Spectrum and fraction of cosmic ray positrons: results of the anomalous diffusion approach

We present the results of new calculations of the energy spectra of cosmic ray electrons, positrons and also positron fraction under assumption that both electrons and positrons are generated by the same Galactic sources, which accelerate particles with same power-law injection spectral index $p$. The value of the injection index $p\approx 2.85$ retrieved in our works from the analysis of the observed CR spectra has been used. The propagation of particles through the highly non-homogeneous interstellar medium has been described by the anomalous diffusion model. We show that proposed approach allows the self-consistent description of the recent AMS-02 data. In contrast to the conclusion made by AMS-02 collaboration about the different origin of the high-energy positrons and electrons, our results demonstrate that the differing behavior of spectral indices of electrons and positrons with energy can be described under the assumption that both positrons and electrons have common Galactic sources. Our prediction (Lagutin et al. Bull. Russian Academy of Sciences. Physics, 2013, Vol. 77, No. 11, p. 1312) that the $e^{+}$ to total $e^{-} + e^{+}$ ratio reaches a constant value for E $\gg 200$ GeV is confirmed.