The extinction profiles in Gamma-Ray Burst (GRB) afterglow spectral energy distributions (SEDs) are usually described by the Small Magellanic Cloud (SMC)-type extinction curve. In different empirical extinction laws, the total-to-selective extinction, RV, is an important quantity because of its relation to dust grain sizes and compositions. We here analyse a sample of 17 GRBs (0.34<z<7.84) where the ultraviolet to near-infrared spectroscopic observations are available through the VLT/X-shooter instrument, giving us an opportunity to fit individual extinction curves of GRBs for the first time. Our sample is compiled on the basis that multi-band photometry is available around the X-shooter observations. The X-shooter data are combined with the Swift X-ray data and a single or broken power-law together with a parametric extinction law is used to model the individual SEDs. We find 10 cases with significant dust, where the derived extinction, AV, ranges from 0.1-1.0mag. In four of those, the inferred extinction curves are consistent with the SMC curve. The GRB individual extinction curves have a flat RV distribution with an optimal weighted combined value of RV = 2.61+/-0.08 (for seven broad coverage cases). The average GRB extinction curve is similar to, but slightly steeper than the typical SMC, and consistent with the SMC Bar extinction curve at ~95% confidence level. The resultant steeper extinction curves imply populations of small grains, where large dust grains may be destroyed due to GRB activity. Another possibility could be that young age and/or lower metallicities of GRBs environments are responsible for the steeper curves.
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