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Astron. Astrophys. 317, 43-53 (1997)

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5. Comparison with models

5.1. Numbers counts and the normalization of the "local" luminosity function

A recurring problem with previous counts has been the normalisation of models at bright magnitudes. Normalizing passively evolving models at [FORMULA] leads to an apparent excess of already 50 to 100% at [FORMULA]. This apparent phenomenon is hard to reconcile with the redshift distributions to [FORMULA] (Glazebrook et al. 1994 , and references therein), which suggest a higher normalisation of the field luminosity function. As our data "push" the bright end of galaxy counts to higher values, we can now test how local determinations of the luminosity function are able to match the counts over the domain [FORMULA].

We therefore constructed a very simple non-evolving model of galaxy counts, intended to be valid at least to [FORMULA]. K-corrections were computed by integrating the spectral energy distributions from Pence ( 1976 ) through the [FORMULA] and [FORMULA] photographic passbands given by Couch & Newell ( 1980 ), which are very close to our blue and red passbands. The morphological mix of galaxy types was taken from Shanks et al. ( 1984 ). This model does not include luminosity or number evolution as in deeper count models (e.g. Guiderdoni & Rocca-Volmerange 1990 , McLeod & Riecke 1995 ), but is sufficient for our normalisation purpose. We chose an Einstein-de Sitter universe for simplicity, although at this depth ( [FORMULA] ) the counts prove to be quite insensitive to (reasonable) cosmological parameters (e.g. Yoshii & Takahara 1988 ).

Fig. 9 shows our data compared to simple galaxy counts models in the blue photographic passband without evolution as described above, using two different luminosity functions (LF). The first one is from Efstathiou et al. ( 1988 , hereafter EEP), from a compilation of results obtained on several redshift surveys, and the second one, more recent, is from Loveday et al. ( 1992 , hereafter LPEM) from a sparse redshift survey of APM galaxies. Schechter parameters are given for both in Table 4. A third, colour dependent, LF from Shanks ( 1990 ), with the normalisation adopted by Metcalfe et al. ( 1991 ) is also shown for comparison. As can be seen, the EEP luminosity function fits the data much better than the one from LPEM, which are however, as expected, in good agreement with the APM counts for [FORMULA]. In fact, most of the discrepancy between the two luminosity functions lies in the value of [FORMULA], with a difference close to 0.4 mag, i.e. about the same one gets when comparing APM magnitudes to those of standard galaxies at [FORMULA] (Fig. 8 ). The best agreement is found with the Shanks LF model. This is not a surprise, as the two other models do not distinguish the luminosity functions of early and late-types, which are indeed quite different; and this shows up when K-corrections become important.

[FIGURE]Fig. 8. Same as Fig. 3 , but with the APM catalog. The dashed line marks the magnitude limit of the APM subsample.

[FIGURE]Fig. 9. Comparison of our [FORMULA] galaxy counts (filled circles) and those of the APM survey (open circles) with the simple models described in the text. Errorbars are [FORMULA] uncertainties deduced from the field-to-field scatter within each bin (assuming galaxy density is uncorrelated from one plate to another). Arrows indicate points affected by incompleteness. The 3 curves correspond to different luminosity functions used in the no-evolution model: Efstathiou et al. 1988 (upper solid line), Loveday et al. 1992 (lower solid line), and Shanks 1990 as normalized by Metcalfe et al. 1991 (dashed line).

[TABLE]

Table 4. Luminosity function parameters for the colour distribution model ( [FORMULA] )

Fig. 9 indicates that the normalisation of the Shanks LF adopted by Metcalfe et al. ( 1991 ) is in excellent agreement with our own counts, but the latter are still slightly too steep on their bright side compared to any non-evolving model. Can this be interpreted as evolution? One can hardly conclude on the basis of the data presented here, as a 10% misclassification of galaxies added to a 0.1 mag. systematic error in measured fluxes at [FORMULA] would be enough to produce this effect.

[FIGURE]Fig. 10. Colour histograms of galaxies compared with the no-evolution model (curves) described in the text, in 4 magnitude intervals. The colour distribution of stars (thin histogram) is plotted for comparison in the faintest subsample.

5.2. Galaxy colours

Galaxy colour distributions for the total catalog (including the field 16&fh;+42o) are presented in Fig. 10 . They are in good agreement with the compilation presented by Koo & Kron ( 1992 ), if one makes allowance for the passband differences between our system and theirs.

We reemployed the Shanks LF model with no evolution described above to model the observed colour distribution. Rest-frame galaxy colours per Hubble type were taken from Metcalfe et al. ( 1991 ) and converted from their CCD photometric passbands to our photographic system with [FORMULA]. Ingredients of the LF are gathered in Table 4. Photometric errors were included in the model, adopting an error distribution with magnitude determined in the overlap between catalogs (see Bertin 1996 ). Photometric errors do not only smear out details in the observed colour distribution, they also distort the wings of the distribution for the dimmest objects (that is, when the error strongly evolves with colour). As our red plates are here significantly less sensitive than the blue ones, the two lower graphs in Fig. 10 exhibit a shallower tail on their blue side than on their red side.

Observed and predicted distributions prove to be in very good agreement, except in the brightest subsample, where we expect some problems with the saturation and the robustness of star/galaxy separation. One can notice a small ( [FORMULA]  mag) systematic colour offset between the two, which might be imputed to uncertainties in our photometric modelling. But no obvious evolution of colour with magnitude is detected, within the uncertainties, up to [FORMULA].

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