Atomic hydrogen column density plotted as a function of extinction for the sightlines associated with every GRB in the sample from the LAB H i survey (Kalberla et al. 2005) and the dust maps of Schlegel et al. (1998). The anticipated linear relation is plotted as a solid line with residuals to this relation in terms of Δχ in the lower panel. The linear relation is clearly a poor fit to the data, suggesting that the dust-to-gas ratio increases as a function of column density. The best-fit non-linear relation is plotted as a dashed line. The non-linearity in the relation may be due to metallicity variations along different sightlines. The metallicity gradient in the Galaxy suggests that sightlines toward the Galactic centre should be more metal rich and therefore show a higher dust-to-gas ratio. Sightlines toward the Galactic centre (cos(l)cos(b) > 0.9) are plotted with open squares and do indeed show a higher dust-to-gas ratio than sightlines with comparable column densities.
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