Temporal Structures in Electron Spectra and Charge Sign Effects in Galactic Cosmic Rays

We present the precision measurements of 11 years of daily cosmic electron fluxes in the rigidity interval from 1.00 to 41.9 GV based on $2.0\times {10}^8$ electrons collected with the Alpha Magnetic Spectrometer (AMS) aboard the International Space Station. The electron fluxes exhibit variations on multiple timescales. Recurrent electron flux variations with periods of 27 days, 13.5 days, and 9 days are observed. We find that the electron fluxes show distinctly different time variations from the proton fluxes. Remarkably, a hysteresis between the electron flux and the proton flux is observed with a significance of greater than $6\sigma$ at rigidities below 8.5 GV. Furthermore, significant structures in the electron-proton hysteresis are observed corresponding to sharp structures in both fluxes. This continuous daily electron data provide unique input to the understanding of the charge sign dependence of cosmic rays over an 11-year solar cycle.

Figure 1

Eleven-year daily AMS electron fluxes ${\mathrm{\Phi }}_{e^{-}}$ and daily proton fluxes ${\mathrm{\Phi }}_p$ in units of [${\mathrm{m}}^{-2}{\mathrm{sr}}^{-1}{\mathrm{s}}^{-1}{\mathrm{GV}}^{-1}$] for four rigidity bins from 1.00 to 11.0 GV from May 20, 2011 to November 2, 2021. Days with solar energetic particle events are removed from ${\mathrm{\Phi }}_p$ for the lowest rigidity bins shown. The gaps in the fluxes are due to detector studies and upgrades. Note that ${\mathrm{\Phi }}_p$ is multiplied by different scale factors as indicated. The scale factor of ${\mathrm{\Phi }}_p$ is chosen such that ${\mathrm{\Phi }}_{e^{-}}$ and ${\mathrm{\Phi }}_p$ for each rigidity bin are at the same magnitude, on average, during 2014 and 2015. The vertical dashed lines indicate the three time intervals studied in Fig. S7 of the SM [34]. As seen, ${\mathrm{\Phi }}_{e^{-}}$ exhibits large variations with time, and the relative magnitude of these variations [(a)–(d)] decreases with increasing rigidity. The time-dependent behavior of the ${\mathrm{\Phi }}_{e^{-}}$ and ${\mathrm{\Phi }}_p$ are distinctly different. From 2011 to 2014, ${\mathrm{\Phi }}_{e^{-}}$ decreases faster with time than ${\mathrm{\Phi }}_p$. From 2015 to mid-2017, ${\mathrm{\Phi }}_{e^{-}}$ increases more slowly than ${\mathrm{\Phi }}_p$ below about 4 GV (a),(b). From mid-2020 to 2021, ${\mathrm{\Phi }}_{e^{-}}$ decreases faster than ${\mathrm{\Phi }}_p$.

Figure 2

Normalized power of (a),(c) electron fluxes and (b),(d) proton fluxes as a function of rigidity and time for (a),(b) the second half of 2011 (May 20 to December 16, 2011) and (c),(d) the first half of 2017 (January 22 to July 2, 2017). The rigidity range is from 1.00 to 22.8 GV. As seen, the rigidity dependence behavior of the normalized power of electrons and protons is different in these two time intervals. In particular, in the second half of 2011 [shown in (a) and (b)], the strength of the 27-day period of electrons is greater than that of protons, while in the first half of 2017 [shown in (c) and (d)], the strength of the 27-day period of electrons is less than that of protons.

Figure 3

Electron fluxes ${\mathrm{\Phi }}_{e^{-}}$ versus the proton fluxes ${\mathrm{\Phi }}_p$ for four rigidity intervals from 1.00 to 11.0 GV. For (a)–(d), the data points are the daily ${\mathrm{\Phi }}_{e^{-}}$ and ${\mathrm{\Phi }}_p$. For (e)–(h), both ${\mathrm{\Phi }}_{e^{-}}$ and ${\mathrm{\Phi }}_p$ are calculated with a moving average of 14 BRs with a step of 1 day. Different colors indicate different years from 2011 to 2021. As seen, a hysteresis between ${\mathrm{\Phi }}_{e^{-}}$ and ${\mathrm{\Phi }}_p$ is observed; that is, from 2011 to 2018 at a given electron flux, the proton flux shows two distinct branches with time, one before 2014–2015 and one after. Both ${\mathrm{\Phi }}_{e^{-}}$ and ${\mathrm{\Phi }}_p$ peak in 2020, after which the hysteresis curve starts to trace the earlier behavior (2018–2020) backwards. Fluxes are in units of [${\mathrm{m}}^{-2}{\mathrm{sr}}^{-1}{\mathrm{s}}^{-1}{\mathrm{GV}}^{-1}$].

Figure 4

(a) Daily electron fluxes ${\mathrm{\Phi }}_{e^{-}}$ (red, left axis) and daily proton fluxes ${\mathrm{\Phi }}_p$ (green, right axis) as a function of time for the rigidity interval of 1.00 to 1.71 GV. The arrows I, II, and III indicate the location of sharp dips in the proton and electron fluxes, and the colored bands IV and V mark the time intervals around the dips in 2015 and 2017. (b) ${\mathrm{\Phi }}_{e^{-}}$ versus ${\mathrm{\Phi }}_p$ both calculated with a moving average of 2 BRs and a step of 1 day. The locations of I, II, and III correspond to the flux dips in (a). To assess the significance of the structures in the hysteresis, during dips IV and V (indicated by white boxes), two pairs (white squares and triangles) of nonoverlapping intervals with the same ${\mathrm{\Phi }}_p$ but different ${\mathrm{\Phi }}_{e^{-}}$ are chosen. As shown in Fig. S25 of the SM [34], the large dips in 2015 (IV) and 2017 (V) correspond to additional structures in the overall hysteresis with significance of $15.9\sigma$ and $7.0\sigma$, respectively. Fluxes are in units of [${\mathrm{m}}^{-2}{\mathrm{sr}}^{-1}{\mathrm{s}}^{-1}{\mathrm{GV}}^{-1}$].