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Astron. Astrophys. 364, 349-368 (2000)

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3. Data reduction

The data were reduced using FLIPS by J.C. Cuillandre as part of the calibration service of the 1998 season of UH8K Camera, Cuillandre (1998a; 1998b). FLIPS suppresses the dark and bias using the CCD over-scans and flattens the response of the 8 detectors using a flat-field made by combining [FORMULA] images of 18 nights of observation with the UH8K Camera. The final images have a corrected sky flux showing variations of less than 1% within each CCD image. The photometric standards were pre-reduced following exactly the same steps. The final dataset consists of 64 2k[FORMULA]4k frames (32 in V, 32 in I), and a set of photometric standard stars.

Photometry was performed using the SExtractor Package (Bertin & Arnouts, 1996) which provides Kron-like elliptical aperture and isophotal fluxes, ([FORMULA]) coordinates, position, elongation and stellarity class for all objects above a given threshold (we choose a threshold of 25 contiguous pixels above 1.5 [FORMULA] of sky value in V and I). The resulting SExtractor files were then calibrated for astrometry and photometry.

3.1. Astrometry

The USNO-A2.0 Astrometric Catalogue (Monet, 1998) is used as the astrometric reference as it gives the equatorial coordinates of most objects in our fields to a red mag[FORMULA] with accuracies of [FORMULA], and because it is easily accessible via on-line astronomical databases. The astrometry is done separately on the 64 frames, with IRAF geomap/geotran second-order Legendre polynomials. A radial correction is applied previously on the ([FORMULA]) coordinates to correct the prime-focus optical corrector distortion, whose equations were provided by J.C. Cuillandre (1996). If R is the actual radial coordinate of an object from the center of the UH8K mosaic (in mm) and r its observed radial coordinate (in mm), then the shift [FORMULA] due to the corrector is

[EQUATION]

[FORMULA] is the angular distance of the object from the center in arcsec. According to Eq. (1), the radial distortion is 0.13 pixel at a radius of 3´, 0.32 pixel at 4´, and it becomes non-negligible for radii greater than 6´ where the distortion is greater then one pixel (e.g. the radial distortion at 14´ is 14.1 pixels). The overlaps between the fields allow us to verify the importance of the optical distortion correction on the accuracy of the final astrometry. Fig. 2 and Fig. 3 show the errors [FORMULA] and [FORMULA] in X and Y directions for the overlap between the fields UD03 (CCD #0) and UD04 (CCD #6) without correction of distortion (Fig. 2) and with correction (Fig. 3). One can see that both the systematic errors and the random errors are bellow 0.5" after correction. We are not able to remove completely the systematic shifts between the fields (Fig. 3 frame a and b). This may be due to unknown misalignments between the chips of the mosaic. One can only minimize the systematic effects to sub-arcsecond values. The final equatorial coordinates are precessed to J2000.

[FIGURE] Fig. 2a-d. Differences between the equatorial coordinates of the objects in the overlapping region of the fields UD03-CCD#0 and UD04-CCD#6 (in arcsec) if no correction is applied for the prime focus optical corrector distortion. a  shows the right ascension difference [FORMULA] vs the CCD X axis, b  shows [FORMULA] vs the CCD Y axis, c  shows the declination difference [FORMULA] vs the CCD X axis, and d  shows [FORMULA] vs the CCD Y axis. Important systematic effects are seen in frame c  and d .

[FIGURE] Fig. 3a-d. Same as Fig. 2 with the correction of the prime focus optical corrector distortion of Eq. (1).

McCracken (priv. comm. 2000) used a finer and more complex approach with the Canada-France Deep Field (CFDF) ([FORMULA] deg2 covering the CFRS in UBVRI, the fields in BVRI bands were observed with the UH8K Camera) by establishing an internal Word-Coordinate System to which all pointing are referred. The claimed dispersion is 0.3 pix [FORMULA] over the entire camera.

3.2. Photometry

A rigorous photometric calibration is usually performed by applying a linear transformation on the instrumental (observed) magnitude m of the objects (given by Sextractor Kron-like elliptical aperture fluxes),

[EQUATION]

where M is the standard magnitude, [FORMULA] is the extinction coefficient, [FORMULA] is the airmass, [FORMULA] is the true-colour coefficient, [FORMULA] is the true colour and [FORMULA] is the zero-point.

