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 broadband afterglow emission of very high redshift gamma-ray bursts (GRBs) using standard relativistic blastwave models with both forward and reverse shock components. For a broad range of parameters, a generic property for GRBs at redshifts $z \sim$ 5--30 is that the emission peaks in the millimeter to far-infrared 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, submillimeter and infrared continuum emission should be readily detectable out to $z \ga 30$ by the Atacama Large Millimeter Array (ALMA), Extended Very Large Array (EVLA), Square Kilometer 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 [OI] 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 Pop III and early Pop II star forming regions. We also remark on potential near-infrared absorption features due to electronic transitions of H$_2$.