solar wind, particularly during times of high solar activity. They are known to play an important role in cosmic ray modulation and the acceleration of energetic particles. ICMEs are also believed to be associated with the large global transient events that swept through the heliosphere during the declining phases of solar cycles 21 and 22. But until recently, little was known about the actual behavior of ICMEs at large heliographic latitudes and large distances from the Sun. Over the past decade, the Ulysses spacecraft has provided in situ observations of ICMEs at moderate heliographic distances over a broad range of heliographic latitudes. More recently, observations of alpha particle enhancements, proton temperature depressions, and magnetic clouds at the Voyager and Pioneer spacecraft have begun to provide comparable information regarding the behavior of ICMEs at extremely large heliocentric distances. At the same time, advances in modeling have provided new insights into the dynamics and evolution of ICMEs and their effects on cosmic rays and energetic particles.     

Anomalous and Galactic Cosmic Rays at 1 AU During the Cycle 23/24 Solar Minimum

Anomalous cosmic ray (ACR) intensities at 1 AU at solar minimum generally track galactic cosmic ray (GCR) intensities such as those measured by neutron monitors, albeit with differences between solar polarity cycles. The unusual cycle 23/24 solar minimum was long-lasting with very low sunspot numbers and significantly reduced interplanetary magnetic field strength and solar wind dynamic pressure and turbulence, but also featured a heliospheric current sheet tilt that remained high for an extended period. Peak ACR intensities did not recover to the maximum values reached during the last two A>0 solar minima and just barely reached the last A<0 levels. However, GCR intensities in 2009 (neutron monitor rates and also at ～200 MeV/nucleon) were the highest recorded during the last 50 years, indicating their intensities were not as heavily modulated during their transport from the outer heliosphere. This unexpected difference in the behavior of ACRs and GCRs remains unexplained, but suggests that either the ACR source intensity may have weakened since the last A<0 epoch, or perhaps that ACR intensities at 1 AU in the ecliptic may be more sensitive than GCRs to the higher tilt angle. This seems plausible if the ACR source intensity is greater at low latitudes during A<0 cycles, while the GCR distribution at the heliospheric boundary is more uniform in latitude. Shortly after an abrupt increase in the current sheet tilt angle in late 2009, both ACR and GCR intensities showed dramatic decreases, marking the end of solar minimum modulation conditions for this cycle.     

Voyager Observations of the Magnetic Field in the Distant Heliosphere

The latitudinal structure of the heliospheric magnetic field during much of the solar cycle is determined by a "sector zone", in which both positive and negative magnetic polarities are observed, and by the unipolar regions above and below the sector zone. Distinct corotating streams and interactions regions are found primarily in the sector zone during the declining phase of the solar cycle. Within a few AU, the streams and interaction regions are distinct and are related to solar features. A restructuring of the solar wind occurs between 1 AU and 15 AU, in which the isolated streams, interaction regions and shocks merge to form compound streams and merged interaction regions ("MIRs"). Memory of the source conditions is lost in this process. In the region between 30 AU and the termination shock (the "distant heliosphere"), the pressure of interstellar pickup protons dominates that of the magnetic field and solar wind particles and largely controls the dynamical processes. During 1983 and 1994, corotating streams and corotating interaction regions were observed at 1 AU. Merged interaction regions were observed at 15 AU in 1983, but not at 45 AU during 1994. This result suggests a further restructuring of the solar wind in the distant heliosphere, but variations from one solar cycle to the next might also contribute to the result. Approaching solar minimum in 1996, the latitudinal extent of the sector zone decreased, and Voyager 2 gradually entered the unipolar region below it. The speed was lower in the sector zone than below it. At Voyagers 1 and 2, the change in cosmic ray intensity is related to the magnetic field strength during each year from 1983 through 1996. The magnetic field strength has a multifractal distribution throughout the heliosphere. This fundamental symmetry of the heliosphere has not been incorporated explicitly in cosmic ray propagation models.     