In principle, the coefficient [FORMULA] must be derived from the observation of a field of standard stars at three different airmasses, and the coefficients [FORMULA], from a large range of star colours. Because the zero-points [FORMULA] and the colour coefficients may vary from CCD chip to CCD chip, one should also observe the standard field separately in the 8 CCDs of the mosaic at least three times through the night.

For the UH8K Camera, this task is clearly beyond the observer's reach because the reading time of the UH8K camera is too long and the whole night would not be sufficient to observe the fields required for a proper photometric calibration. In fact, the dataset provided by the service observing consists of one field of standard stars SA104 (Landolt, 1992), observed in the middle of the night, in I and V. This minimal observation only allows one to measure an average zero-point over the whole mosaic in each filter by combining all the standard stars (one or two per CCD chips).

We derive the colour coefficients [FORMULA] and [FORMULA] and the magnitude zero-points [FORMULA] and [FORMULA] by least-square fit of the colour transformation equations to the SA104 sequence:

[EQUATION]

The airmass correction is included in the [FORMULA] magnitudes, and we use the standard CFHT values for a thick CCD, [FORMULA] and [FORMULA] (http://www.cfht.hawaii.edu/Instruments/Imaging/FOCAM/appen.html#F ). The results appear in Table 2. For comparison, the table also lists another UH8K measurement obtained by J.C. Cuillandre as part of the calibration service of the UH8K 1996 season; no corresponding errors are provided.


[TABLE]

Table 2. Colour coefficients k for the V and I bands derived from the standard field SA104, J.C. Cuillandre's calibration service, and S. Arnouts' routine (labeled Synthetic, cf text). The average zero-points [FORMULA]zero-point[FORMULA] were derived using the associated k.


For further control, we also derive the [FORMULA] and [FORMULA] coefficients from a synthetic standard sequence: synthetic "instrumental" magnitudes are computed for a set of stellar template spectra of different colours by a routine which uses the theoretical transmission curve of the instrument optics + filter (Arnouts, priv. comm. 1999). Application of Eqs. (3) and (4) to the synthetic sequence yields the "synthetic" [FORMULA] and [FORMULA], also listed in Table 2. The corresponding zero-points [FORMULA] and [FORMULA] are derived in a second step by application of Eqs. (3) and (4) to all stars of the SA104 sequence, this time with the "synthetic" [FORMULA] and [FORMULA].

The colour coefficient [FORMULA] derived from the synthetic sequence is compatible with the other values listed in Table 2. A significant dispersion appears in the [FORMULA] measurements, probably because this coefficient is small. The zero-points [FORMULA] and [FORMULA] listed in Table 2 are also consistent within the error bars and are poorly dependent on the colour coefficients. Because the colour coefficients [FORMULA] and [FORMULA] derived from SA104 display large errors, we choose to adopt the colour coefficients from the synthetic sequence and the corresponding zero-points calibrated on SA104: [FORMULA] and [FORMULA]; [FORMULA] and [FORMULA].

For all observed objects in the catalogue, the instrumental magnitudes are converted into standard V and I magnitudes by re-writing the colour equations Eqs. (3) and (4), written in terms of the standard colour [FORMULA], into functions of the measured instrumental colours [FORMULA]:

[EQUATION]

[FORMULA] are the observed magnitudes (Kron elliptical apertures), and [FORMULA] [FORMULA] [FORMULA] and [FORMULA] are the values labeled "synthetic" in Table 2. The other coefficients have the same meaning as those of Eq. (2), and we use, as in Eqs. (3) and (4), the standard CFH values [FORMULA] and [FORMULA].

The astronomer in charge of the service observing stated that the night was clear with only thin cirrus visible near the horizon at sunrise (Picat, priv. comm. 1998). The overlapping regions between the various mosaic fields observed can be used to estimate the possible variations in the zero-points during the night. The fields were observed in the following sequence: UD02-I, UD03-I, UD04-I, UD05-I, UD05-V, UD04-V, UD03-V, UD02-V. Fig. 4 plots the average of the magnitude differences [FORMULA]mag for the bright objects (with [FORMULA] and [FORMULA]) detected in the overlapping CCD regions as a function of sidereal time. For each mosaic field observed, there are 2 to 4 CCD's presenting an overlap with a CCD within another field, and each average [FORMULA]mag is plotted at the sidereal time of the first observed overlap.

