Spectrophotometric Redshifts. A New Approach to the Reduction of Noisy
  Spectra and its Application to GRB090423
  We have developed a new method, close in philosophy to the photometric
redshift technique, which can be applied to spectral data of very low
signal-to-noise ratio. Using it we intend to measure redshifts while minimising
the dangers posed by the usual extraction techniques. GRB afterglows have
generally very simple optical spectra 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 model carefully the effects of the
telescope-spectrograph combination and the properties of noise in the data,
which are then applied on 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 using
statistical tools. We show how our method works by applying it to our data of
the NIR afterglow of GRB090423. At z ~ 8.2, this was the most distant object
ever observed. We use the spectrum taken by our team with the Telescopio
Nazionale Galileo to derive the GRB redshift and its intrinsic neutral Hydrogen
column density. Our best fit yields z=8.4^+0.05/-0.03 and N(HI)<5x10^20 cm^-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 to maximise the
recovered information from low-quality spectra, particularly when the set of
possible spectra is limited or easily parameterisable while at the same time
ensuring an adequate confidence analysis.
