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

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6. Discussion

6.1. A magnitude scale error in the APM data?

The apparent rapid increase in number counts of galaxies in the magnitude range [FORMULA] reported by Maddox et al. ( 1990d ) is thus absent from our counts (or those of Weir et al. 1995 ), although our slope of dN/dm is still slightly higher than what predict no-evolution models at [FORMULA]. As the comparison with the APM data seems to indicate, this might be essentially due to a difference in magnitude scale of [FORMULA]  0.1-0.2 mag./magnitude. Serious suspicions about systematic residual errors in the APM magnitudes at [FORMULA] have recently been raised by Metcalfe et al. ( 1995a ). If our data are correct, they support and even strengthen this hypothesis. Other arguments also consolidate this idea.

First, our data (Fig. 10 ), as well as previous ones (see Koo & Kron 1992 ), do not present evidence for evolution of galaxy colours over the range [FORMULA]. and rule out strong luminosity evolution scenarios in the visible (McLeod & Rieke 1995 ) for bright field galaxies, out to [FORMULA].

One might also think of a "giant local void" that would affect the bright end of the counts. Although there are indications of large fluctuations in projected galaxy density at the level of a Schmidt field (Fig. 4 , Picard 1991b ) for [FORMULA], or over the full sky for [FORMULA] (Paturel et al. 1994 ), the analysis of a large spectroscopic subsample (Loveday et al. 1992 ) seems to exclude this possiblity in the APM survey.

Statistics of CCD calibrations (Maddox et al. 1990d , Loveday et al. 1992 ) done on the APM magnitudes do not reveal any important trend like the one in Fig. 7 and 8 . This is quite puzzling, and one might wonder if the effects seen here are not purely local and compensated somewhere else in the APM survey. If this were true, correlated systematic magnitude errors of [FORMULA]  mag., over such large areas (100 sq. deg. in our case) would artificially boost the two-point correlation function on scales [FORMULA] in [FORMULA] magnitude bins. This does not appear prominently in Fig. 2 of Maddox et al. ( 1990a ). Another clue is that the trend found by Metcalfe et al. ( 1995a ) concerns the whole area of the APM catalog, and therefore supports the hypothesis of a global magnitude scale error (which does not exclude large scale variations of the zero-point).

6.2. Uncertainties in the "local" field luminosity function

To partially bypass uncertainties in the optimum Schechter parameters of the local luminosity function for field galaxies, count models are generally "renormalized" by adjusting the Schechter density parameter [FORMULA] to counts at some bright magnitude. However, the [FORMULA] parameter itself is directly affected by any systematic error in the magnitude zero-point of a redshift survey. Such errors are known to exist at bright magnitudes in photographic catalogs (Metcalfe et al. 1995b , Yasuda et al. 1995 ) on which are essentially based all the determinations of the local field luminosity function. In fact, decreasing the [FORMULA] found by LPEM by about 0.4 mag., like our photometric comparison with the APM catalog suggests, brings their luminosity function in good agreement with both the one from EEP and our bright galaxy counts (Fig. 9 ), without having to increase [FORMULA]. One should also note that such a"bright" normalisation in [FORMULA] of the luminosity function removes any significant luminosity evolution6 of luminous galaxies in the blue band to [FORMULA] (Lonsdale & Chokshi 1993 ).

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