Acceleration of cosmic rays in the outer heliosphere

Abstract

Shortly before the Voyager spacecraft crossed the heliospheric termination shock, they encountered narrow, peak-like enhancements in the intensities of low-energy electrons. These enhancements were associated at the time of their observation with diffusive shock acceleration, however it had not been formally confirmed whether this acceleration mechanism can indeed reproduce such intensity increases. This provided the impetus for a study revisiting the features of diffusive shock acceleration, considered within the global context of the heliospheric transport of cosmic rays. The distribution of cosmic rays in two spatial dimensions and energy, and the modulation thereof, are simulated by solving a transport equation using a comprehensive numerical model that also accounts for the effects of diffusive shock acceleration. The model is initially applied to the acceleration of anomalous cosmic rays, using their features to illustrate the characteristics of the acceleration mechanism. The primary focus of the study, however, is to investigate the spectral imprints of diffusive shock acceleration on galactic electron distributions. It is found that in addition to the well-known dependence of the spectral indices of accelerated spectra on the shock compression ratio, the acceleration process is also largely dependent on the form of the energy distribution of particles incident at the termination shock: It is revealed that while energy spectra with large spectral indices are not appreciably affected by diffusive shock acceleration, those with smaller spectral indices are more susceptible to it, with large intensity increases accompanying their acceleration. It follows that the efficiency of diffusive shock acceleration as a re-accelerator of galactic electrons is strongly influenced by any process or characteristic that affects their energy distribution at the termination shock, including their local interstellar energy spectra, the properties of their diffusion, and even the effects of drifts. The diffusion properties following from dissipation-range turbulence yield spectral forms that are particularly conducive to acceleration. It can be inferred from the modelling results that the effects of diffusive shock acceleration on electrons at Voyager-observed energies cannot necessarily be discerned from changes in their spectral slopes across the termination shock. This is because their spectra are already too hard and the compression ratio of the shock too small to induce them. The intensity increases this mechanism induces, however, are not only essential in reproducing radial profiles and energy spectra observed by Voyager 1 in the heliosheath, but are in fact large enough under these observationally constrained conditions to account for the magnitudes of the peak-like intensity enhancements detected near the termination shock. Diffusive shock acceleration emerges in this study as a prominent mechanism for the re-acceleration of galactic electrons.