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

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3. Data processing

3.1. Digitization

The 14 plates were scanned in density mode, with the MAMA microdensitometer, using a 10  [FORMULA] m step (0.65"). The MAMA is able to scan a full plate in a few hours, and provides images with a usable dynamic range quite large compared to that of similar machines like COSMOS or APM: more than 3 in density (a description of the microdensitometer and its performances can be found in Berger et al. 1991 ). Because of limitations in acquisition and storage capabilities with the MAMA at that time, the image data were acquired as 12´ [FORMULA] 12´ frames, and recombined as 18´ [FORMULA] 18´ images, with an overlap of 6´ (which therefore defines the maximum size allowed for objects to be reliably measured).

To insure a maximum reliability of the catalog, only the central "clean" 4.5o [FORMULA] 4.5o of each field were kept for analysis (ESO and CERGA plates cover only slightly more than 5o [FORMULA] 5o in total, and full coverage was not needed here). The exact areas retained for the final catalogs are reported in Table  1 .

3.2. Astrometry

The standard MAMA procedure was adopted to calibrate the plates astrometrically (see Berger et al. 1991 ). Between 150 and 300 suitable astrometric standards (PPM catalog, Röser & Bastian 1991 ) can be found per plate. A third order fit on projected coordinates leads to a mean residual of [FORMULA] ", similar to the value obtained when comparing bright object positions between the two passbands. However, this figure degrades noticeably ( [FORMULA] 1") at the extreme borders of some plates. We had to adjust ESO plates 200 and 249 to their blue counterparts SERC 200 and 249 using a neural network mapping1 on bright stars to secure blue/red object matching.

3.3. Detection

A dedicated version of the SExtractor software (Bertin & Arnouts 1996 , hereafter BA96) was used in PHOTO mode for source extraction. The standard 2 pixels (1.3") FWHM Sextractor's convolution mask was applied in order to improve the detectability of low surface brightnesses2 . Although emulsion noise becomes strongly correlated on small scales (especially on copies), this technique enables one to lower the detection threshold to a secure [FORMULA] of the sky background fluctuations, corresponding to mean surface brightnesses [FORMULA] (CERGA blue plates), [FORMULA] (CERGA red plates), [FORMULA] (SERC blue plates) and [FORMULA] (ESO red plates).

The deblending capabilities of SExtractor give no limitation to the size of objects which can be extracted; spiral arms and other peripheral substructures of bright galaxies are not "separated" from the central region. Therefore the catalog is expected to be complete for all objects smaller than the overlap between subframes: 6´ (corresponding here to [FORMULA] ).

3.4. Star/galaxy separation

Star-galaxy separation was performed with a dedicated neural network (Bertin 1994 ) trained on a sample made of bright objects classified by eye, and fainter ones from the CCD photometric fields (§ 3.5.3 ). The latter were classified automatically using SExtractor's tunable neural network classifier (see BA96). Briefly, each detected object is translated into a pattern vector containing basic information about its profile (7 isophotal areas plus the peak density). This combination of parameters, added to the ability of neural networks to deal with complex distributions in multidimensional space, leads to a very robust star/galaxy classifier. In particular, objects affected by optical distortions (in the corner of the plates) or merging (we chose to classify undeblended pairs as "stars" if and only if the brightest component is a star) are properly handled. Unfortunately, as we will see, such a set of parameters is not well fitted to the classification of very bright stars and galaxies, which show similar profiles.

A minimum of 500 sample patterns is necessary for the neural network to achieve performances close to its asymptotic values (Bertin 1996 ); we used [FORMULA] per field.

Extensive visual checks and colour histograms show that stellar contamination among catalogued galaxies due to misclassifications is less than 4% for [FORMULA], rising to 10% at [FORMULA] (CERGA plates) and [FORMULA] (UKST plates). [FORMULA] and [FORMULA] therefore define the upper magnitude limits for the northern and southern sets of plates, respectively. The estimated loss of galaxies due to misclassifications is similar to stellar contamination at faint magnitudes. We can rely on statistics from the identifications of optically bright IRAS galaxies (Bertin et al. 1996 ), which contain less than 10% of objects classified as "stars" for [FORMULA]. As a high fraction of IRAS galaxies turn out to be rather compact and difficult to separate from point-sources on photographic images (Sutherland et al. 1991 ), this gives us an upper limit of the loss we might expect at these magnitudes. It is more difficult to estimate it precisely at the bright end of our counts (( [FORMULA] ), because stars outnumber galaxies by a factor > 50 . We examined 600 detections with [FORMULA], classified as stars, and found indeed that 4 of them were galaxies. There seems therefore to be some loss of galaxies at the bright end of our catalog, and counts below [FORMULA] (or [FORMULA] ) should only be considered as lower limits.

