On the perils of curve-of-growth analysis: Systematic abundance underestimates for the gas in gamma-ray burst host galaxies

We examine the practice of deriving interstellar medium (ISM) abundances from low- resolution spectroscopy of gamma-ray burst ( GRB) afterglows. We argue that the multi-ion single-component curve-of-growth analysis technique systematically underestimates the column densities of the metal-line profiles commonly observed for GRBs. This systematic underestimate is accentuated by the fact that many GRB line profiles (e.g., GRB 050730, GRB 050820, GRB 051111) are comprised of clouds'' with a bimodal distribution of column density. Such line profiles may be characteristic of a sight line that penetrates both a high-density star-forming region and more distant, ambient ISM material. Our analysis suggests that the majority of abundances reported in the literature are systematically underestimates and that the reported errors are frequently overoptimistic. Further, we demonstrate that one cannot even report relative abundances with confidence. The implications are profound for our current understanding of the metallicity, dust-to-gas ratio, and chemical abundances of the ISM in GRB host galaxies. For example, we argue that all but a few sight lines allow for the gas to have at least solar metallicity. Finally, we suggest new approaches for constraining the abundances.