Modulation of Galactic Protons in an Asymmetrical Heliosphere

Abstract

A previously used two-dimensional model of the heliospheric modulation of cosmic rays including a solar wind termination shock is extended to include an outer modulation boundary that is asymmetrically shaped with respect to the Sun. The modulation process is described kinetically using the Parker transport equation. The model includes drifts, adiabatic energy changes, diffusion, convection, a solar wind termination shock, and a heliosheath and is used here to compute modulation differences between a symmetrical and an asymmetrical modeled heliosphere, as well as differences between an asymmetrical heliosphere including a termination shock and one without such a shock for Galactic cosmic-ray protons. The solutions are for solar minimum and moderate maximum conditions for both heliospheric magnetic field polarity cycles. It is found that the modulation produced for cosmic-ray protons with an asymmetrical heliospheric model differs from that produced with a symmetrical model, but significantly mostly for the A < 0 polarity cycle, especially in the tail region of the heliosphere. The results of the symmetrical model are, however, surprisingly reasonable for studies of the heliospheric nose region, measured against the asymmetrical model.