Through the heliospheric lens: Directional deflection of high-energy cosmic-ray electrons and positrons

We investigate how the large-scale heliosphere alters the arrival directions of high-energy cosmic-ray electrons and positrons and ask if and when this “heliospheric lens” can be ignored for anisotropy and source — association studies — an especially timely topic given, for instance, the persistent cosmic-ray positron fraction and its unknown origin. Using a modular back-tracing framework, we explore a set of widely used magnetic-field descriptions—from a Parker spiral baseline to more structured configurations that include latitudinal wind contrasts, Smith–Bieber–type azimuthal strengthening, and tilted or wavy heliospheric current sheets. We model the deterministic deflections of high-energy cosmic-ray electrons and positrons (CREs) induced by large-scale heliospheric magnetic-field structures using a back-tracing approach. Our results apply to CREs above tens of GeV, where diffusion, convection, and adiabatic energy losses play a subdominant role; these processes are neglected in the present study and will be addressed in future work. Across these models the picture is consistent: most bending is accumulated within the inner tens of astronomical units and decreases rapidly with energy. Field choices and solar-cycle geometry set the overall normalization, with stronger spiral winding or a more highly tilted current sheet producing larger deflections at the same energy. Differences between electrons and positrons are most apparent at lower energies, where drift histories and current-sheet encounters diverge, and become increasingly small at multi-TeV energies. We summarize these trends with a practical threshold energy describing when heliospheric bending falls below an instrument’s angular resolution, and we verify that our conclusions are robust to numerical settings. For current instruments, heliospheric effects can usually be treated as a small correction at the highest energies, while sub-TeV analyses benefit from a calibrated envelope that accounts for plausible field configurations during the observing epoch.