Electron Acceleration in Supernova Remnants and Diffuse Gamma Rays above 1 GeV

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Abstract
The recently observed X-ray synchrotron emission from four supernova remnants (SNRs) has strengthened the evidence that cosmic-ray electrons are accelerated in SNRs. We show that if this is indeed the case, the local electron spectrum will be strongly time-dependent, at least above roughly 30 GeV. The time dependence stems from the Poisson fluctuations in the number of SNRs within a certain volume and within a certain time interval. As far as cosmic-ray electrons are concerned, the Galaxy looks like actively bubbling Swiss cheese rather than a steady, homogeneously filled system. Our finding has important consequences for studies of the Galactic diffuse gamma-ray emission, for which a strong excess over model predictions above 1 GeV has recently been reported. While these models relied on an electron injection spectrum with index 2.4 (chosen to fit the local electron flux up to 1 TeV), we show that an electron injection index of around 2.0 would (1) be consistent with the expected Poisson fluctuations in the locally observable electron spectrum and (2) explain the above-mentioned gamma-ray excess above 1 GeV. An electron injection index of around 2 would also correspond to the average radio synchrotron spectrum of individual SNRs. We use a three-dimensional propagation code to calculate the spectra of electrons throughout the Galaxy and show that the longitude and latitude distribution of the leptonic gamma-ray production above 1 GeV is in accord with the respective distributions for the gamma-ray excess. Finally, we point out that our model implies a strong systematic uncertainty in the determination of the spectrum of the extragalactic gamma-ray background.
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