Cosmic ray models compared to Fermi-LAT positron and electron separate spectra

In this symposium the Fermi-LAT collaboration released the results of its measurement of the $e^-$ and $e^+$ separate spectra, obtained using the Earth magnetic field. Those results confirm PAMELA finding of an increasing positron fraction above 10 GeV and allow, for the first time independently on the electron spectrum, to reject cosmic ray spallation onto the ISM as the dominant positron production mechanism above that energy. We show, for two different propagation setups, that double component models which were developed to provide a consistent interpretation of PAMELA positron fraction and Fermi-LAT $e^+ + e^-$ data, naturally reproduce also the Fermi-LAT $e^-$ and $e^+$ separate spectra.