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The recently reported positron fraction up to $\sim 350$ GeV by AMS-02 seemsto have tension with the total electron/positron spectra detected by Fermi andHESS, for either pulsar or dark matter annihilation/decay scenario as theprimary positron sources. In this work we will show that the tension will beremoved by an adjustment of the primary electron spectrum. If the primaryelectron spectrum becomes harder above $\sim50$ GeV, similar as the cosmic raynuclei spectrum, the AMS-02 positron fraction and Fermi/HESS data can be wellfitted by both the pulsar and dark matter models. This result indicates thatthere should be a common origin of the cosmic ray nuclei and the primaryelectrons. Furthermore, this study also implies that the properties of theextra sources derived from the fitting to the AMS-02 data should depend on theform of background.

Reconcile the AMS-02 positron fraction and Fermi-LAT/HESS total $e^{\pm}$ spectra by the primary electron spectrum hardening