1 Introduction

The determination of galaxy distances is so crucial for clues on galaxy evolution and cosmic structures that a large variety of methods is currently being explored. Spectroscopic determinations are the most precise but they consume excessive observing time for deeper and deeper large galaxy samples. For instance, the redshift surveys such as CFRS (Le Fèvre 1995), 2dF (Folkes et al. 1999), Hawaii (Cowie et al. 1994) and more recently the SLOAN, with millions of targets with various spectral types, are complete to $z \leq 1.5$. At higher redshifts z > 1.5, the galaxy populations observed at faint magnitudes in deep surveys cover a large range of redshifts which will be easily accessible from photometry. However many problems of degeneracy, number and width of filters and extinction first have to be clarified. Typical SED features like the 4000 Å discontinuity or the Lyman break are known to be fruitful signatures for evaluation of redshifts when compared with template SEDs. Steidel et al. (1999) proposed an empirical method based on these discontinuities to detect $z \geq 4$ galaxies. Successful in discovering distant sources, the method is however imprecise and prone to degeneracies. The comparison of observed SEDs with calibrated templates on an extended wavelength range is the best way to rapidly determine redshifts of a large number of faint galaxies, on a continuous range $0 \leq z \leq 4$ . Such comparisons were proposed with templates from no-evolution models by Baum (1962), Koo (1985), Loh & Spillar (1986) and more recently Fernández-Soto et al. (1999) (hereafter FSLY); others proposed evolutionary SED methods such as Bolzonella et al. (2000) and Massarotti et al. (2001a) using templates derived from a variety of evolutionary codes. However the evolutionary codes and their applications may differ. If results are roughly similar at low redshifts (see Leitherer et al. 1996), they may actually strongly differ from each other at high redshifts, depending on adopted star formation laws and the corresponding age constraints, initial mass function, dust and metal effects as well as interpolation algorithms.

An essential property of most codes is the large wavelength coverage from the far-UV to the near-infrared needed to compute SEDs that are highly redshifted. Moreover our code PÉGASE.2, Fioc & Rocca-Volmerange (1997), in its current version (see next footnote) is able to take into account metallicity effects in its stellar library and isochrones. Evolution scenarios of nine spectral types, defined by star formation parameters, have been selected to reproduce the observed statistical SEDs of z=0 galaxy templates, Fioc & Rocca-Volmerange (1999b). Then two correction factors (cosmological k-correction and evolutionary e-correction) are computed with the model to predict redshifted SEDs, in order to be used as comparison templates to observations. Other PEGASE.2 scenarios based on different prescriptions of dust properties or star formation parameters might be computed and used as templates only if they respect fits of $z \simeq 0$ galaxy properties. This is beyond the objectives of this paper. Another method of photometric redshift determination supposes that the evolution effect is dominated by shot noise, Connolly et al. (1995).

We present in Sect. 2 a new tool, Z-PEG, to estimate photometric redshifts on a continuous redshift range $0 \leq z \leq 6$ or more. Observed colors or spectra are statistically compared to the PÉGASE.2 atlas for 9 spectral types (starburst: SB, irregular: Im, spiral: Sd, Sc, Sbc, Sb, Sa, SO and elliptical: E galaxies). Section 3 presents the results for the well-known Hubble Deep Field North and the comparison with spectroscopic redshifts allows us to derive average values of evolution factors. Section 4 shows the sensitivity to various parameters such as the NIR colors and IGM absorption. Interesting consequences for the redshifts of formation of the sample are derived in Sect. 5. Discussion and conclusions are proposed in Sects. 6 and 7 respectively.