PAMELA and AMS-02 positron and electron spectra are reproduced by three-dimensional cosmic-ray modeling

Abstract

The PAMELA collaboration recently released the $e^+$ absolute spectrum between 1 and 300 GeV in addition to the positron fraction and the $e^-$ spectrum previously measured in the same period. We use the newly developed three-dimensional upgrade of the DRAGON package to model those data. This code allows us to consider a realistic spiral arm source distribution in the Galaxy, which impacts the high-energy shape of the propagated spectra. At low energy we treat solar modulation with the HelioProp code and compare its results with those obtained using the usual force-field approximation. We show that all PAMELA data sets can be consistently, and accurately, described in terms of a standard background on top of which a charge symmetric $e^+$ + $e^-$ extra component with harder injection spectrum is added; this extra contribution is peaked at about 1 - 10 TeV and may originate from a diffuse population of sources located in the Galactic arms. For the first time, we compute the energy required to sustain such a relevant positron flux in the Galaxy, finding that it is naturally compatible with an astrophysical origin. We considered several reference propagation setups; we find that models with a low (or null) reacceleration - tuned against light nuclei data - nicely describe both PAMELA leptonic and hadronic data with no need to introduce a low-energy break in the proton and helium spectra, as it would be required for high reacceleration models. We also compare our models with the preliminary $e^-$ and $e^+$ absolute spectra recently measured by AMS-02. We find that those data, differently from what is inferred from the positron fraction alone, favor a high energy cutoff (about 10 TeV) of the extra component if this is uniquely generated in the Galactic arms. A lower cutoff may be allowed if a relevant contribution from powerful $e^-$ + $e^+$ nearby accelerators is invoked.