We used the package developed by Olivier Le Fèvre (Le Fèvre et al.
1986; Lilly et al. 1995) to reduce
the data and obtain a catalogue with () position, isophotal radius and
magnitude within the 26.5 isophote, and central surface brightness for more
than 11000 stars and galaxies.
This software has the advantage of having been created especially for this
kind of photometry and extensively tested on MOS CFHT observations.
Star-galaxy separation was performed based on a compactness parameter determined by Le Fèvre et al. (1986, see also Slezak et al. 1988). For each object we computed its compactness Q by:
where , V, r and are, respectively, the central surface brightness, the isophotal magnitude, the corresponding radius and the FWHM for that frame. By normalizing Q, we expect that its value will approach unity for objects with a gaussian profile, that is stars. Actually, in some of the cases, it will be slightly different from 1 due to a natural dispersion in this relation and to possible saturation of some of the brightest objects. The separation value () was then determined by eye inspection of the plot normalized-Q vs. V displayed in Fig. 2 (click here). Stars are expected to be placed under the line, while galaxies will be randomly distributed above the same line. It is evident from that same figure that the stellar sequence with V < 15 presents but these are the saturated objects that were carefully flagged by visual inspection and classified as stars a priori. After separation, stars represent approximately 35% of the total sample, and 36% if we restrict the sample to , which is the completeness magnitude of our data as estimated by the turnover of the raw counts (see Fig. 3 (click here)).
A pitfall of this classification procedure could be the misclassification of compact galaxies as stars. In order to test the reliability of the separation, we carried out a simple test. After having transformed our CCD coordinates into the GMP reference system (see Sect. 5 (click here)), we identified our objects with those belonging to the Coma redshift catalogue obtained by Biviano et al. (1995). We thus estimated that, out of 278 identifications, less than 2% of the objects classified as galaxies by our procedure actually had star-like velocities.
It is obvious that this test is limited to a small number of identifications, since we can only apply it to objects with V > 15, due to saturation, and , which is the 95% completeness limit of the redshift catalogue. Nevertheless, it gives a representative result for the whole sample and reassures us on the efficiency and accurateness of the distinguishing procedure.
After elimination of repeated detections of some of the objects (see Sect. 5 (click here)) we ended up with a catalogue containing 7023 galaxies and 4096 stars.
In order to test the detection limit of our observations imposed by the surface brightness we plot vs. V in Fig. 4 (click here). In this plot the diagonal cut shows the sequence of compact objects. Practically all objects below completeness magnitude 22.5 are placed at , as confirmed by the turnover value of the histogram of . Above that value detections are sparse. This limiting detection value might make us miss some very faint surface brightness objects, but below it we estimate our catalogue to be complete in surface brightness.
Figure 5: Magnitude total errors for all catalogued objects computed by means of Eq. (2 (click here)) (upper panel). We also show, per magnitude bin, the mean error and dispersion (lower panel)
Figure 6: Galaxies measured twice: for each one we compare its magnitude as obtained in two different frames
Figure 7: Crosses give the modulus of the difference between both magnitudes plotted in Fig. 6 (click here), for each one of the double measured galaxies, as a function of the galaxy's magnitude as measured in one of the frames. Circles stand for the median value of this difference in each magnitude bin, and error bars show the dispersion around that median
The estimate of magnitude errors is done frame by frame, according to the variations detected in the sky flux for each exposure. By doing so we are certain of estimating a total error that includes both internal errors inherent to the measurement algorithm, as well as external errors produced by the observational conditions such as differential absorption in the different nights of the run. We compute, for all of the objects in a given frame, a typical measure of the magnitude error that is given by:
where the first term of the right-hand side of the equation is the
magnitude in the catalogue. In the second term, has been computed by averaging, for each
frame, different values of the standard deviation of the sky flux measured in
different regions devoid of objects in that frame, and scaling the result to
the surface of each object. The errors introduced by the flat-field procedure
(large scale residuals) are less than 0.3%, and this factor was neglected
in the standard deviation estimation of the flux measurement.
In Fig. 5 (click here) we plot vs. V for all the objects individually (upper pannel) and its mean value and dispersion per magnitude bin in the lower pannel. The mean value is below 0.1 magnitude.
Another point we set out to deal with in this section - zero point variations - is tackled by means of the 1082 galaxies with V brighter than the completeness magnitude value that were measured twice in the overlapping CCD areas (see Sect. 5 (click here)). Figure 6 (click here) displays magnitudes for these objects. The points cluster closely around the quadrant line y=x with a larger dispersion for fainter magnitudes, as expected. One can notice that differences are not systematic. In Fig. 7 (click here) we quantify these results by computing, for each of the 1082 galaxies, the modulus of the difference between the magnitudes measured in two distinct frames (that is, the values plotted in the 2 axis of the previous figure). We also display, for each magnitude bin, the median and dispersion of those absolute differences for the objects belonging to that bin. Below completeness magnitude the median does not exceed 0.15 and one should bear in mind that this value comprises the magnitude errors (discussed above) for both measures. It is thus by far an overestimate of the zero point accuracy.
In what concerns , errors range from 0.02 to for bright to faint objects below the completeness magnitude limit.