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4. Photometry

4.1. Choice of the isophotal level and magnitudecalibration

  The isophote we selected to measure the flux of the objects, taking into account the S/N of the images, corresponds to tex2html_wrap_inline984. Subsequent tests confirmed that this value provides magnitudes very close to total ones : for objects with isophotal magnitude (simply noted as V hereafter) up to tex2html_wrap_inline988, the difference between our measured value and a total magnitude (as estimated by a Kron magnitude) is lower than 0.05 magnitudes and the shift is non-systematic. In what concerns fainter objects, the isophotal radius seems to be overestimating the object radius and we thus measure isophotal magnitudes that can be, at most, 0.2 magnitudes brighter than the total estimates.
Several standard stars in the M 92 star cluster field were used to calibrate the photometry. The calibrated magnitudes for these objects, ranging from tex2html_wrap_inline990 up to tex2html_wrap_inline992, were catalogued by Christian et al. (1985). We measured their fluxes in the image and computed the corresponding apparent magnitudes, which were then compared to the calibrated ones. By taking into account the different exposure times (90 seconds for the M 92 image vs. 3 minutes for the Coma frames) we thus produced a zero-point calibration constant. All nights were photometric and, in such conditions, the zero point variation throughout one night and from night to night is less than 0.1 magnitude (see Sect. 4.5 (click here)). So, we have assumed this same calibration zero-point to be valid for all Coma frames. The airmass term is negligible for all frames.
This relatively large photometric uncertainty is probably mostly due to the lack of a color term in the photometrical calibration: the absence of a second filter makes it impossible to compute such a correction term.

4.2. Data reduction

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 (tex2html_wrap_inline994) 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.

4.3. Star-galaxy separation

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 tex2html_wrap_inline998, V, r and tex2html_wrap_inline1004 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 (tex2html_wrap_inline1008) 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 tex2html_wrap_inline1014 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 tex2html_wrap_inline1018 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 tex2html_wrap_inline1020, 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 tex2html_wrap_inline1024, 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.

4.4. Surface brightness selection effects

In order to test the detection limit of our observations imposed by the surface brightness we plot tex2html_wrap_inline1026 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 tex2html_wrap_inline1030, as confirmed by the turnover value of the histogram of tex2html_wrap_inline1032. 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

4.5. Zero point accuracy and errors estimated for the photometry derived parameters


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, tex2html_wrap_inline1040 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 tex2html_wrap_inline1042 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 tex2html_wrap_inline1050, errors range from 0.02 to tex2html_wrap_inline1052 for bright to faint objects below the completeness magnitude limit.

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