Cosmic-Ray Modulation in the Heliosphere A Phenomenological Study

The heliospheric cosmic-ray network–Pioneer 10/11, Voyager 1/2, Ulysses and IMP 8 have provided detailed observations of galactic and anomalous cosmic rays over a period of time that now exceeds 25 years and extends to heliocentric distances beyond 65 AU. These data, when compared over consecutive 11 year solar cycles, clearly establishes the existence of a 22-year cosmic ray modulation cycle that is dominated by the 11-year solar activity cycle but is strongly influenced by gradient and curvature drifts in association with the tilt of the heliospheric neutral current sheet as well as the mediation of the enhanced magnetic turbulence above the solar poles. Over successive solar minima these effects manifest themselves in the remarkable differences in the energetic particle time histories, in the magnitude and sign of the radial and latitudinal intensity gradients and in the changes in the energy spectra of anomalous cosmic rays as a function of heliocentric distance.From solar minimum to solar maximum the long term modulation is principally a combination of two solar related phenomena, the cumulative effect of long-lived global merged interaction regions (GMIRs) and gradient and curvature drifts in the interplanetary magnetic field. For the periods when positive ions flow in over the solar poles and out along the heliospheric current sheet, the modulation of ions is dominated by GMIRs. When this flow pattern is reversed it is found that drifts are an important but not dominant factor for cosmic ray modulation with the current sheet related drift effects decreasing with increasing rigidity R, heliolatitude and heliocentric distance. Over a single solar cycle these conclusions are confirmed at 1 AU by comparing the relative modulation of cosmic-ray helium nuclei and electrons.     

Physical Processes in the Outer Heliosphere

This chapter covers the theory of physical processes in the outer heliosphere that are particularly important for the IBEX Mission, excluding global magnetohydrodynamic/Boltzmann modeling of the entire heliosphere. Topics addressed include the structure and parameters of the solar wind termination shock, the transmission of ions through the termination shock including possible reflections at the shock electrostatic potential, the acceleration and transport of suprathermal ions and anomalous cosmic rays at the termination shock and in the heliosheath, charge-exchange interactions in the outer heliosphere including mass and momentum loading of the solar wind, the transport of interstellar pickup ions, and the production and anticipated intensities of energetic neutral atoms (ENAs) in the heliosphere.     

Cosmic ray modulation in the 3-D heliosphere

The basic physical processes that lead to the long-term modulation of cosmic rays by the solar wind have been known for many years. However our knowledge of the structure of the heliosphere, which determines which processes are most important for the modulation, and of the variation of this structure with time and solar activity level is still incomplete. Study of the modulation provides a tool for probing the scale and structure of the heliosphere. While the Pioneer and Voyager spacecraft are surveying the radial structure and extent of the heliosphere at modest heliographic latitudes, theUlysses mission is the first to undertake a nearly complete scan of the latitudinal structure of the modulated cosmic ray intensity in the inner heliosphere (R<5.4 AU).Ulysses will reach latitudes of 80°S in September 1994 and 80°N in July 1995 during the approach to minimum activity in the 11 year solar cycle. We present a first report of measurements extending to latitudes of 52°S, which show surprisingly little latitudinal effect in the modulated intensities and suggest that at this time modulation in the inner heliosphere may be much more spherically symmetric than had generally been believed based upon models and previous observations.     

Time-Variability in the Interstellar Boundary Conditions of the Heliosphere: Effect of the Solar Journey on the Galactic Cosmic Ray Flux at Earth

During the solar journey through galactic space, variations in the physical properties of the surrounding interstellar medium (ISM) modify the heliosphere and modulate the flux of galactic cosmic rays (GCR) at the surface of the Earth, with consequences for the terrestrial record of cosmogenic radionuclides. One phenomenon that needs studying is the effect on cosmogenic isotope production of changing anomalous cosmic ray fluxes at Earth due to variable interstellar ionizations. The possible range of interstellar ram pressures and ionization levels in the low density solar environment generate dramatically different possible heliosphere configurations, with a wide range of particle fluxes of interstellar neutrals, their secondary products, and GCRs arriving at Earth. Simple models of the distribution and densities of ISM in the downwind direction give cloud transition timescales that can be directly compared with cosmogenic radionuclide geologic records. Both the interstellar data and cosmogenic radionuclide data are consistent with two cloud transitions, within the past 10,000 years and a second one 20,000–30,000 years ago, with large and assumption-dependent uncertainties. The geomagnetic timeline derived from cosmic ray fluxes at Earth may require adjustment to account for the disappearance of anomalous cosmic rays when the Sun is immersed in ionized gas.     

