The Effect of a Fisk-Type Heliospheric Magnetic Field on Cosmic-Ray Modulation

Abstract

The Fisk model of the heliospheric magnetic field (HMF) has proved to be quite difficult to implement in three-dimensional numerical modulation codes. We have developed a divergence-free Fisk-Parker hybrid HMF that is easier to implement and that should be a reasonable approximation for the case when field lines open into the heliosphere both in the polar coronal holes and at low latitudes. To study the effects of this hybrid field on galactic cosmic rays, we solve the three-dimensional steady state Parker transport equation numerically, covering the entire model heliosphere. We find that latitudinal cosmic-ray gradients are reduced as expected, but only during epochs when particles are drifting from the polar regions of the heliosphere toward the ecliptic plane. We investigate 26 day recurrent variations of both protons and electrons and find that the amplitude of these variations are directly proportional to the latitudinal intensity gradient, independent of species, in agreement with observational studies. In the absence of drifts in the code, electrons and protons obey different but still linear relationships.