Indication of a Local "Fog" of Sub-Ankle UHECR
  During their propagation through intergalactic space, ultrahigh energy cosmic rays (UHECRs) interact with the background radiation fields. These interactions give rise to energetic electron/positron pairs and photons which in turn feed electromagnetic cascades, contributing to the isotropic gamma-ray background (IGRB). The gamma-ray flux level generated in this way highly depends upon the UHECR propagation distance, as well as the evolution of their sources with redshift. Recently, the Fermi-LAT collaboration reported that the majority of the total extragalactic gamma-ray flux originates from extragalactic point sources. This posits a stringent upper limit on the IGRB generated via UHECR propagation, and subsequently constrains their abundance in the distant Universe. Focusing on the contribution of UHECR at energies below the ankle within a narrow energy band ($(1-4)\times 10^{18}$eV), we calculate the diffuse gamma-ray flux generated through UHECR propagation, normalizing the total cosmic ray energy budget in this band to that measured. We find that in order to not over-produce the new IGRB limit, a local "fog" of UHECR produced by nearby sources may exist, with a possible non-negligible contribution from our Galaxy. Following the assumption that a given fraction of the observed IGRB at 820GeV originates from UHECR, we obtain a constraint on the maximum distance for the majority of their sources. With other unresolved source populations still contaminating the new IGRB limit, and UHECR above the ankle invariably contributing also to this background, the results presented here are rather conservative. 
Ruo-Yu Liu, Andrew M. Taylor, Xiang-Yu Wang, Felix A. Aharonian
astro-ph.HE