Cosmic-ray modulation and anisotropies at high rigidities: Theoretical modeling

The standard diffusion-convection theory of cosmic-ray transport is unable to properly describe solar modulation at the highest rigidities where the g yroradius and mean free path of particles become large and the diffusion pi cture breaks down. Present models need to invoke an ad hoc upper cutoff rig idity. We report on an attempt to extend the theoretical description of sol ar modulation to high rigidities, including the regime where diffusion appr oximation is not applicable. A scheme retaining the full directional distri bution is outlined that includes scattering but does not rely upon the conc ept of diffusive streaming and thus remains valid at arbitrarily large valu es of the scattering mean free path. The scattering process is briefly disc ussed. We consider isotropic scattering and the simplest form of anisotropi c scattering, but our formalism can accommodate more complex scattering pro cesses as well. The application of the method is illustrated by numerical s imulations obtained in a simplified two-dimensional scenario which includes a flat heliospheric current sheet (HCS). We find that the anisotropies pre dicted in the inner heliosphere turn out to be largely independent of the c onditions assumed at the outer boundary, and the anisotropies decrease grad ually as the particle rigidity increases. Isotropic scattering gives rise t o very small anisotropies in the inner heliosphere, where the solutions con verge to an isotropic three-dimensional (3-D) force-field solution. Anisotr opic scattering, however, can produce reasonable anisotropies at the Earth' s orbit. While the model is still greatly idealized and we do not attempt q uantitative fits to observations at this stage, some important tendencies c an already clearly be demonstrated. For instance, the polarity dependence o f the solar diurnal variation is reproduced, the sense of the observed phas e shift of the solar diurnal wave at polarity reversals of the sun is corre ctly predicted. The present two-dimensional (2-D) model fails to explain th e sector-dependent North-South anisotropy, which is a direct result of the wavy structure of the current skeet and cannot be interpreted in terms of a 2-D model.