Delayed GeV–TeV Photons from Gamma-Ray Bursts Producing High-Energy Cosmic Rays

A scenario in which cosmic rays (CRs) above 10 20 eV are produced by cosmological gamma-ray bursts (GRBs) is consistent with observations, provided that deflections by the intergalactic magnetic field (IGMF) delay and spread the arrival time of the CRs over ≥50 yr. The energy lost by the CRs as they propagate and interact with the microwave background is transformed by cascading into secondary GeV-TeV photons. We show that a significant fraction of these photons can arrive with delays much smaller than the CR delay if much of intergalactic space is occupied by large-scale magnetic "voids," regions of a size ≳5 Mpc and a field weaker than 10 -15 G. Such voids might be expected, for example, in models where a weak primordial field is amplified in shocked, turbulent regions of the intergalactic medium during the formation of large-scale structure. For a field strength ~4 × 10 -11 G in the high-field regions, the value required to account for observed galactic fields if the IGMF were frozen in the protogalactic plasma, the delay of CRs produced by a burst at a distance of 100 Mpc is ~100 yr, and the fluence of secondary photons above 10 GeV on hour-day timescales is I (> E ) ~ 10 -6 E cm -2 . This fluence is close to the detection threshold of current high-energy gamma-ray experiments. Detection of the delayed flux would support the GRB-CR association and would also provide information on the IGMF structure.