Probing the nature of the weakest intergalactic magnetic fields with the high-energy emission of gamma-ray bursts

We investigate the delayed, secondary GeV-TeV emission of gamma-ray bursts and its potential to probe the nature of intergalactic magnetic fields. Geometrical effects are properly taken into account for the time delay between primary high- energy photons and secondary inverse Compton photons from electron- positron pairs, which are produced in gamma-gamma interactions with background radiation fields and deflected by intervening magnetic fields. The time- dependent spectra of the delayed emission are evaluated for a wide range of magnetic field strengths and redshifts. The typical flux and delay time of secondary photons from bursts at z similar to 1 are, respectively, similar to 10(-8) GeV cm(-2) s (-1) and similar to 10(4) s if the field strengths are similar to 10(-18) G, as might be the case in intergalactic void regions. We find crucial differences between the cases of coherent and tangled magnetic fields, as well as dependences on the field coherence length.