3D distribution of cosmic rays in the Galaxy, anisotropic diffusion, computation of the proton spectrum along the Sun's orbit, heliospheric modulation of interstellar proton spectra
Final Report Abstract
The project had, first, the goal to compute the variation of the flux of galactic cosmic ray protons with energies up to 100 GeV along the Sun’s orbit in the Galaxy and through its spiral arms, i.e. to compute the corresponding variation of the local interstellar spectrum. It was, second, intended to particularly include anisotropic diffusion for the first time into a model of large-scale galactic cosmic ray propagation. Third, with the local interstellar spectrum as an input into our transport and modulation models, the cosmic ray flux through the heliosphere up to Earth orbit was to be determined. Fourth, our transport and modulation models were to be adapted to include the modulation in the so-called outer heliosheath between the bow (shock) wave and the heliopause. Finally, the contribution of locally accelerated protons to the local interstellar spectrum should be specified. The project work developed generally according to the work plan defined in the proposal and the three important milestones were reached, namely (a) the derivation of a new, and most general representation of the tensor describing the fully anisotropic diffusion of charged energetic particles in arbitrary magnetic field configurations, (b) the application of the results on the anisotropic diffusion to the galactic propagation of cosmic ray protons, and (c) the quantitative prediction of the modulation of interstellar cosmic ray spectra even beyond the heliopause, namely in the outer heliosheath. The most important findings in the context of these milestones are, first, that with a glance at earlier approaches to fully anisotropic diffusion, inconsistencies (missing second rotation angle) could be removed and differences (in the first rotation angle) were clarified. Second, the computed energy spectra at different positions along the Sun’s galactic orbit show larger variations for the anisotropic cases when compared to the scalar diffusion model. Furthermore, for the chosen parameters, a comparatively moderate diffusion anisotropy of 0.1, i.e. a ten times less efficient perpendicular than parallel diffusion, leads to a result being more consistent with recent estimates of the local interstellar proton spectrum than those for purely isotropic diffusion. And, third, the study of cosmic ray modulation beyond the heliopause revealed that it is unlikely that the Voyager spacecraft will ever measure the pristine local interstellar spectra below about 1 GeV. Thus, the necessity to distinguish between ‘heliopause spectra’ and ‘(true) local interstellar spectra’ has been established. With these results we have (i) provided valuable input to the debate on the significance of galactic cosmic rays for the interstellar-terrestrial relations, (ii) given new insight into the determinability of the low energy end of the interstellar proton spectrum from spacecraft data, and (iii) contributed constraints for the structure of the heliosphere. This work, with which the proposals goals were reached, was carried out in collaboration with scientist from Germany (mainly Ruhr-Universität Bochum and Universität Kiel) and mainly South Africa (North-West University, Potchefstroom) and resulted in a number of related joint publications.
Publications
- Comparison of Different Analytic Heliospheric Magnetic Field Configurations and their Significance for the Particle Injection at the Termination Shock, Astronomy and Astrophysics, 521, id.A1, 2010
Scherer, K., Fichtner, H., Effenberger, F., Burger, R.A., Wiengarten, T.
- Perpendicular diffusion of cosmic rays for a Goldreich-Sridhar spectrum, The Astrophysical Journal 725, 2117, 2010
Shalchi, A., Büsching, I., Lazarian, A., Schlickeiser, R.
- On Cosmic Ray Modulation beyond the Heliopause: Where is the Modulation Boundary? The Astrophysical Journal, 735, 128, 2011
Scherer, K.; Fichtner, H.; Strauss, R. D.; Ferreira, S. E. S.; Potgieter, M. S.; Fahr, H.-J.
- A Generalized Diffusion Tensor for Fully Anisotropic Diffusion of Energetic Particles in the Heliospheric Magnetic Field, The Astrophysical Journal, 750, article id. 108, 2012
Effenberger, F., Fichtner, H., Scherer, K., Barra, S., Kleimann, J., Strauss, R. D.
(See online at https://doi.org/10.1088/0004-637X/750/2/108) - Anisotropic Diffusion of Energetic Particles in Galactic and Heliospheric Magnetic Fields, Ph.D. thesis, Ruhr-Universität Bochum, 2012
Effenberger, F.
- Anisotropic diffusion of Galactic cosmic ray protons and their steady-state azimuthal distribution, Astronomy and Astrophysics, 547, id.A120, 2012
Effenberger, F., Fichtner, H., Scherer, K., Büsching, I.
(See online at https://doi.org/10.1051/0004-6361/201220203)
