2011A&A...525A..75S

The measurement of redshifts for objects on the verge of instrumental observability is difficult and prone to error. This is especially true for almost featureless spectra, as is the case for GRB afterglows. They can be detected out to the farthest distances, and usually spectroscopy poses a serious problem because they fade quickly. We have developed a new method that is close in philosophy to the photometric redshift technique, which can be applied to spectral data with a very low signal-to-noise ratio. We intend to measure redshifts, while minimising the dangers posed by the usual extraction techniques. GRB afterglows have generally very simple optical spectra, which can be described well by a pure power law, over which the separate effects of absorption and reddening in the GRB host, the intergalactic medium, and our own Galaxy are superimposed. We model all these effects over a series of template afterglow spectra to produce a set of clean spectra that reproduce what would reach our telescope. We also carefully model the effects of the telescope-spectrograph combination and the properties of noise in the data, which are then applied to the template spectra. The final templates are compared to the two-dimensional spectral data, and the basic parameters (redshift, spectral index, hydrogen absorption column) are estimated with statistical tools. We show how our method works by applying it to our data of the NIR afterglow of Swift GRB 090423. At z≃8.2, this was the most distant object ever observed. Our team took a spectrum using the Telescopio Nazionale Galileo, which we use in this article to derive its redshift and its intrinsic neutral hydrogen column density. Our best fit yields z=8.4^+0.05_–0.03 and N(HI)<5x10²⁰cm^–2, but with a highly non-Gaussian uncertainty including the redshift range z∈[6.7, 8.5] at the 2-sigma confidence level. Our method will be useful for maximising the recovered information from low-quality spectra, particularly when the set of possible spectra is limited or easily parameterisable (as is the case in GRB afterglows), while at the same time ensuring adequate confidence analysis.