Three-dimensional Solar Modulation of Cosmic Ray and Anomalous Components in the Inner Heliosphere

Our picture of modulation in the inner heliosphere has been greatly affected by observations from the Ulysses mission, which since 1992 has provided the first comprehensive exploration of modulation as a function of latitude from 80° S to 80° N heliographic latitude. Among the principal findings for the inner heliosphere are: a) the cosmic ray intensity depends only weakly on heliographic latitude; b) for the nuclear components, and especially for the anomalous components, the intensity increases towards the poles, qualitatively consistent with predictions of drift models for the current sign of the solar magnetic dipole; c) no change in the level of modulation was observed across the shear layer separating fast polar from slow equatorial solar wind near 1 AU; d) 26-day recurrent variations in the intensity persist to the highest latitudes, even in the absence of clearly correlated signatures in the solar wind and magnetic field; e) the surface of symmetry of the modulation in 1994-95 was offset about 10° south of the heliographic equator; f) the intensity of electrons and of low energy (< 100 MeV) protons showed essentially no dependence on heliographic latitude.     

The Theory of Anomalous Cosmic Rays

Anomalous cosmic rays are a heliospheric phenomenon in which interstellar neutral atoms stream into the heliosphere, are ionized by either solar radiation or the solar wind, and are subsequently accelerated to very high energies, greater than 1 GeV. Current thinking has the bulk of the acceleration to very-high energies taking place, by the mechanism of diffusive shock acceleration, at the termination shock of the solar wind. Detailed two-dimensional numerical simulations and models based on this picture show broad agreement with a number of the observed properties of anomalous cosmic rays. Recent improvements to this picture include the observation of multiply charged cosmic rays and the suggestion that some "preacceleration" of the initially ionized particles occurs in the inner heliosphere.     

Cosmic Rays in the Inner Heliosphere: Insights from Observations, Theory and Models

The global modulation of galactic cosmic rays in the inner heliosphere is determined by four major mechanisms: convection, diffusion, particle drifts (gradient, curvature and current sheet drifts), and adiabatic energy losses. When these processes combine to produce modulation, the complexity increases significantly especially when one wants to describe how they evolve spatially in all three dimensions throughout the heliosphere, and with time, as a function of solar activity over at least 22 years. In this context also the global structure and features of the solar wind, the heliospheric magnetic field, the wavy current sheet, and of the heliosphere and its interface with the interstellar medium, play important roles. Space missions have contributed significantly to our knowledge during the past decade. In the inner heliosphere, Ulysses and several other missions have contributed to establish the relative importance of these major mechanisms, leading to renewed interest in developing more sophisticated theories and numerical models to explain these observations, and to understand the underlying physics that determines galactic cosmic ray modulation at Earth. An overview is given of some of the observational and modeling highlights over the past decade.     

Global Processes that Determine Cosmic Ray Modulation

The global processes that determine cosmic ray modulation are reviewed. The essential elements of the theory which describes cosmic ray behavior in the heliosphere are summarized, and a series of discussions is presented which compare the expectations of this theory with observations of the spatial and temporal behavior of both galactic cosmic rays and the anomalous component; the behavior of cosmic ray electrons and ions; and the 26-day variations in cosmic rays as a function of heliographic latitude. The general conclusion is that the current theory is essentially correct. There is clear evidence, in solar minimum conditions, that the cosmic rays and the anomalous component behave as is expected from theory, with strong effects of gradient and curvature drifts. There is strong evidence of considerable latitude transport of the cosmic rays, at all energies, but the mechanism by which this occurs is unclear. Despite the apparent success of the theory, there is no single choice for the parameters which describe cosmic ray behavior, which can account for all of the observed temporal and spatial variations, spectra, and electron vs. ion behavior.     

Low Energy Particles in the Global Heliosphere 2001–2004: 1 to 90 AU

Charged particle instrumentation that will be flying on six spacecraft in the heliosphere between 1 and 90 AU during 2001–2004 will provide a global view of the interplanetary medium that has not heretofore been available. Comparative analyses of the data that will be obtained will provide new understanding of the global evolution of heliospheric features such as traveling shock waves, coronal mass ejections, solar activity-produced particle injections, and anomalous cosmic rays. This revised version was published online in August 2006 with corrections to the Cover Date.     

