Despite significant progress over more than 100 years, no accelerator has
been unambiguously identified as the source of the locally measured flux of
cosmic rays. High-energy electrons and positrons are of particular importance
in the search for nearby sources as radiative energy losses constrain their
propagation to distances of about 1 kpc around 1 TeV. At the highest energies,
the spectrum is therefore dominated and shaped by only a few sources whose
properties can be inferred from the fine structure of the spectrum at energies
currently accessed by experiments like AMS-02, CALET, DAMPE, Fermi-LAT,
H.E.S.S. and ISS-CREAM. We present a stochastic model of the Galactic
all-electron flux and evaluate its compatibility with the measurement recently
presented by the H.E.S.S. collaboration. To this end, we have MC generated a
large sample of the all-electron flux from an ensemble of random distributions
of sources. We confirm the non-Gaussian nature of the probability density of
fluxes at individual energies previously reported in analytical computations.
For the first time, we also consider the correlations between the fluxes at
different energies, treating the binned spectrum as a random vector and
parametrising its joint distribution with the help of a pair-copula
construction. We show that the spectral break observed in the all-electron
spectrum by H.E.S.S. and DAMPE is statistically compatible with a distribution
of astrophysical sources like supernova remnants or pulsars, but requires a
rate smaller than the canonical supernova rate. This important result provides
an astrophysical interpretation of the spectrum at TeV energies and allows
differentiating astrophysical source models from exotic explanations, like dark
matter annihilation. We also critically assess the reliability of using
catalogues of known sources to model the electron-positron flux.Comment: 30 pages, 12 figures; extended discussion; accepted for publication
in JCA
