The extinction curves of star-forming regions from z=0.1 to 6.7 using GRB afterglow spectroscopy
GRB afterglows are well suited to extinction studies due to their brightness, simple power-law spectra and the occurrence of GRBs in distant star forming galaxies. In this paper we present results from the SED analysis of a sample of 41 GRB afterglows, from X-ray to NIR wavelengths. This is the largest sample of extinction curves outside the Local Group and, to date, the only extragalactic sample of absolute extinction curves based on spectroscopy. Visual extinction correlation with HI column density as well as total and gas-phase metal column density are examined. Approximately half the sample require a cooling break between the optical and X-ray regimes. The broken power-law SEDs show an average change in the spectral index of delta_beta=0.51 with a standard deviation of 0.02. This is consistent with the expectation from a simple synchrotron model. Of the sample, 63% are well described by the SMC-type extinction curve and have moderate or low extinction, with AV<0.65. Almost a quarter of our sample is consistent with no significant extinction (typically AV<0.1). The 2175AA extinction bump is detected unequivocally in 7% of our sample (3 GRBs), which all have A_V>1.0. We find an anti-correlation between gas-to-dust ratio and metallicity consistent with the Local Group relation. Our metals-to-dust ratios derived from the soft X-ray absorption are always larger (3-30 times) than the Local Group value, which may mean that GRB hosts may be less efficient at turning their metals into dust. However, we find that gas, dust, and metal column densities are all likely to be influenced by photo-ionization and dust destruction effects from the GRB. [abridged]