Inhomogeneity in the Supernova Remnant Distribution as the Origin of the PAMELA Anomaly

Recent measurements of the positron/electron ratio in the cosmic ray (CR) flux exhibits an apparent anomaly, whereby this ratio increases between 10 and 100 GeV. We show that inhomogeneity of CR sources on a scale of order a kpc, can naturally explain this anomaly. If the nearest major CR source is about a kpc away, then low energy electrons ($\sim 1$ GeV) can easily reach us. At higher energies ($\gtrsim 10$ GeV), the source electrons cool via synchrotron and inverse-Compton before reaching Earth. Pairs formed in the local vicinity through the proton/ISM interactions can reach Earth also at high energies, thus increasing the positron/electron ratio. A natural origin of source inhomogeneity is the strong concentration of supernovae in the galactic spiral arms. Assuming supernova remnants (SNRs) as the sole primary source of CRs, and taking into account their concentration near the galactic spiral arms, we consistently recover the observed positron fraction between 1 and 100 GeV. ATIC's electron excess at $\sim 600$ GeV is explained, in this picture, as the contribution of a few known nearby SNRs. The apparent coincident similarity between the cooling time of electrons at 10 GeV (where the positron/electron ratio upturn), $\sim 10$ Myr, and the CRs protons cosmogenic age at the same energy is predicted by this model.