Long-term Cosmic-ray Modulation in the Heliosphere

A time-dependent model based on a numerical solution of Parker’s transport equation is used to model the modulation of cosmic-ray protons, electrons, and helium for full 11 year and 22 year modulation cycles using a compound approach. This approach incorporates the concept of propagating diffusion barriers, increases in the heliospheric magnetic field as they propagate from the Sun throughout the heliosphere, time-dependent gradient, curvature, and current-sheet drifts, and other basic modulation mechanisms. The model results are compared with those of the observed 11 year and 22 year cycles for 1.2 GV electrons and 1.2 GV helium at Earth for the period of 1975–1998. The model solutions are also compared with the observed charge-sign–dependent modulation along the Ulysses trajectory for the period of 1990–1998. This compound approach to long-term modulation, especially charge-sign–dependent modulation, is found to be remarkably successful. It is shown that the model can account for the latitude dependence of cosmic-ray protons and electrons by assuming a large perpendicular diffusion in the polar direction. This approach contributes to an improved understanding of how diffusion and drifts vary from solar minimum to maximum modulation and what the time dependence of the heliospheric diffusion coefficients may be. It is found that less than 10% of the available drifts are needed at solar maximum, when the solar magnetic field reverses, to explain, e.g., the observed electron-to-proton ratio along the Ulysses trajectory. Subject headings: convection — cosmic rays — diffusion — ISM: magnetic fields — solar-terrestrial relations — solar wind