Time–dependent modulation of cosmic rays in the outer heliosphere
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The time-dependent modulation of galactic cosmic rays in the heliosphere is studied by computing intensities using a two-dimensional, time-dependent modulation model. The compound approach of Ferreira and Potgieter (2004), which describes changes in the cosmic ray transport coefficients over a solar cycle, is improved by introducing recent theoretical advances in the model. Computed intensities are compared with Voyager 1 and 2, IMP 8 and Ulysses proton observations in search of compatibility. It is shown that this approach gives realistic cosmic ray proton intensities on a global scale at Earth and along both Voyager spacecraft trajectories. The results show that cosmic ray modulation, in particular during the present polarity cycle, is not just determined by changes in the drift coefficient but is also dependent on changes in the diffusion coefficients. Furthermore, a comparison of computations to observations along the Voyager 1 and Voyager 2 trajectories illustrates that the heliosphere is asymmetrical. Assuming the latter, E > 70 MeV and 133-242 MeV cosmic ray proton intensities along Voyager 1 and 2 trajectories are predicted from 2012 onwards. It is shown that the computed intensities along Voyager 1 can increase with an almost constant rate since the spacecraft is close to the heliopause. However, the model shows that Voyager 2 is still under the influence of temporal solar activity changes because of the relatively large distance to the heliopause when compared to Voyager 1. Along the Voyager 2 trajectory the intensities should remain generally constant for the next few years and then should start to steadily increase. It is also found that without knowing the exact location of heliopause and transport parameters one cannot conclude anything about local interstellar spectra. The effect of a dynamic inner heliosheath width on cosmic ray modulation is also studied by implementing a time-dependent termination shock position in the model. This does not lead to improved compatibility with spacecraft observations so that a time-dependent termination shock along with a time-dependent heliopause position is required. The variation of the heliopause position over a solar cycle is found to be smaller compared to that of the termination shock. The model predicts the heliopause and termination shock positions along Voyager 1 in 2012 at 119 AU and 88 AU respectively and along Voyager 2 at 100 AU and 84 AU respectively.