2010ApJ...710..648L

The quantities and wavelength dependencies of the dust extinction along the lines of sight toward 33 nearby gamma-ray bursts (GRBs) with redshifts z < 2 are derived from fitting their afterglow spectral energy distributions. Unlike previous studies which often assume a specific extinction law like that of the Milky Way (MW) and the Large and Small Magellanic Clouds (LMC/SMC), our approach–we call it the "Drude" approach–is more flexible in determining the true wavelength dependence of the extinction (while the shape of the extinction curve inferred from that relying on a priori assumption of a template extinction law is, of course, fixed). The extinction curves deduced from the Drude approach display a wide diversity of shapes, ranging from relatively flat curves to curves which are featureless and steeply rise toward the far-ultraviolet, and from curves just like that of the MW, LMC, and SMC to curves resembling that of the MW and LMC but lacking the 2175 Å bump. The visual extinction A_V derived from the Drude approach is generally larger by a factor of ∼2-5 than that inferred by assuming a SMC-type template extinction law. Consistent with previous studies, the extinction-to-gas ratio is mostly smaller than that of the MW, and does not seem to correlate with the shape of the extinction curve. It is shown that the standard silicate-graphite interstellar grain model closely reproduces the extinction curves of all 33 GRBs host galaxies. For these 33 bursts at z < 2, we find no evidence for the evolution of the dust extinction, dust sizes, and relative abundances of silicate to graphite on redshifts.