The anomalous component of cosmic rays in the 3-D heliosphere

More than 20 years ago, in 1972, anomalous flux increases of helium and heavy ions were discovered during solar quiet times. These flux increases in the energy range<50 MeV/nucleon showed peculiar elemental abundances and energy spectra, e.g. a C/O ratio0.1 around 10 MeV/nucleon, different from the abundances of solar energetic particles and galactic cosmic rays. Since then, this anomalous cosmic ray component (ACR) has been studied extensively and at least six elements have been found (He,N,O,Ne,Ar,C) whose energy spectra show anomalous increases above the quiet time solar and galactic energetic particle spectrum. There have been a number of models proposed to explain the ACR component. The presently most plausible theory for the origin of ACR ions identifies neutral interstellar gas as the source material. After penetration into the inner heliosphere, the neutral particles are ionized by solar UV radiation and by charge exchange reactions with the solar wind protons. After ionization, the now singly charged ions are picked up by the interplanetary magnetic field and are then convected with the solar wind to the outer solar system. There, the ions are accelerated to high energies, possibly at the solar wind termination shock, and then propagate back into the inner heliosphere. A unique prediction of this model is that ACR ions should be singly ionized. Meanwhile, several predictions of this model have been verified, e.g. low energy pick-up ions have been detected and the single charge of ACR ions in the energy range at MeV/nucleon has been observed. However, some important aspects such as, for example, the importance of drift effects for the acceleration and propagation process and the location of the acceleration site are still under debate. In this paper the present status of experimental and theoretical results on the ACR component are reviewed and constraints on the acceleration process derived from the newly available ACR ionic charge measurements will be presented. Possible new constraints provided by correlative measurements at high and low latitudes during the upcoming solar pole passes of the ULYSSES spacecraft in 1994 and 1995 will be discussed.     

Recurrent Solar Modulation of the Galactic Cosmic Rays and the Anomalous Nuclear Component in Three Dimensions of the Heliosphere

Ulysses Mission investigations, extending from pole-to-pole of the Sun and inner heliosphere in the period 1993-1996, have led to discoveries that will change dramatically models to account for the physical phenomena underlying the 26-day modulation of galactic cosmic rays and anomalous nuclear components and their propagation modes. These new findings also relate to the propagation of low energy nucleons and electrons accelerated by corotating interaction region shocks. Also included are some unpublished measurements that will need to be taken into account in any model for the 26-day modulation phenomena. This report is a brief summary of the principal results from the solar wind, magnetic field and charged particle investigations, and their alternate interpretations.     

Transient Effects and Disturbed Conditions

In the present phase of the solar cycle no big transients leading to strong modulation had been observed after 1991. Apart from a few minor disturbances cosmic rays were still recovering to a new intensity maximum. It was suggested, therefore, that existing literature from previous cycles should be critically reviewed. The scene was set by the introductory papers on— phenomenology of cosmic ray modulation in successive solar cycles throughout the heliosphere— the present state of models for long term modulation and their shortcomings— the relation between cosmic ray variations and the magnitude of the interplanetary magnetic field (the CR-B-relation)— charge dependent effects.In the discussions, the study of propagating diffusive disturbances and the CR-B-relation played a central role. The difference was stressed between isolated transient disturbances in the inner solar system (Forbush decreases), and the long lasting, step-like decreases caused by merged interaction regions in the outer heliosphere. The recovery rates following the step-like decreases vary with the phase in the 22-year solar cycle. In some cases this requires a modification of existing drift models. In the outer heliosphere, the CR-B-relation leads to the result 1/ between the diffusion coefficient and the field magnitude . This simple result is a challenge for theoreticians to derive the perpendicular diffusion coefficient fromfirst principles. The three articles in this report essentially follow the list of open points and arguments just presented.The article "Observations and Simple Models" is organised around the model of a propagating diffusive barrier, its application to Forbush effects in the inner heliosphere and to decreases caused by merged interaction regions in the outer heliosphere. Acomparison of observed Forbush decreases with model predictions requires a careful separation of the two steps related to the turbulent region behind the shock front and the closed magnetic field regions of the ejecta (the interplanetary counterparts of coronal mass ejections). It is shown that models for propagating disturbances can be used to derive values of the diffusion coefficients phenomenologically, not only during the disturbance, but also in the ambient medium.The "Modeling of Merged Interaction Regions" summarizes the dynamic and time-dependent process of cosmic ray modulation in the heliosphere. Numerical models with only a time-dependent neutral sheet prove to be successful when moderate to low solar activity occurs but fail to describe large and discrete steps in modulated cosmic rays when solar activity is high. To explain this feature of heliospheric modulation, the concept of global merged interaction regions is required. The com-bination of gradient, curvature and neutral sheet drifts with these global merged interaction regions has so far been the most successful approach in explaining the 11-year and 22-year cycles in the long-term modulation of cosmic rays.The "Remarks on the Diffusion Tensor in the Heliosphere" describe available theories of perpen-dicular diffusion and drift, and discuss their relevance to cosmic rays in the heliosphere. In addition, the information about diffusion coefficients and spatial gradients obtained from the analysis of steady state anisotropies at neutron monitor energies is summarized. These topics are intimately related to the other two articles. They are also part of the general discussion about the "Diffusion Tensor throughout the Heliosphere" which played an important role in all working groups.