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 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 GRB. 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 bi-modal distribution of column density. Such line-profiles may be characteristic of a sightline which 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 over-optimistic. Further, we demonstrate that one cannot even report precise relative abundances with confidence. The implications are profound for our current understanding on 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 sightlines allow for the gas to have at least solar metallicity. Finally, we suggests new approaches for constraining the abundances.