On the dynamics of the heliosphere on intermediate and long time-scales

A time-dependent, three-dimensional model of the dynamics of the heliosphere as a result of solar activity and a time-varying local interstellar medium is presented. The model is based on a recent version of the well known ZEUS code and employs parallel processing. It includes the solar and interstellar plasma components as well as neutral atoms, and contains the heliospheric magnetic field in a kinematic fashion. We study the dynamics of the heliosphere due to solar activity on periods of months to years up to the so-called Schwabe (11-year) cycle as well as due to time variations of the local interstellar medium, all of which have drawn increasing attention during recent years, as the significance of their direct or indirect effect on the Earth and its environment is under lively debate.     

Solar wind structure in the outer heliosphere

A solar wind parcel evolves as it moves outward, interacting with the solar wind plasma ahead of and behind it and with the interstellar neutrals. This structure varies over a solar cycle as the latitudinal speed profile and current sheet tilt change. We model the evolution of the solar wind with distance, using inner heliosphere data to predict plasma parameters at Voyager. The shocks which pass Voyager 2 often have different structure than expected; changes in the plasma and/or magnetic field do not always occur simultaneously. We use the recent latitudinal alignment of Ulysses and Voyager 2 to determine the solar wind slowdown due to interstellar neutrals at 80 AU and estimate the interstellar neutral density. We use Voyager data to predict the termination shock motion and location as a function of time.     

Spectral properties of backscattered solar Ly-α radiation in the heliosphere: A search for heliospheric boundary effects

We explore the imprints of the solar wind interaction with the local interstellar medium on spectral properties of backscattered solar Ly-α radiation. We employ a newly developed effective model for the interstellar H atom velocity distribution function in the heliosphere ( Katushkina and Izmodenov, 2011). The model takes into account both global effects of H atom perturbations at the heliospheric boundaries and local (i.e. within 10–20 AU from the Sun) effects of the solar ionization, charge exchange, solar gravitation and radiation pressure.     

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.     

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.     

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 composition and distribution of anomalous cosmic rays

The composition of anomalous cosmic rays (ACR), is thought to reflect that of the neutral atoms in the very local interstellar medium, such as helium, nitrogen and neon. Recent observations in the outer heliosphere have provided the first unambiguous evidence for ACR argon, carbon and hydrogen, as well, and a method has been developed to relate the ACR abundances to those of the interstellar medium. The observations also indicate persistent negative latitudinal gradients, opposite to that observed by Pioneer 11 during the previous minimum in solar activity. These and other results are consistent with the presence of gradient and curvature drift during solar minimum periods when the tilt of the interplanetary neutral sheet is small.     

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.     

MHD modeling of the outer heliosphere: Achievements and challenges

An overview is presented of magnetic-field-related effects in the solar wind (SW) interaction with the local interstellar medium (LISM) and the different theoretical approaches used in their investigation. We discuss the possibility that the interstellar magnetic field (ISMF) introduces north–south and east–west asymmetries of the heliosphere, which might explain observational data obtained by the Voyager 1 and Voyager 2 spacecraft. The SW–LISM interaction parameters that are responsible for the deflection of the interstellar neutral hydrogen flow from the direction of propagation of neutral helium in the inner heliosheath are outlined. The possibility of a strong ISMF, which increases the heliospheric asymmetry and the H–He flow deflection, is discussed. The effect of the combination of a slow-fast solar wind during solar minimum over the Sun’s 11-year activity cycle is illustrated. The consequences of a tilt between the Sun’s magnetic and rotational axes are analyzed. Band-like areas of an increased magnetic field distribution in the outer heliosheath are sought in order to discover regions of possible 2–3 kHz radio emission.     

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 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.     

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 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.     

In situ observations of magnetic field fluctuations

It is well known that the irregularities of the magnetic field are intimately related to the motion of charged particles. Although transport theories need the spatial and time variations of the magnetic field as input, in situ observations are very limited. Ulysses observations have provided a major step forward by entering the unexplored high latitude regions of the heliosphere, the knowledge of which is vital to interpret particle flux measurements, even at the ecliptic. We analyze the magnetic field data of Ulysses during the mission to study the waves and discontinuities in the heliosphere at different locations, covering a total sunspot cycle. Various tools are employed, including power spectral and structure function analysis. A remarkable difference was found between the fluctuations in the fast and slow solar wind. We argue that the latitudinal extent of the high speed solar wind contributes significantly to the latitudinal variation of the transport parameters, which should also affect the 11 (and 22) year modulation cycle.     

Modeling the time-intensity profile of solar flare generated particle fluxes in the inner heliosphere.

It is possible to model the time-intensity profile of solar particles expected in space after the occurrence of a significant solar flare on the sun. After the particles are accelerated in the flare process, if conditions are favorable, they may be released into the solar corona and then into space. The heliolongitudinal gradients observed in the inner heliosphere are extremely variable, reflecting the major magnetic structures in the solar corona which extend into space. These magnetic structures control the particle gradients in the inner heliosphere. The most extensive solar particle measurements are those observed by earth-orbiting spacecraft, and forecast and prediction procedures are best for the position of the earth. There is no consensus of how to extend the earth-based models to other locations in space. Local interplanetary conditions and structures exert considerable influence on the time-intensity profiles observed. The interplanetary shock may either reduce or enhance the particle intensity observed at a specific point in space and the observed effects are very dependent on energy.     

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.     

Viewing radiation signatures of solar energetic particles in interplanetary space

A current serious limitation on the studies of solar energetic particle (SEP) events is that their properties in the inner heliosphere are studied only through in situ spacecraft observations. Our understanding of spatial distributions and temporal variations of SEP events has come through statistical studies of many such events over several solar cycles. In contrast, flare SEPs in the solar corona can be imaged through their radiative and collisional interactions with solar fields and particles. We suggest that the heliospheric SEPs may also interact with heliospheric particles and fields to produce signatures which can be remotely observed and imaged. A challenge with any such candidate signature is to separate it from that of flare SEPs. The optimum case for imaging high-energy (E > 100 MeV) heliospheric protons may be the emission of π⁰-decay γ-rays following proton collisions with solar wind (SW) ions. In the case of E > 1 MeV electrons, gyrosynchrotron radio emission may be the most readily detectible remote signal. In both cases we may already have observed one or two such events. Another radiative signature from nonthermal particles may be resonant transition radiation, which has likely already been observed from solar flare electrons. We discuss energetic neutrons as another possible remote signature, but we rule out γ-ray line and 0.511 MeV positron annihilation emission as observable signatures of heliospheric energetic ions. We are already acquiring global signatures of large inner-heliospheric SW density features and of heliosheath interactions between the SW and interstellar neutral ions. By finding an appropriate observable signature of remote heliospheric SEPs, we could supplement the in situ observations with global maps of energetic SEP events to provide a comprehensive view of SEP events.