A Numerical Study of the Galactic Cosmic Positron Anisotropy Induced by Solar Modulation

As the galactic cosmic ray positrons with energies below 30 GeV enter the heliosphere, they interact with the solar wind and the heliospheric magnetic field which get frozen inside. The overall modulation effects, including the solar wind convection, diffusion and drift, lead to galactic cosmic ray positrons anisotropy. In this study, Parker's transport equation is used to study the transport process of positrons in the heliosphere. The local interstellar spectrum of positrons at the heliosphere boundary (120 AU) is used as the simulation boundary. Using the alternating direction implicit (ADI) method, the flux of galactic cosmic ray positrons in the heliosphere is calculated, as well as the gradient of galactic cosmic ray positrons. Based on these numerical results, the polar and radial components of the anisotropy with energies of 0.01 GeV, 0.1 GeV, 1 GeV are obtained. It has been found that: (1) For low energy positrons, Since their drift of low energy positrons is almost negligible, the polar anisotropy component is only determined by diffusion. Its magnitude is equivalent at the same latitude in the northern and southern heliosphere, and it is vanishing at the equator. On the other hand, the positrons with high energy are affected by drift process, resulting in non-zero polar anisotropy component at the equator and different magnitude at the same latitude in the northern and southern heliosphere. (2) The radial anisotropy component of low-energy positrons are only determined by diffusion and convection. On the other hand, the positrons with high energy are affected by drift process, the radial anisotropy component is determined by diffusion, convection and drift. In addition, the polar gradient of positrons is almost negligible, so the radial anisotropy of any energy positrons here is only determined by diffusion and convection; Positrons exhibit significant radial anisotropy in high latitude regions of the heliosphere due to their large diffusion and drift.