Modulation of cosmic-ray electrons in the outer heliosphere

A new cosmic-ray transport model, which investigates the modulation of cosmic-ray electrons in the outer heliospheric regions, including all major modulation mechanisms and the asymmetry of the heliospheric shock structures, is developed. The transport of Galactic cosmic rays into the heliosphere is directly calculated from the local interstellar medium, while for the mutual interaction between the solar wind and the interstellar medium, the three-fluid two-dimensional hydrodynamic Bonn model is used to calculate the geometry of the heliosphere and solar wind flow profiles as input to the transport model. There are considerable differences in the modulation that cosmic rays experience between the heliospheric nose and tail regions, but because of large transport parameters, no modulation of Galactic cosmic rays occurs beyond the heliopause. It is shown that for energetic particles in the range of 1 GeV the termination shock has a significant influence on the modeled Galactic cosmic-ray flux intensities in the equatorial regions in direction to the heliospheric nose, while it is decreasing toward the poles and in the tail. Depending on energy, most of the modulation that the particles experience occurs at radial distances less than the shock radius. It is also shown that the cosmic-ray distribution in the inner heliosphere is not sensitive to the nose-tail asymmetry of the termination shock and heliopause. Finally, the effect of perpendicular transport parameter in the polar region is calculated. It is shown that depending on energy, this parameter influence computed latitudinal gradients, especially at, and to a lesser extend beyond, the termination shock, and in the heliospheric tail.