Time and Charge-sign Dependence of the Heliospheric Modulation of Cosmic Rays

Simultaneous and continuous observations of galactic cosmic-ray electrons (e ⁻) and positrons (e ⁺) from the PAMELA and AMS02 space experiments are most suitable for numerical modeling studies of the heliospheric modulation of these particles below 50 GeV. A well-established comprehensive three-dimensional modulation model is applied to compute full spectra for e ⁻ and e ⁺ with the purpose of reproducing the observed ratio e ⁺/e ⁻ for a period that covers the previous long and unusual deep solar minimum activity and the recent maximum activity phase, including the polarity reversal of the solar magnetic field. For this purpose, the very local interstellar spectra for these particles were established first. Our study is focused on how the main modulation processes, including particle drifts, and other parameters, such as the three major diffusion coefficients, evolved and how the corresponding charge-sign dependent modulation subsequently occurred. The end result of our effort is the detailed reproduction of e ⁺/e ⁻ from 2006 to 2015, displaying both qualitative and quantitative agreement with the main observed features. Particularly, we determine how much particle drift is needed to explain the time dependence exhibited by the observed e ⁺/e ⁻ during each solar activity phase, especially during the polarity reversal phase, when no well-defined magnetic polarity was found.