Detectability of ultrahigh energy cosmic-ray signatures in gamma-rays

The injection of ultrahigh energy cosmic-rays in the intergalactic medium leads to the production of a GeV-TeV gamma-ray halo centered on the source location, through the production of a high electromagnetic component in the interactions of the primary particles with the radiation backgrounds. This paper examines the prospects for the detectability of such gamma-ray halos. We explore a broad range of astrophysical parameters, including the inhomogeneous distribution of magnetic fields in the large-scale structure, as well as various possible chemical compositions and injection spectra; and we consider the case of a source located outside clusters of galaxies. We demonstrate that the gamma-ray flux associated to synchrotron radiation of ultrahigh energy secondary pairs does not depend strongly on these parameters, and conclude that its magnitude ultimately depends on the energy injected into the primary cosmic-rays. We find that the gamma-ray halo produced by equal luminosity sources (with cosmic ray luminosity and source density chosen to reproduce the measured cosmic-ray spectrum) is far fainter than current or planned instrument sensitivities. Only rare and powerful steady sources, located at distances larger than several hundreds of Mpc and contributing to a fraction greater than or similar to 10% of the flux at 10(19) eV might be detectable. We also discuss the gamma-ray halos that are produced by inverse Compton/pair production cascades seeded by ultrahigh energy cosmic-rays. This depends strongly on the configuration of the extragalactic magnetic fields; it is dominated by the synchrotron signal on a degree scale if the filling factor of magnetic fields with B greater than or similar to 10(-14) G is smaller than a few percent. Finally, we briefly discuss the case of nearby potential sources such as Centaurus A.