The heliospheric modulation of electrons and positrons over a complete solar cycle

Abstract

The solutions of a comprehensive three-dimensional drift model are compared to PAMELA and AMS-02 spectra of electrons and positrons in order to describe and understand their different modulation down to 1 MeV. This is based on newly constructed very local interstellar spectra. The focus of the study is on a full solar cycle, the period from 2006 to 2017. Comparison of observations and modeling provides insight into how the three major diffusion coefficients change during a complete solar cycle, especially during a prolonged solar minimum and the period of the polarity reversal of the magnetic field during solar maximum activity, and to what extent drift effects evolve. In this context, the electron to positron ratio is computed from 1 MeV to 50 GeV, explaining the PAMELA and AMS-02 observed ratio in detail. Predictions are made of what may be observed during the next, imminent solar minimum.

A Perspective on the Solar Modulation of Cosmic Anti-Matter

“…The relationship between, e.g., λ and K is given then by K || = (v/3)λ || = (βc/3)λ || , similarly for K ⊥r ,K ⊥θ and K D . The rigidity dependence of the three relevant MFPs λ ,λ ⊥r ,λ ⊥θ and the drift scale λ D are shown in Figure 2 for positrons in the left panel and for anti-protons in the right panel for yearly averages from 2006 to 2017 as established in [45,60,66,67] in order to reproduce the corresponding observed electron and positron spectra, and the proton and anti-proton spectra at Earth. with the calculated 15-month smoothed moving averages (SMA; red dots) as applied in the model.…”

“…During an A < 0 phase, it is expected that the changing wavy HCS plays an important even dominant role in the modulation of positively charged particles, whereas for an A > 0 polarity phase the drift directions become reversed so that negatively charged particles encounter the HCS during their entry. [60,66,67]; shaded band as in Figure 4.…”

“…Utilizing the precise observations at the Earth, the VLISs for all GCRs may be fine-tuned based on the output of the modulation model at high rigidity. This procedure has been followed for protons [48], for total helium and separately for the two helium isotopes [48][49][50][51], as well as for electrons and positrons [45,60,67] and for protons and anti-protons [66].…”

“…First, they established the VLISs for electrons using the process described above [46] by adjusting the appropriate physics in the web version of the GALPROP code [146] (and references there-in) to reproduce both the observed Voyager 1 and 2 electron intensity levels from beyond the HP and the high KE observations from PAMELA where solar modulation is considered negligible. Since positron data is not available beyond the HP, the spectral shape of the positron VLIS at low KE is based on what GALPROP produced but empirically modified as explained in [45,67] to improve the reproduction of observed spectra at Earth. As mentioned, the only known differences in the heliospheric modulation of electrons and positrons are the particle drifts that they experience and their respective VLISs.…”

“…In Figure 8, the modulation of positrons during extraordinary quite modulation conditions is shown as computed spectra at Earth compared to PAMELA data [113] for the period July to December 2009 (A > 0 cycle), and corresponding computed spectra throughout the heliosphere at 10 AU, 50 AU and 100 AU in the equatorial plane with respect to the VLIS at 122 AU. Examples of how large this modulation may be for an A > 0 cycle were given in [67], which can be tested once AMS-02 positron spectra are published for the present solar minimum period. Neutron monitors at ground level have already reached maximum counts in mid-2020 (see, e.g., [147]).…”