The radio to infrared emission of very high redshift gamma-ray bursts: probing early star formation through molecular and atomic absorption lines

We evaluate the broad-band afterglow emission of very high redshift gamma-ray bursts (GRBs) using standard relativistic blast-wave models with both forward and reverse shock components. For a broad range of parameters, a generic property for GRBs at redshifts z similar to 5-30 is that the emission peaks in the millimetre to far-infrared (far-IR) bands with milli-Jansky flux levels, first at a few hours after the burst due to the reverse shock, and then again for several days afterwards with somewhat lower flux due to the forward shock. The radio, submillimetre and IR continuum emission should be readily detectable out to z greater than or similar to 30 by the Atacama Large Millimetre Array (ALMA), Extended Very Large Array, Square Kilometre Array (SKA) and other facilities. For relatively bright bursts, spectroscopic measurements of molecular and atomic absorption lines due to ambient protostellar gas may be possible. Utilizing models of primordial protostellar clouds, we show that under certain conditions, appreciable absorption may be caused by HD rotational transitions even in metal-free environments. After sufficient metal enrichment, absorption from CO rotational transitions and [O I] fine-structure transitions can also become strong. With appropriate observing strategies in combination with optical telescopes, ALMA and/or SKA may be able to detect such lines, offering a unique probe of physical conditions in individual Population III (Pop III) and early Pop II star-forming regions. We also remark on potential near-IR absorption features due to electronic transitions of H-2.