The estimate of redshifts through photometric techniques is one of the most promising techniques in deep universe studies, and certainly a key point to optimize field surveys with Megacam. We briefly discuss the limits and the expected accuracy of such a method through simulations. These results determine the observational strategy for some suggested programs.

The technique used to compute photometric redshifts (hereafter z_phot) is a standard ² minimization procedure. The observed spectral energy distribution (SED) of each galaxy is compared to a set of template spectra

(5)

where F_i^O and F_i^T are the observed and the template fluxes in the i band, and (F_i) is the photometric error. F_i^T is normalized to match the observed flux in an arbitrary reference band. The difference with respect to other similar methods (Gwyn & Hartwick 1996, Sawicki et al. 1997 among others) is the large number of template spectra used here. The new Bruzual & Charlot evolutionary code (GISSEL96) has been used to build eight different synthetic star formation histories, roughly matching the observed properties of field galaxies in the close neighbourhood, from E to Im: a pure burst of 0.1 Gyr, a constant star-forming system, and six µ models (e-decaying SFR) with characteristic time-decays chosen to match the sequence of colors from E to Sd. For each of these galaxy types, we select 50 synthetic spectra corresponding to different relevant ages for the stellar population, in order to closely follow all the significant changes in the SEDs. The template database includes all these synthetic spectra.

We have studied the accuracy of z_phot as a function of the relevant parameters, namely the photometric errors, the filter bands available and the type of galaxy. For each test galaxy, a value of z_phot has been computed as well as the z corresponding to different confidence levels, which give an estimate of individual errors. Different sets of simulated catalogues were created for this exercise, basically reproducing the photometric properties of two extreme spectrophotometric types of galaxies, taken at different ages and redshifts, with and without evolution: E/S0 galaxy (evolving 0.1 Gyr burst, z_form = 5.3, aged 15 Gyr at z = 0, with H₀ = 50 km s^-1 Mpc^-1 and q₀ = 0.1), and a constant star forming system. Photometric errors were introduced as gaussian noise distributions of fixed FWHM for each filter band, and they are uncorrelated for different filters.

Figure 10 shows the behaviour of a set of simulated objects when the z_phot, computed from UBVRI photometry, is compared to the true z (model). BVRI filter responses are similar to Focam, and U is a ``red'' Johnson (_c ~ 3750 Å). As expected, the errors on individual galaxies (at 90% confidence level) become huge at ~1.2 z ~2.2 because of the lack of strong spectral features in the visible band. This problem is solved when near-IR photometry is included.

The results of these simulations are summarized in Tables 1 and 2, for the dispersion in the z_phot and the mean uncertainties for individual galaxies respectively. The dispersions are not strongly dependent on the type of galaxy, provided that the evolving population of stars is older than ~10⁷ yr typically. This limitation arises from the stellar libraries used to build the templates. Nevertheless, errors for individual galaxies tend to be higher for continuous star forming galaxies, when all the other parameters are fixed. It is worth noting that no contribution from the ISM of galaxies has been taken into account and, in particular, the presence of emission lines in real SEDs has to be considered as noise included in the photometric uncertainties (0.1 to 0.2 magnitudes at worst). According to our results in a reduced set of data, neither absorption nor metallicity effects will change these results significantly.

Table1: Dispersion in the photometric redshift as a function of photometric errors, filters and galaxy types

			z(z)
Galaxy type	$\Delta m$	Filters [z=	0 - 0.4	0.4 - 0.8	0.8 - 1.2	1.2 - 1.8	1.8 - 3.0	3.0 - 5.0
E/S0	0.01	UBVRI	0.03	0.05	0.05	0.07	0.11	0.11
Cont. SFR	0.01	UBVRI	0.03	0.03	0.03	0.03	0.02	0.11
E/S0	0.1	UBVRI	0.05	0.06	0.36	0.23	0.22	0.11
Cont. SFR	0.1	UBVRI	0.04	0.04	0.41	0.32	0.25	0.11
all	0.1	UBVRIJK	0.02	0.05	0.07	0.14	0.08	0.09
all	0.2	UBVRI	0.08	0.11	0.51	0.57	0.30	0.17
all	0.3	UBVRI	0.13	0.14	0.51	0.58	0.94	0.29

Table 2: Mean z for individual galaxies at 90% confidence level as a function of photometric errors, filters and galaxy type

			z (z)
Galaxy type	m	Filters [ z =	0 - 0.4	0.4 - 0.8	0.8 - 1.2	1.2 - 1.8	1.8 - 3.0	3.0 - 5.0]
E/S0	0.1	UBVRI	0.08	0.07	0.11	0.42	0.48	0.12
Cont. SFR	0.1	UBVRI	0.13	0.18	0.35	0.58	0.46	0.22
E/S0	0.1	UBVRIJK	0.10	0.09	0.10	0.23	0.23	0.13
E/S0	0.2	UBVRI	0.19	0.22	0.33	0.88	0.73	0.28
E/S0	0.3	UBVRI	0.35	0.35	0.65	1.31	1.18	0.42

The dispersion in the estimate of z_phot is strongly dependent on photometric uncertainties. There is no significant gain for m 0.1, but the dispersion and the number of multiple solutions with similar weight increases rapidly up to m ~ 0.3, which is probably a limiting value for individual objects. Including near-IR J and K photometry does not improve significantly the uncertainties in z_phot outside the ~1.2 z ~2.2 range, where it is absolutely needed, and where the individual errors are strongly reduced. When the number of filters in the visible band is reduced to UBRI, the dispersion in z_phot increases roughly to 0.09 for z ~1.5 and 0.3 for z ~2.2. The dispersion in z_phot is quite similar to the values found in the literature, even when the techniques used are appreciably different (Brunner et al. 1997, Conolly et al. 1995), but it is extremely difficult to compare the accuracy of z_phot as a function of the relevant parameters (photometric errors in particular).

References

Connolly A.J., Csabai I., Szalay A.S., 1995, AJ 110, 2655

Gwyn S.D.J., Hartwick F.D.A. 1996, ApJ 468, L77

Sawicki M.J., Lin H., Yee H.K.C., 1997, AJ 113, 1