Constraining the redshift distribution of ultrahigh–energy–cosmic–ray sources by isotropic gamma-ray background

Abstract

By interacting with the cosmic background photons during their propagation through intergalactic space, ultrahigh energy cosmic rays (UHECRs) produce energetic electron/positron pairs and photons which will initiate electromagnetic cascades, contributing to the isotropic gamma-ray background (IGRB). The generated gamma-ray flux level highly depends on the redshift evolution of the UHECR sources. Recently, the Fermi-LAT collaboration reported that 86−14+16 of the total extragalactic gamma-ray flux comes from extragalactic point sources including those unresolved ones. This leaves a limited room for the diffusive gamma ray generated via UHECR propagation, and subsequently constrains their source distribution in the Universe. Normalizing the total cosmic ray energy budget with the observed UHECR flux in the energy band of (1–4)×1018 eV, we calculate the diffuse gamma-ray flux generated through UHECR propagation. We find that in order to not overshoot the new IGRB limit, these sub–ankle UHECRs should be produced mainly by nearby sources, with a possible non-negligible contribution from our Galaxy. The distance for the majority of UHECR sources can be further constrained if a given fraction of the observed IGRB at 820 GeV originates from UHECR. We note that our result should be conservative since there may be various other contributions to the IGRB that is not included here.