Identifying the environment and redshift of gamma-ray burst afterglows from the time dependence of their absorption spectra

The discovery of gamma-ray burst (GRB) afterglows revealed a new class of variable sources at optical and radio wavelengths. At present, the environment and precise redshift of the detected afterglows are still unknown. We show that if a GRB source resides in a compact (less than or similar to 100 pc) gas-rich environment, the afterglow spectrum will show time-dependent absorption features due to the gradual ionization of the surrounding medium by the afterglow radiation. Detection of this time dependence can be used to constrain the size and density of the surrounding gaseous system. For example, the Mg II absorption line detected in GRB 970508 should have weakened considerably during the first month if the absorption occurred in a gas cloud of size less than or similar to 100 pc around the source. The time-dependent H I or metal absorption features provide a precise determination of the GRB redshift.