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

Abstract

A scenario in which cosmic rays (CRs) above $10^{20}\mathrm{eV}$ are produced by cosmological gamma-ray bursts (GRBs) is consistent with observations provided that deflections by the inter-galactic magnetic field (IGMF) delay and spread the arrival time of the CRs over $\ge 50\mathrm{yr}$. 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 inter-galactic space is occupied by large-scale magnetic ``voids'', regions of size $\gtrsim 5\mathrm{Mpc}$ and field weaker than $10^{-15}\mathrm{G}$. 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 $\sim 4\times 10^{-11}\mathrm{G}$ 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 $100\mathrm{Mpc}$ is $\sim 100\mathrm{yr}$, and the fluence of secondary photons above $10\mathrm{GeV}$ on hour--day time scales is $I(>E)\sim 10^{-6}{E}_{\mathrm{TeV}}^{-1}{\mathrm{cm}}^{-2}$. 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.

ApJ Letters in press; 10 pages (LaTeX file, 2 PostScript figures, aaspp4.sty style file, tar'ed, gzip'ed and uuencoded)

References in corpus (2)

• Cosmological Origin for Cosmic Rays Above $10^{19}$ eV
• Extragalactic Magnetic Field and the Highest Energy Cosmic Rays

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