Expected number and flux distribution of gamma-ray burst afterglows with high redshifts

If gamma-ray bursts (GRBs) occur at high redshifts, then their bright afterglow emission can be used to probe the ionization and metal enrichment histories of the intervening intergalactic medium during the epoch of reionization. In contrast to other sources, such as galaxies or quasars, which fade rapidly with increasing redshift, the observed infrared flux from a GRB afterglow at a fixed observed age is only a weak function of its redshift. This results from a combination of the spectral slope of GRB afterglows and the time stretching of their evolution in the observer's frame. Assuming that the GRB rate is proportional to the star formation rate and that the characteristic energy output of GRBs is similar to 10(52) ergs, we predict that there are always similar to 15 GRBs from redshifts z greater than or similar to 5 across the sky that are brighter than similar to 100 nJy at an observed wavelength of similar to 2 mu m. The infrared spectrum of these sources could be taken with the future Next Generation Space Telescope as a follow-up to early X-ray localization with the Swift satellite.