Modulation effects of anisotropic perpendicular diffusion on cosmic ray electron intensities in the heliosphere

Abstract

The modulation of cosmic ray electrons provides a useful tool to study the diffusion tensor applicable to heliospheric modulation. Electron modulation responds directly to the assumed energy dependence of the diffusion coefficients below ∼500 MeV in contrast to protons which experience large adiabatic energy losses below this energy. As a result of this and because drifts become unimportant for electrons at these low energies, conclusions can be made about the appropriate diffusion coefficients. Using a modulation model, we illustrate the role of anisotropic perpendicular diffusion on electron modulation. In general, we find that perpendicular diffusion dominates electron modulation below ∼100 MeV. Enhancing it in the polar direction typically produced an increase in modulation for both the A > O (e.g., ∼1990 to ∼2000) and A < 0 (e.g., ∼1980 to ∼1990) solar magnetic polarity cycles. It also causes the radial dependence of the intensity to become more uniform throughout the heliosphere, and causes a significant reduction in the latitude dependence of the intensities at all radial distances, with the largest effects in the inner heliosphere and at low energies. This agrees with studies of cosmic ray protons, which suggest that perpendicular diffusion enhanced in the polar direction of the heliosphere is required in conventional drift models to explain the small latitudinal gradients observed for protons on board the Ulysses spacecraft. The role of enhanced perpendicular diffusion was further investigated by examining electron modulation as a function of the “tilt angle” α of the wavy current sheet. In general, a reduction occurred between the modulation differences caused by drifts as a function of α for both polarity cycles. This work illustrates that anisotropic perpendicular diffusion has profound effects on the modulation of galactic cosmic ray electrons during both polarity cycles.