Images of Bursting Sources of High-Energy Cosmic Rays: Effects of Magnetic Fields

It has recently been shown that the highest energy cosmic rays (CRs) mayoriginate in the same cosmological objects producing $\gamma$-ray bursts. Thismodel requires the presence of intergalactic magnetic fields (IGMF) to delaythe arrival times of $\sim 10^{20}$ eV CRs by 50 years or longer relative tothe $\gamma$-rays, of an amplitude that is consistent with other observationalconstraints. Sources of CRs coming from individual bursts should be resolvedwith the planned ``Auger'' experiment, with as many as hundreds of CRs for thebrightest sources. We analyze here the apparent angular and energy distributionof CRs from bright sources below the pion production threshold (in the energyrange $10^{19}{\rm eV} < E < 4\times10^{19}{\rm eV}$) expected in this model.This observable distribution depends on the structure of the IGMF: the apparentspectral width $\Delta E$ is small, $\Delta E/E\lesssim1\%$, if theintergalactic field correlation length $\lambda$ is much larger than $1{\rmMpc}$, and large, $\Delta E/E=0.3$, in the opposite limit $\lambda\ll 1{\rmMpc}$. The apparent angular size is also larger for smaller $\lambda$. If thesources of CRs we predict are found, they will corroborate the bursting modeland they will provide us with a technique to investigate the structure of theIGMF.Comment: Submitted to the ApJL; 10 pages AASTeX, including 2 PostScript figure