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Astron. Astrophys. 363, 476-492 (2000)

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1. Introduction

The estimate of redshifts through photometry is one of the most promising techniques in deep universe studies, and certainly a key point to optimize field surveys with large-field detectors. It is in fact an old idea of Baum (1962), who originally applied it to the measure of redshifts for elliptical galaxies in distant clusters. It was later used by several authors in the eighties (Couch et al. 1983; Koo 1985) on relatively low-redshift samples, observed in the [FORMULA] to 8000 Å domain. Later in the nineties, the interest for this technique has increased with the development of large field and deep field surveys, in particular the Hubble Deep Field North and South (HDF-N and HDF-S).

Basically two different photometric redshift techniques can be found in the literature: the so-called empirical training set method, and the fitting of the observed Spectral Energy Distributions (hereafter SED) by synthetic or empirical template spectra. The first approach, proposed originally by Connolly et al. (1995, 1997), derives an empirical relation between magnitudes and redshifts using a subsample of objects with measured spectroscopic redshifts, i.e. the training set. A slightly modified version of this method was used by Wang et al. (1998) to derive redshifts in the HDF-N by means of a linear function of colours. This method produces small dispersions, even when the number of filters available is small, and it has the advantage that it does not make any assumption concerning the galaxy spectra or evolution, thus bypassing the problem of our poor knowledge of high redshift spectra. However, this approach is not flexible: when different filter sets are considered, the empirical relation between magnitudes and redshifts must be recomputed for each survey on a suitable spectroscopic subsample. Moreover, the training set is constituted by the brightest objects, for which it is possible to measure the redshift. Thus, this kind of procedure could in principle introduce some bias when computing the redshifts for the faintest sources, because there is no guarantee that we are dealing with the same type of objects from the spectrophotometrical point of view. Also, the redshift range between 1.4 and 2.2 had been hardly reached by spectroscopy up to now, because of the lack of strong spectral features accessible to optical spectrographs. Thus, no reliable empirical relation can be found in this interval.

The SED fitting procedure, described in detail in the following section, bases its efficiency on the fit of the overall shape of spectra and on the detection of strong spectral properties. The observed photometric SEDs are compared to those obtained from a set of reference spectra, using the same photometric system. The photometric redshift of a given object corresponds to the best fit of its photometric SED by the set of template spectra. This method is used mainly for applications on the HDF, using either observed or synthetic SEDs (e.g. Mobasher et al. 1996; Lanzetta et al. 1996; Gwyn & Hartwick 1996; Sawicki et al. 1997; Giallongo et al. 1998; Fernández-Soto et al. 1999; Arnouts et al. 1999; Furusawa et al. 2000). A crucial test in all cases is the comparison between the photometric and the spectroscopic redshifts obtained on a restricted subsample of relatively bright objects. A combination of this method with the Bayesian marginalization introducing a prior probability was proposed by Benítez (2000).

The aim of this paper is to explain in a straightforward way the expected performances and limitations of photometric redshifts computed from broad-band photometry. This study has been conducted with our public code called hyperz , which adopts a standard SED fitting method, but most results should be completely general in this kind of calculations. This program was originally developed by Miralles (1998) (see also Pelló et al. 1999), and the present version of the code hyperz is available on the web at the following address: http://webast.ast.obs-mip.fr/hyperz. The plan of the paper is the following. In Sect. 2 we present the method used by hyperz and the involved set of parameters. The accuracy of the redshift determinations and the expected percentage of catastrophic identifications, as a function of the filter set and the photometric errors, are studied through simulations in Sect. 3. The influence of the different parameters on the accuracy of photometric redshifts is investigated in Sect. 4, using both simulations and spectroscopic data from the HDF. Sect. 5 is devoted to the analysis on the expected accuracy and possible systematics when exploring real data, coming from deep photometric surveys. A general discussion is given in Sect. 6 and conclusions are listed in Sect. 7.

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© European Southern Observatory (ESO) 2000

Online publication: December 11, 2000