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Astron. Astrophys. 363, 517-525 (2000)

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2. Photometric redshift technique

For a given galaxy, the photometric redshift can be estimated by comparing its observed SED with a set of template SEDs, corresponding to different morphological types and shifted to different redshifts, accounting for galaxy evolution with look-back time. The redshift and spectral type associated with the template SED closest to the observed SED will then be assigned to that galaxy. The comparison is carried out by minimising the [FORMULA] function


where the summation, i, is over the passbands with [FORMULA] and [FORMULA] being, respectively, the observed and template fluxes at a given passband, n, [FORMULA] the uncertainty in the observed flux and [FORMULA] the normalisation, estimated in two different ways. First, it is estimated by forcing the template SED to have the same total energy (calculated by integrating the SED over the observed wavelength range) as the observed SED. Second, the normalisation is used as a free parameter in the fit in minimising the [FORMULA]. The two methods give very close results. The comparison between the observed and model SEDs, over the entire range of observed SEDs, will constrain the three free parameters (i.e. redshift, spectral type and normalisation). However, due to changes with redshift in the properties of galaxies, we also need to allow for evolutionary effects on the model SEDs. This introduces more free parameters which will be constrained using observed data, as discussed in the following sections.

In order to construct the template SEDs needed for photometric redshift measurements, we use EPS models, required to estimate changes in properties of galaxies with redshift. These models allow us to develope the template SEDs as a function of redshift for different types of galaxies. In the next section, the EPS models used to derive the template SEDs for different types of galaxies, and their underlying assumptions are discussed. The models are constrained, using observed local SEDs for different types of galaxies and by optimising the estimated photometric redshifts to produce their spectroscopic counterparts for a calibrating sample of HDF galaxies with known spectroscopic redshifts. Details of the procedure adopted in this study are summarised in the flow chart in Fig. 1.

[FIGURE] Fig. 1. Flow chart summarizing the photometric redshift technique.

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© European Southern Observatory (ESO) 2000

Online publication: December 11, 2000