2. The method
Photometric redshifts (hereafter ) are based on the detection of strong spectral features, such as the 4000 Å break, Balmer break, Lyman decrement or strong emission lines. In general, broad-band filters will allow to detect only "breaks", and they are not sensitive to the presence of emission lines, except when their contribution to the total flux in a given filter is higher or of the same order of photometric errors, as it happens in the case of AGNs (Hatziminaoglou et al. 2000).
The method used in this paper to compute photometric redshifts is a SED fitting through a standard minimization procedure, computed with our code hyperz . The observed SED of a given galaxy is compared to a set of template spectra:
where , and are the observed and template fluxes and their uncertainty in filter i, respectively, and b is a normalization constant.
The new Bruzual & Charlot evolutionary code (GISSEL98, Bruzual & Charlot 1993) has been used to build 8 different synthetic star-formation histories, roughly matching the observed properties of local field galaxies from E to Im type: a delta burst, a constant star-forming system, and six µ-models (exponentially decaying SFR) with characteristic time-decays chosen to match the sequence of colours from E-S0 to Sd. We use the Initial Mass Function (IMF) by Miller & Scalo (1979), but this choice has a negligible impact on the final results, as discussed in Sect. 4.6. The upper mass limit for star formation is . The basic database includes only solar metallicity SEDs, but other possibilities are discussed in Sect. 4. The library also includes a set of empirical SEDs compiled by Coleman et al. (1980) (hereafter CWW) to represent the local population of galaxies. CWW spectra were extended to wavelengths Å and Å using the equivalent GISSEL spectra. The synthetic database derived from Bruzual & Charlot includes 408 spectra (51 different ages for the stellar population and 8 star-formation regimes). In most applications, there is no sensible gain when the number of µ-models is reduced to only 3, thus including only 255 spectra.
Throughout this paper we use the same set of broad-band filters, with characteristics presented in Table 1. These filters cover all the wavelength domain under study, without major overlap or gap. We also include the HDF filters used in Sects. 4 and 5 (from Biretta et al. 1996). The hyperz filter library is an enlarged version of the original Bruzual & Charlot one, and presently includes 163 filters and detector responses. All magnitudes given in this paper refer to the Vega system.
Hyperz has been optimized to gain in efficiency when computing on large catalogues. The input data for a given catalogue are magnitudes and photometric errors. To compute a reliable estimate of , the colours and the corresponding photometric errors must be obtained with particular care, including uncertainties due to zero-points, intrinsic accuracy, etc. Magnitudes are obtained within the same aperture in all filters, after correction for seeing differences between images. For a given catalogue, the relevant parameters introduced in the calculation are:
Table 1. Characteristics of filters used in the simulations: the effective wavelength and the surface of the normalized response function.
Due to the degeneracy in the parameter space defined by the SFR type, age, metallicity and reddening, the computation for a given object is equivalent to finding the most likely solution for the redshift across this parameter space, regardless to details on the best-fit SED (see Fig. 1). Both the and the SED are obtained through hyperz , together with the best fit parameters (, spectral type, metallicity and age). Because of the degeneracy between these parameters, the relevant information shall be the redshift and the rough SED type, in the sense that a given object has a "blue" or "red" continuum at a given z, but no reliable information can be obtained about the other parameters from broad-band photometry alone.
© European Southern Observatory (ESO) 2000
Online publication: December 11, 2000