Aspects of the modulation of cosmic rays in the outer heliosphere

Abstract

A time-dependent two-dimensional (2D) modulation model including drifts, the solar wind tennination shock (TS) with diffusive shock acceleration and a heliosheath based on the Parker (1965) transport equation is used to study the modulation of galactic cosmic rays (GCRs) and the anomalous component of cosmic rays (ACRs) in the heliosphere. In particular, the latitude dependence of the TS compression ratio and injection efficiency of the ACRs (source strength) based on the hydrodynamic modeling results of Scherer et al. (2006) is used for the first time in a modulation model. The subsequent effects on differential intensities for both GCRs and ACRs are illustrated, comparing them to the values without a latitude dependence for these parameters. It is found that the latitude dependence of these parameters is important and that it enables an improved description of the modulation of ACRs beyond the TS. With this modeling approach (without fitting observations) to the latitude dependence of the two parameters, it is possible to obtain a TS spectrum for ACRs at a polar angle of B = 55" that qualitatively approximates the main features of the Voyager 1 observations. This positive result has to be investigated further. Additionally, it is shown that the enhancement of the cosmic ray intensity just below the cut-off energy found for the ACR at the TS in an A < 0 magnetic polarity cycle in the equatorial plane with the latitude independent scenario, disappears in this region when the latitude dependence of the compression ratio and injection efficiency is assumed. Subsequent effects of these scenarios are illustrated on the global anisotropy vector of both GCRs and ACRs as the main theme of this work. For this purpose the radial and latitudinal gradients for GCRs and ACRs were accurately computed. The radial and latitudinal anisotropy components were then computed as a function of energy, radial distance and polar angle. It is also the first time that the anisotropy vector is comprehensively calculated in such a global approach to cosmic ray modeling in the heliosphere, in particular for ACRs. It is shown that the anisotropy vector inside (up-stream) and outside (down-stream) the TS behaves in a complicated way, so care must be taken in interpreting it. It is found that the latitude dependence of the two mentioned parameters can alter the direction (sign) of the anisotropy vector. Its behaviour beyond the TS is markedly different from inside the TS, mainly because of the slower solar wind velocity, with less dependence on the magnetic polarity cycles.