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

Abstract

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.

A simulation study of galactic proton modulation from solar minimum to maximum conditions

“…The three-dimensional (3D) steady-state modulation model as described by [4], and recently improved by [8], is used to calculate proton spectra for monthly (and 27-day averages) up to sixmonth averages depending on the GCRs being studied and the particular application. The model is based on the numerical solution of Parker's [13] transport equation (TPE):…”

“…The rigidity dependence of K , indicating the two power-law slopes, at Earth is illustrated in Figure 1 as the corresponding parallel mean free paths (MFP; λ ) for four selected times; with K = λ(v/3) where v is the particle speed and β = v/c, with c the speed of light. How K relates to K ⊥r and K ⊥θ has been described in detail by [6,8] and is not repeated here; see also [9]. The model requires the determination of 27-day averaged values for all modulation parameters that vary with time and as such with solar activity e.g.…”

“…These calculated averages establish realistic heliospheric conditions as they are propagated into the heliosphere with the solar wind, which latitudinal dependence is also changing from solar minimum to maximum. See [5,6,8] for an elaborate discussion of the details of this approach as applied to GCR data sets observed by PAMELA (e.g. [10,17]) and for AMS02 (e.g.…”

“…This study takes advantage of simultaneous and continuous observations of galactic protons from the PAMELA [10] and AMS02 [11] space experiments to achieve the objective of the study. Both [7,8] successfully computed time and charge-sign dependent modulation for the period that covers the previous long and unusual deep solar minimum activity and the recent maximum period. The mentioned studies investigated how the main modulation processes including particle drifts and the major diffusion coefficients had evolved during the period investigated and subsequently how the corresponding charge-sign dependent modulation had occurred.…”

Study Galactic Cosmic Ray Modulation with AMS-02 observation

“…Solar Xiaojian Song model. Therefore, a widely used empirical formula is used in this work [e.g., [13][14][15]:…”