The Galactic Center GeV excess from a series of leptonic cosmic-ray outbursts

It has been proposed that a recent out burst of cosmic-ray electrons could account for the excess of GeV-scale gamma rays observed from the region surrounding the Galactic Center. After studying this possibility in some detail, we identify scenarios in which a series of leptonic cosmic-ray outbursts could plausibly generate the observed excess. The morphology of the emission observed outside of similar to 1 degrees - 2 degrees from the Galactic Center can be accommodated with two outbursts, one which took place approximately similar to 10(6) years ago, and another (injecting only about 10% as much energy as the first) about similar to 10(5) years ago. The (emission observed from the innermost similar to 1 degrees - 2 degrees requires one or more additional recent outbursts and/or a contribution from a centrally concentrated population of unresolved millisecond pulsars. In order to produce a spectrum that is compatible with the measured excess (whose shape is approximately uniform over the region of the excess), the electrons from the older outburst must be injected with significantly greater average energy than those injected more recently, enabling their spectra to be similar after similar to 10(6) years of energy losses.