. 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
, 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.
up to 
, 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.
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.
