Focusing on the electron and positron spectrum measured with the Calorimetric Electron Telescope (CALET), which shows characteristic structures, we calculate the flux contributions of cosmic rays that have escaped from randomly appearing supernova remnants. We adopt a Monte Carlo method to take into account the stochastic nature of the appearance of nearby sources. We find that without a complicated energy dependence of the diffusion coefficient, simple power-law diffusion coefficients can produce spectra similar to the CALET spectrum, even with a dispersion in the injection index. The positron component measured with AMS-02 is consistent with a bump-like structure around 300 GeV in the CALET spectrum. One to three nearby supernovae can contribute up to a few tens of percent of the CALET flux at 2-4 TeV, while ten or more unknown and distant (≳500 pc) supernovae account for the remaining several tens of percent of the flux. The CALET spectrum, showing a sharp drop at ∼1 TeV, allows for a contribution of cosmic rays from an extraordinary event that occurred ∼400 kyr ago. This type of event releases electrons/positrons with a total energy more than 10 times the average energy for usual supernovae, and its occurrence rate is lower than one three-hundredth of the usual supernova rate.
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