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Most of the diffuse Galactic GeV gamma-ray emission is produced viacollisions of cosmic ray (CR) protons with ISM protons. As such the observedspectra of the gamma-rays and the CRs should be strongly linked. Recentobservations of Fermi-LAT exhibit a hardening of the gamma-ray spectrum ataround a hundred GeV, between the Sagittarius and Carina tangents, and afurther hardening at a few degrees above and below the Galactic plane. However,standard CR propagation models that assume a time independent sourcedistribution and a location independent diffusion cannot give rise to aspatially dependent CR (and hence gamma-ray) spectral slopes. Here we considera dynamic spiral arm model in which the distribution of CR sources isconcentrated in the (dynamic) spiral arms, and we study the effects of thismodel on the $\pi^0$-decay produced gamma-ray spectra. Within this model, nearthe Galactic arms the observed gamma-ray spectral slope is not triviallyrelated to the CR injection spectrum and energy dependence of the diffusioncoefficient. We find unique signatures that agree with the Fermi-LATobservations. This model also provides a physical explanation for thedifference between the local CR spectral slope and the CR slope inferred fromthe average gamma-ray spectrum.

Reconciling the diffuse Galactic gamma-ray and the cosmic ray spectra