[FIGURE] Fig. 4. Average magnitude differences [FORMULA] of the bright objects present in the overlapping regions versus the sidereal time. The I-band data are shown as filled symbols, and the V-band data as open symbols. Time variations are always smaller than chip-to-chip zero-point errors.

A small systematic variation of the average [FORMULA]mag, denoted [FORMULA]mag[FORMULA], with sidereal time is detected in the I filter, and possibly in the V filter. A field-to-field correction of the zero-points is done to account for these small variations during the night: we apply to each field a correction in its zero-point measured by the [FORMULA]mag[FORMULA] in Fig. 4, taking the fields UD02-I and UD02-V as references, and following the sidereal sequence; the same zero-point correction is applied for all the CCD of each mosaic field. The residual magnitude variations measured after correction in the CCD overlaps are [FORMULA] mag in both the V and I filters. These put an upper limit on the variations in the zero-points and colour coefficients between the different CCD's of the mosaic which are not accounted for in the present analysis. Note that a gradient remains in the V data (see Sect. 6.3), which will be removed using the variation of the average galaxy number counts variations with right ascension.

To evaluate the final photometric errors in the obtained catalogue, the V and I magnitudes of objects in the overlapping sections are also compared individually. Fig. 5 gives the residuals in the V and I bands versus magnitude for all objects having V-I colours (cf Sect. 3.3) and Table 3 gives the corresponding standard deviations. The [FORMULA] errors are taken to be [FORMULA]. The large dispersion at bright magnitudes in Fig. 5 is due to saturation effects. The "tilted" variation of the residuals with magnitude for residuals larger than 0.5 mag in absolute values (in both the V and I bands) is caused by the following effect: each object in the overlaps is given the magnitude measured in one of the overlap, arbitrarily. If the average of the 2 magnitudes in the overlap were used, this "tilt" would vanish. However, this affects only [FORMULA]% of the objects, and we consider that it would make no significant difference in any of the results reported here.

[FIGURE] Fig. 5. Photometric residuals [FORMULA] and [FORMULA] in the overlapping frames versus magnitude V and I. The vertical lines indicate the completeness limits. The associated standard deviations are given in Table 3.


[TABLE]

Table 3. Photometric errors in V and I (see Fig. 5). The errors combine random noise, residual variations from field-to-field in the zero-points during the night, and the uncorrected variations of the zero-points and colour coefficients from CCD-to-CCD within the mosaic.


3.3. Magnitude and colour completeness

Three catalogues are generated from the data: one catalogue in the V band, one in the I band, and one catalogue containing objects with measured [FORMULA] obtained by merging the two catalogues. All objects whose centroids are separated by less than [FORMULA] were merged, and their [FORMULA] are computed.

The completeness magnitudes of the V and I catalogues are defined to be one half magnitude brighter than the peak of the distributions. This corresponds to [FORMULA] and [FORMULA]. Because some chips go deeper than others and because the correlation analysis is sensitive to chip-to-chip number density variations, we lower the completeness limit to the least sensitive chip (0.2 magnitude brighter), and we subtract the chip-to-chip dispersion of [FORMULA] mag measured from Fig. 4. Hence, the final completeness limits are [FORMULA] and [FORMULA].

The colour completenesses in the V and I bands are given relative to one another in Fig. 6. The red galaxy completeness limit is determined primarily by how deep the V-band data extend. Because the V-band catalogue is only complete to [FORMULA], faint objects redder than [FORMULA] will be missed near the limit of the I catalogue. (see Fig. 9 and Fig. 10 in Sect. 4.3). This is an important fact to be remembered when making colour-selected correlation analyses.

[FIGURE] Fig. 6. Ratio of galaxies that are detected in the two bands (completeness) versus V and I magnitudes. At faint I magnitudes, the catalogue is biased against red objects

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Online publication: January 29, 2001
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