The dust extinction of gamma-ray bursts ( GRBs ) host galaxies , containing important clues to the nature of GRB progenitors and crucial for dereddening , is still poorly known .
Here we propose a straightforward method to determine the extinction of GRB host galaxies by comparing the observed optical spectra to the intrinsic ones extrapolated from the X-ray spectra .
The rationale for this method is from the standard fireball model : if the optical flux decay index equals to that of the X-ray flux , then there is no break frequency between the optical and X-ray bands , therefore we can derive the intrinsic optical flux from the X-ray spectra .
We apply this method to three GRBs of which the optical and X-ray fluxes have the same decay indices and another one with inferred cooling break frequency , and obtain the rest-frame extinction curves of their host galaxies .
The derived extinction curves are gray and do not resemble any extinction curves of local galaxies ( e.g .
the Milk Way , the Small/Large Magellanic Clouds , or nearby starburst galaxies ) .
The amount of extinction is rather large ( with visual extinction A _ { V } \sim 1.6–3.4 { mag } ) .
We model the derived extinction curves in terms of the silicate-graphite interstellar grain model .
As expected from the “ gray ” nature of the derived extinction curve , the dust size distribution is skewed to large grains .
We determine , for the first time , the local dust-to-gas ratios of GRB host galaxies using the model-derived dust parameters and the hydrogen column densities determined from X-ray absorptions .