3.5. Photometry

3.5.1. Estimation of magnitudes

The way SExtractor estimates "total" magnitudes on CCD images is described in details in BA96. In the "PHOTO " mode, the program applies a density-to-intensity transformation (see § 3.5.2 ) before summing pixel fluxes. Briefly, for each object, two kinds of magnitudes are computed. The first one is an improvement of Kron's ( 1980 ) method: it measures the flux integrated in an elliptical aperture whose size and shape are function of the object's profile. The second one is isophotal, and corrects for the fraction of flux lost in the wings (assuming a gaussian profile) as in the APM survey (Maddox et al. 1990c ). As this second method is more subject to biases than the first one, we take the aperture magnitude as an estimate of "total" magnitude, unless it is suspected to be contaminated by the presence of neighbours by more than 0.1 mag; in which case we rely on corrected isophotal magnitude. Such a situation occurs in less than 20% of the cases in our images; SExtractor's total magnitude is thus essentially an aperture magnitude.

The behaviour of SExtractor's magnitudes on simulated Schmidt plate images is shown in Fig. 1 . The predicted fraction of flux measured for galaxies is remarkably constant with magnitude, even beyond the completeness limit. As can be seen, the mean offset one needs to apply to SExtractor's magnitude to get an estimate of "total magnitude" is [FORMULA]  mag.

[FIGURE]Fig. 1. Prediction of the mean flux lost (expressed in magnitude) by SExtractor's isophotal, corrected isophotal and adaptive aperture magnitudes, as a function of the "true" total magnitude. These estimates are from simulated Schmidt plates images, generated as described in BA96. The simulations are done in the blue photographic passband; they assume a logarithmic response of the emulsion and image parameters typical of CERGA Schmidt plates, with a seeing FWHM of 2". The apparent drop seen at [FORMULA] is an artefact due to poor statistics.

3.5.2. Linearization of the photographic response

In PHOTO mode, SExtractor transforms densities D to intensities I during image analysis assuming a logarithmic response of the emulsion in the "linear part":

[EQUATION]

where [FORMULA] defines the contrast of the emulsion (as measured with MAMA), and [FORMULA] is the intensity zero-point. Both parameters were adjusted for each plate by minimizing the [FORMULA] on "total magnitudes" estimated by SExtractor for a set of CCD standard galaxies. For all plates but one we found [FORMULA]. Differential desensitization and telescope vignetting were compensated for by substracting the local background density from D before applying the calibration law (Eq. 1 ). This correction is perfectly valid here as no interstellar emission is expected in these fields, and reduces large-scale sensitivity variations to [FORMULA]  mag (Bertin 1996 ).

Finally, for galaxies, a linear least-square fit was applied separately to the magnitude scale in each field to correct for residual differences of [FORMULA] % in the slope of the relation between photographic and CCD magnitudes. Bright stellar images are affected by a mix of photographic saturation, complex chemical proximity effects and, above all, light diffusion inside the emulsion during the scanning process. Stars thus need a specific calibration which was carried out using polynomial and neural network fits between their photographic and CCD magnitudes.

Eq. ( 1 ) provides a good fit to photographic calibration curves of sky-limited exposures measured with MAMA (Moreau 1992 , Bertin 1996 ), although it does not take into account possible saturation effects. Thanks to the fairly large dynamic range of MAMA, saturation affects our galaxy magnitudes to a lesser extent than e.g. APM or COSMOS scans. Nevertheless, southern copy plate images unambiguously show some signs of saturation on cores of galaxies with [FORMULA]. We therefore expect that both systematic and random errors increase significantly towards brighter magnitudes on these plates (see Metcalfe et al. 1995b for a discussion about the consequences of saturation on galaxy photometry).

3.5.3. CCD calibration and colour equations

A total of 30 photometric CCD fields ( [FORMULA]  4 per Schmidt field, centered on groups of bright galaxies) were taken essentially at the OHP 1.2m and the ESO 2.2 and 3.6 meter telescopes, and matched to Cousins B and R magnitudes. SExtractor was also used at all stages of the CCD data reduction, leading to "total magnitudes" for about 1000 objects. As northern and southern plate sets have been taken with slightly different filter combinations, we naturally expect differences in their related colour equations. However we need to keep the survey as close as possible to a uniform (and as standard as possible) passband system. Following Blair & Gilmore ( 1982 ), we define here the blue passband [FORMULA] as

[EQUATION]

which is the transformation also adopted in the APM survey. The [FORMULA] band is defined as

[EQUATION]

[FORMULA], [FORMULA] and [FORMULA] are in the Cousins system3 . Fig. 2 shows the distribution of the residuals as a function of the [FORMULA] CCD colour index for each of the 4 types of plates. Although they are moderate, one can see systematic colour effects. The "best fit" colour coefficients are reported in Table 2. For CERGA blue plates the results are in good agreement with the estimates of Majewski ( 1992 ), who finds [FORMULA]. We find a stronger colour coefficient for the SERC passband than the one traditionally used at the APM ( [FORMULA] ), and conflicting even more with the COSMOS ( [FORMULA] )4 . However our estimate is in remarkable agreement with the recent and accurate measurements by Metcalfe et al. ( 1995b ), which give [FORMULA] and [FORMULA].

