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

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4. Galaxy number counts

4.1. Results

The differential number counts are shown for each field in Fig. 4 . One can notice a great homogeneity over the whole magnitude range between the plates, except for the 16&fh;+42o field. In fact this field contains no less than 12 Abell clusters, and is part of the Hercules supercluster. One can estimate the variance in number counts at a given depth on a Schmidt plate from the Maddox et al. ( 1990a ) angular two-point correlation function (e.g. Peebles 1980). We find that the projected density of galaxies in the 16&fh;+42o field exceeds the mean one from the other fields by a factor of [FORMULA] times the expected deviation at [FORMULA], reducing to [FORMULA] for [FORMULA]. This field is therefore one of the densest in the sky at the bright end of our catalog, and including it in the total number counts shown in Fig. 5 severely changes the slope at [FORMULA]. For this reason we decided to discard it from the samples for the statistical analysis of number counts, remembering however that we might underestimate in this way the true density of bright galaxies.

[FIGURE]Fig. 5. Total differential number counts in [FORMULA] and [FORMULA] in our catalog, including (open circles) or not (filled circles) the 16&fh;+42o field. Error bars indicate poissonian ( [FORMULA] ) uncertainties whereas lines bracket the rms excursion of the total counts assuming the galaxy density is uncorrelated from plate to plate.

4.2. Comparison with previous counts

Bright galaxy counts published so far were all conducted on photographic material, in quite similar passbands. This enables us to compare easily our results with previous work. The transformations we applied are described below.

Many of the existing bright galaxy counts (Shanks et al. 1984 , Stevenson et al. 1986 , Heydon-Dumbleton et al. 1989 ) make use of the [FORMULA] passband definition established by Kron ( 1980 ), and which transforms to our [FORMULA] through

[EQUATION]

assuming [FORMULA]. The recent counts of Weir et al. ( 1995 ) were done in the Gunn-g passband, for which they give the approximate transformation

[EQUATION]

to the APM survey magnitude system (Maddox et al. 1990c ), which is identical to ours.

Gunn-r observations (Sebok 1986 , Picard 1991b , Weir at al. 1995 ) were transformed to the Cousins [FORMULA] system using

[EQUATION]

from a fit to 16 Landolt standards, giving a standard error of only 0.014 mag (P. Fouqué, private communication). Shanks et al. ( 1984 ) [FORMULA] magnitudes were converted with

[EQUATION]

inserting [FORMULA] in their Eq. (5).

As shown on Fig. 6 , our counts agree well with those from other studies, especially with the preliminary counts done on POSSII plates (Weir et al. 1995 ), despite the uncertainties in the conversion from their photometric system to ours. In [FORMULA], the major discrepancies observed are with Shanks et al. ( 1984 ), and the Picard ( 1991b ) northern and southern counts, although our results lie in-between. The Schanks et al. counts are based on only one Schmidt plate, so the fact that they show an offset is perhaps not surprising. As pointed out by Weir et al. ( 1995 ), it is yet unclear whether the difference between the Picard counts originates from the presence of very large scale structures, as claimed by Picard ( 1991a ), or are simply caused by unexpected photometric errors in his photometry. We note here that one of our plates lies at about 20o from Picard's northern field, and that no particular enhancement in galaxy density is seen there.

[FIGURE]Fig. 6. Comparison of published bright galaxy counts converted to our [FORMULA], [FORMULA] photometric system. Arrows indicate counts underestimated because of incompleteness ( 3.4 ).

At their faint end ( [FORMULA] ), our blue counts are about 10% lower than those of Weir et al. ( 1995 ) and Maddox et al. ( 1990d ); however the raw counts (Fig. 4 ) do not indicate any obvious drop in completeness at that level. As a matter of fact, two points should be considered here: (1) half of the difference (5%) can be explained by detections that were not matched between the two colours and dropped in the final catalog (although there is no proof that these are real objects), and (2) Weir et al. ( 1995 ) showed on simulations that both their counts and those derived by the APM survey might be slightly overestimated (by about 10%) for [FORMULA]. Therefore it is likely that this difference at the faint end between our counts and others should not be interpreted as something significant, but only as a consequence of a different data processing. This is confirmed by the recent medium-deep CCD counts by Arnouts et al. 1996 , which are in perfect agreement with ours over this magnitude range, in both colours.

But the most interesting discrepancy in this comparison is the one seen with some other galaxy counts at bright magnitudes. At [FORMULA] for instance, we count nearly twice as many galaxies as do Maddox et al. ( 1990d ) or Heydon-Dumbleton et al. ( 1989 ). The recent Weir et al. ( 1995 ) counts stay however in perfect agreement with ours down to their brightest limit. As the APM survey, because of its statistical weight, is traditionaly used to normalize galaxy counts models at bright magnitudes, it is worth investigating further what may be the origin of this difference. Recently, Metcalfe et al. ( 1995b ) have discovered some scale error on the [FORMULA] domain in the APM galaxy magnitudes. The APM survey shares four Schmidt fields in common with us, and the corresponding part of the catalog, down to [FORMULA], was kindly provided by J. Loveday for comparison.

[FIGURE]Fig. 7. Comparison of galaxy magnitudes between the APM and our MAMA catalog on four UKST Schmidt plates. The tilted frontier on the right side of the plot is caused by the [FORMULA] limit in the APM subsample.

[TABLE]

Table 3. Global Schechter parameters of local luminosity functions ( [FORMULA] )

Fig. 7 shows the difference between the APM catalog and our magnitudes for each of these four fields5 . Although both magnitudes are in agreement within [FORMULA]  mag. at the faint end ( [FORMULA] ), one can immediately notice a systematic difference at brighter magnitudes, reaching 0.3 to 0.5 mag. at [FORMULA]. To find out whether this was due to our calibration or was intrinsic to the APM data, we cross-identified our list of southern standard galaxies with the APM catalog to produce a plot similar to Fig. 3 . Fig. 8 shows indeed that there seems to be some problem in the magnitude scale of this APM galaxy sample. The magnitude overestimate starts to rise at [FORMULA] and increases until [FORMULA] where it culminates at about 0.4 mag. Brighter than this point, it is unclear whether it stays at the same level or decreases again, but at [FORMULA] the offset is still at least about 0.2 mag. Of course these estimates are in principle only valid for the small subsample of the APM catalog considered here, and might not be applicable to the full catalog. But one can see that compensating for this average trend in the magnitude scale would bring the total APM counts in very good agreement with ours.

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