Constraining the emissivity of ultrahigh energy cosmic rays in the distant universe with the diffuse gamma-ray emission

Abstract

Ultrahigh cosmic rays (UHECRs) with energies ≳ 1019eV emitted at cosmological distances will be attenuated by cosmic microwave and infrared background radiation through photohadronic processes. Lower energy extragalactic cosmic rays (∼1018-1019eV) can only travel a linear distance smaller than ∼Gpc in a Hubble time due to the diffusion if the extragalactic magnetic fields are as strong as nano-Gauss. These prevent us from directly observing most of the UHECRs in the universe, and thus the observed UHECR intensity reflects only the emissivity in the nearby universe within hundreds of Mpc. However, UHECRs in the distant universe, through interactions with the cosmic background photons, produce UHE electrons and gamma rays that in turn initiate electromagnetic cascades on cosmic background photons. This secondary cascade radiation forms part of the extragalactic diffuse GeV-TeV gamma-ray radiation and, unlike the original UHECRs, is observable. Motivated by new measurements of extragalactic diffuse gamma-ray background radiation by Fermi/Large Area Telescope, we obtained upper limit placed on the UHECR emissivity in the distant universe by requiring that the cascade radiation they produce not exceed the observed levels. By comparison with the gamma-ray emissivity of candidate UHECR sources (such as gamma-ray bursts (GRBs) and active galactic nuclei) at high redshifts, we find that the obtained upper limit for a flat proton spectrum is ≃ 101.5 times larger than the gamma-ray emissivity in GRBs and ≃ 10 times smaller than the gamma-ray emissivity in BL Lac objects. In the case of iron nuclei composition, the derived upper limit of UHECR emissivity is a factor of 3-5 times higher. Robust upper limit on the cosmogenic neutrino flux is further obtained, which is marginally reachable by the Icecube detector and the next-generation detector JEM-EUSO. © 2011. The American Astronomical Society. All rights reserved.