The acceleration of Anomalous Cosmic Rays by stochastic acceleration in the heliosheath

Stochastic acceleration in the heliosheath appears to be a likely mechanism by which Anomalous Cosmic Rays (ACRs) are accelerated. However, most stochastic acceleration mechanisms are not appropriate. The energy density in the ACRs and in the interstellar pickup ions out of which the ACRs are accelerated greatly exceeds the energy density in the turbulence in the heliosheath. Thus, a traditional stochastic acceleration mechanism in which particles are accelerated by damping the turbulence will not work. A stochastic acceleration mechanism has been developed in which the total energy of the pickup ions and the ACRs is conserved. Energy is redistributed from the core pickup ions into a suprathermal tail to create the ACRs. A model for the acceleration of the ACRs in the heliosheath, based on this stochastic acceleration mechanism, is presented. The model provides reasonable fits to the spectra of suprathermal particles and ACRs observed by Voyager.     

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.     

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.     

Possible physical properties of the flow in the vicinity of the heliopause

An interface between the fully ionized hydrogen plasma of the solar wind (SW) and the partially ionized hydrogen gas flow of the local interstellar medium (LISM) is formed as a region where there is a strong interaction between these two flows. The interface is bounded by the solar wind termination shock (TS) and the LISM bow shock (BS) and is separated on two regions by the heliopause (HP) separating the solar wind and charged component of the LISM (plasma component below). The BS is formed due to the deceleration of the supersonic LISM flow relative to the solar system. Regions of the interface between the TS and HP and between the HP and BS were in literature named as the inner and outer heliosheaths, respectively. An investigation of the structure and physical properties of the heliosheath is at present especially interested due to the fact that Voyager-1 and Voyager-2 have crossed the TS in December 2004 (Burlaga, L.F., Ness, N.F., Acuna, M.Y., et al. Crossing the termination shock into the the heliosheath. Magnetic fields. Science 309, 2027–2029, 2005; Fisk, L.A. Journey into the unknown beyond. Science 309, 2016–2017, 2005; Decker, R.B., Krimigis, S.M., Roelof, E.C., et al. Voyager 1 in the foreshock, termination shock and heliosheath. Science 309, 2020–2024, 2005; Stone, E.C., Cummings, A.C., McDonald, F.B., et al. Voyager 1 explores the termination shock region and the heliosheath beyond. Science 309, 2017–2020, 2005) and in September 2007 (Jokipii, J.R. A shock for Voyager 2. Nature 454, 38–39, 2008; Gurnett, D.A., Kurth, W.S. Intense plasma waves at and near the solar wind termination shock. Nature 454, 78–80, 2008. doi: 10.1038/nature07023; Wang, L., Lin, R.P., Larson, D.E., Luhmann, J.G. Domination of heliosheath pressure by shock-accelerated pickup ions from observations of neutral atoms. Nature 454, 81–83, 2008. doi: 10.1038/nature07068.14; Burlaga, L.F., Ness, N.F., Acuna, M.H., et al. Magnetic fields at the solar wind termination shock. Nature 454, 75–77, 2008. doi: 10.1038/nature07029; Richardson, J.D., Kasper, J.C., Wang, C., et al. Cool heliosheath plasma and deceleration of the upstream solar wind at the termination shock. Nature 454, 63–66, 2008. doi: 10.1038/nature07024; Stone, E.C., Cummings, A.C., McDonald, F.B., et al. An asymmetric solar wind termination shock. Nature 454, 71–74, 2008. doi: 10.1038/nature07022; Decker, R.B., Krimigis, S.M., Roelof, E.C., et al. Mediation of the solar wind termination shock by non-thermal ions. Nature 454, 67–70, 2008. doi: 10.1038/nature 07030), respectively, and entered to the inner heliosheath.     

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.     

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.     

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.     

On the transport of cosmic rays in the distant heliosheath

This paper discusses the transport of energetic charged particles through a sectored magnetic field in distant regions of the inner heliosheath. As the plasma flow slows down on approach to the stagnation point on the heliopause, the distance between the folds of the current sheet decreases to the point where it becomes comparable to the cyclotron radius of a cosmic ray particle. Under these conditions a particle can effectively drift across the stack of magnetic sectors with a speed comparable with the particle’s velocity. For a random distribution of current sheet separation distances, a diffusive transport across the stack of sectors occurs instead. The proposed mechanism could have contributed to unusually high intensities of galactic cosmic rays measured by Voyager 1 in the heliosheath during 2009–2010.     

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.     

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.