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

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3. Filters and photometric accuracy

In this section we study through simulations the quality of the [FORMULA] as a function of the filter set, the photometric accuracy and the redshift, i.e. the robustness of the redshift determination and the expected percentage of catastrophic identifications and spurious detections. The aim of this exercise is to study the systematic effects produced by the sampling of the SED and the associated noise coming from photometry. Catastrophic identifications ([FORMULA]) are those with [FORMULA], and such objects are thus lost from their original redshift bin. The accuracy of [FORMULA] in a given redshift bin is defined by the mean difference [FORMULA] of the sample with respect to the model redshift, excluding catastrophic identifications, and the standard deviation [FORMULA]. Spurious identifications ([FORMULA]) correspond to objects which are incorrectly assigned to a given [FORMULA] interval, and thus susceptible to contaminate the statistics within this [FORMULA] interval; in this case [FORMULA].

Some of these quantities, in particular [FORMULA] and g%, depend on assumptions about redshift number counts and photometric depth. For this reason we compute them only for a set of simulations with a more realistic modeling for galaxy counts, according to a Pure Luminosity Evolution (PLE) scenario. We discuss the results as a function of the photometric parameters in Sect. 5.

Simulated catalogues of 1000 objects were produced, with a homogeneous redshift distribution, in order to compute the above mentioned parameters as a function of the filter set and photometric accuracy. In all cases, the types and ages assigned to the different galaxies in a redshift bin are randomly chosen from the 8 GISSEL98 template families mentioned above, with solar metallicity. Photometric errors in these homogeneous catalogues are introduced as a noise following a Gaussian distribution of fixed [FORMULA] in magnitudes for each band (0.05 to 0.3 magnitudes, i.e. [FORMULA] 5 to 30 % photometric accuracy), and they are uncorrelated for different filters. For each filter set we study the quality of [FORMULA] as a function of the photometric accuracy, In this particular case, photometric errors do not scale with magnitudes. A realistic error distribution is used in Sect. 5. The value of the visual extinction [FORMULA] ranges between 0 and 1. For each simulated galaxy, hyperz computes a [FORMULA] value, as well as the [FORMULA] error bars corresponding to [FORMULA]% confidence levels, computed by means of the [FORMULA] increment for a single parameter (Avni 1976). The redshift step used to search solutions between [FORMULA] and [FORMULA] is [FORMULA], with an internal accuracy which is 10 times better. The choice of the primary z-step between 0.1 and 0.05 does not affect significantly the results.

Fig. 2 shows the behaviour of the different sets of simulated samples when the [FORMULA] is compared to the true [FORMULA]. The results of these simulations are summarized in Table 2. Without near-IR photometry, the errors on individual galaxies become huge at [FORMULA] as expected due to the lack of strong spectral features in the visible band. In particular, in this redshift range the 4000 Å break goes out of the I band and the Lyman break does not yet affect the photometry in the filter U. This problem is solved when near-IR is included. In fact, J, H, and K filters allow to bracket the 4000 Å break. Also, the lack of U band photometry introduces an enhanced uncertainty in the [FORMULA] domain (mainly because of the contribution at [FORMULA]), because at [FORMULA] none of the other filters is able to detect a strong break.

[FIGURE] Fig. 2. Comparison between [FORMULA] and [FORMULA] for simulated catalogues with [FORMULA] and filters sets BVRI , UBVRI , UBVRIJ , UBVRIK , BVRIJK , UBVRIJHK . Dotted lines correspond to [FORMULA], dashed lines to [FORMULA] and thin solid lines to [FORMULA].


[TABLE]

Table 2. Summary of results obtained on simulated catalogues with a homogeneous redshift distribution as a function of the redshift bin, filters set and photometric errors [FORMULA]. See the text for a complete description.


All these results are almost independent of the type of galaxy, provided that the evolving population of stars is older than a few [FORMULA] years typically. This point is discussed in details in next section.

The dispersion in [FORMULA] is strongly sensitive to the photometric uncertainties. There is no significant gain for [FORMULA] magnitudes (about 5% accuracy). This value roughly corresponds to the typical photometric uncertainties in deep photometric surveys, when all the error sources are included. The dispersion and the number of multiple solutions with similar weight rapidly increase up to [FORMULA] magnitudes. Including near-IR JHK photometry strongly reduces the error bars within the [FORMULA] range, without significantly improving the uncertainties in [FORMULA] outside this interval. If the filter Z is considered in addition to the five optical filters, the resulting dispersion at low redshift become smaller up to [FORMULA], but the degeneracy at [FORMULA] - 3 still remains, even if less dramatic.

In Fig. 3 we illustrate the probability functions for two simulated galaxies at low and high redshift: the solution becomes better constrained around the model value and the degeneracy between high and low redshift solutions disappears with increasing photometric accuracy and when the wavelength range extends up to the near infrared region.

[FIGURE] Fig. 3. Examples of the evolution of the probability distributions associated to [FORMULA] as a function of the filter set and photometric errors, for two simulated objects. Left: [FORMULA]. Right: [FORMULA]. Dotted lines refer to [FORMULA], dashed lines: [FORMULA], solid lines: [FORMULA]. The vertical line marks the true [FORMULA] value.

The typical dispersion in [FORMULA] obtained here is similar to the values found in the literature, even when the techniques used are appreciably different (Brunner et al. 1997; Connolly et al 1997; ...). In most published studies it is extremely difficult to compare the accuracy of [FORMULA] as a function of photometric errors.

These results are useful to understand the general trends expected from a given configuration of filters and photometric accuracy. Nevertheless, [FORMULA] techniques are often applied to statistical studies, which require more "realistic" simulations in order to define the right observational strategy for the photometric survey. Then, a realistic redshift distribution is needed. For most applications, a PLE model is enough to determine the main trends. Also, photometric uncertainties have to be scaled with magnitude, to reproduce the behaviour of real catalogues. These points are discussed in Sect. 5.

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© European Southern Observatory (ESO) 2000

Online publication: December 11, 2000
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