Are cosmic rays modulated beyond the heliopause?

Abstract

We discuss the possible spatial variation of Galactic and anomalous cosmic rays (GCRs and ACRs) at and beyond the heliopause (HP). Remaining within the framework of the Parker transport equation and assuming incompressible plasma in the heliosheath, we consider highly idealized simple-flow models and compare our GCR results with recent publications of Scherer et al. and Strauss et al. First, we discuss an order-of-magnitude estimate and a simple spherical model to demonstrate that the modulation of GCRs beyond the HP must be quite small if the diffusion coefficient beyond the HP is greater than 1026 cm 2 s-1, a value that is two orders of magnitude smaller than the value of 1028 cm2 s-1 determined from observations of GCR composition. Second, we construct a non-spherical model, which allows lateral deflection of the flow and uses different diffusion coefficients parallel and perpendicular to the magnetic field. We find that modulation of GCRs beyond the HP remains small even if the perpendicular diffusion coefficient beyond the HP is quite small (1022 cm 2 s-1) as long as the parallel diffusion is sufficiently fast. We also consider the case when the parallel diffusion beyond the HP is fast, but the perpendicular diffusion is as small as 1020 cm 2 s-1; this results in a sharp, almost step-like increase of GCR flux (and decrease of ACRs) at the HP. Possible implications are briefly discussed. We further suggest the possibility that the observed sharp gradient of GCRs at the HP might push the HP closer to the Sun than previously thought. © 2014. The American Astronomical Society. All rights reserved..