[FIGURE]Fig. 2. Differences between "pure" (but calibrated) photographic and CCD magnitudes as a function of the [FORMULA] colour index for the brightest standards: [FORMULA] (CERGA blue), [FORMULA] (UKST blue), [FORMULA] (CERGA red) and [FORMULA] (ESO red). The standards contain about 2/3 of stars and 1/3 of galaxies (which show similar behaviour). A few points (crosses) deviate by more than [FORMULA] from the mean relation and have not been taken into account for the chi-square fit (solid line).

Lastly, we find in average the red photographic passbands slightly bluer than the Cousins [FORMULA]. This contradicts the traditional correction established photoelectrically, and then extrapolated to photography by Couch & Newell ( 1980 ), who proposed a response for the combination IIIaF+RG630 redder than Cousins [FORMULA]. Note that more recent determinations (Cunow & Wargau 1993 ) also support the idea that the Couch & Newell equation is inappropriate.

[TABLE]

Table 2. Photographic passbands and their link to standard photometric systems

In the end, the photographic magnitudes from each plate where corrected using the equations of Table 2 to yield magnitudes in a unified system. Given the smallness of the colour coefficients, the resulting degradation in photometric accuracy is negligible. The rms residual of the calibration above the completeness limit ranges between 0.07 and 0.17 mag (including the contribution from large scale inhomogeneities). Assuming that the intensity scale is perfectly linearized, the formal uncertainty on the individual plate zero-points would be [FORMULA]  mag. But such an assumption is by far too optimistic with photographic plates. Given the number of bright standard galaxies per plate (between 1 and 3 per magnitude), and the rms uncertainty on their magnitudes (about 0.15 mag), we estimate the individual zero-point systematic errors to be [FORMULA] mag in the range [FORMULA], and [FORMULA]. As Fig. 3 shows, below these fluxes the photometric errors grow rapidly.

3.5.4. Comparison with other photometries

Fig. 3 shows the differences between photo and CCD magnitudes for our CCD standard galaxies, as well as the comparison with the photometry of bright galaxies by several authors. Nine of the galaxies measured by Metcalfe et al. ( 1995b ) are found in our catalog; we find mean differences (MAMA-Metcalfe) [FORMULA], and [FORMULA]. Note that 3 of these galaxies also figure among our CCD standards; in both [FORMULA] and [FORMULA], our magnitudes are in agreement with theirs within 0.02 mag.

Although their photographic photometry does not reach the same accuracy and is more subject to biases than CCD or photoelectric standards, galaxies from the LV catalog (Lauberts & Valentijn 1989 ) have proven to be in good agreement with the RC3 system (Paturel et al. 1994 ), and can be used to trace an eventual large systematic trend at bright magnitudes ( [FORMULA] ). Over the 4 southern fields we find mean differences (MAMA-LV) [FORMULA] and [FORMULA]. These discrepancies might be interpreted as some loss of flux at the bright end ( [FORMULA] ) of our catalog. However, in the same magnitude range, "CCD galaxies" photometered here or by Metcalfe et al. do not show this offset, which could argue for a small, local zero-point error in the LV magnitudes.

Some bright galaxies ( [FORMULA] ) from the northern plates do also have photoelectric [FORMULA] and [FORMULA] "total" magnitudes in the RC3 catalog. From these we get a mean difference (MAMA-RC3) [FORMULA] which reveals the influence of plate saturation at the bright end of our catalog.

Finally, 5 of the galaxies photometered with a CCD by Maddox et al. ( 1990c ) to calibrate the APM survey lie in our field 201 and give an offset (MAMA-APM) [FORMULA]. More than this significant offset, the unexpectedly large dispersion of magnitudes almost 0.3, that is, as much as with the photographic LV sample! casts some doubt over the reliability of the Maddox et al. calibration set for this plate.

In conclusion, we believe our magnitude scale to be free from any large systematic error, except brightwards of [FORMULA], where fluxes might possibly be underestimated by [FORMULA]  mag.

[FIGURE]Fig. 3. Difference between photographic and CCD magnitude for standard galaxies as a function of CCD magnitude. Photographically unsaturated stars (with [FORMULA] or [FORMULA] ) are added at the faint end. Also displayed are bright galaxies measured by different authors.

3.6. Merging of catalogs

The "blue" and "red" catalogs were cross-identified in alpha, delta, to yield a unique two-color catalog. Differences in seeing or image quality, as well as imbricated detections (i.e. stars lying on disks of galaxies) were handled through a complex matching algorithm taking into account the shape of detected objects. This procedure leads to a highly reliable catalog, virtually suppressing all false detections like pieces of hair, satellite trails, optical ghosts or spikes around bright stars (these are generally classified as galaxies). One might fear some loss of objects with extreme colours in the final catalog; however the fraction of non-paired detections is almost constant with magnitude, and is about 1% (most of which are spurious), rising to 5% in the last half-magnitude bin imposed by star/galaxy separation.

[FIGURE]Fig. 4. "Raw" differential number counts in [FORMULA] and [FORMULA] for each of the Schmidt fields (continous line = southern fields; dashed lines = northern fields). Note the excess of galaxies in the northern field 16&fh;+42o (thicker lines), especially at bright magnitudes.

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