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Astron. Astrophys. 320, 757-775 (1997)

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2. Observations, data reduction, comparisons and completeness

2.1. Observations and cluster sampling

The CCD data were obtained at the 3.6m CFHT telescope on April 1991 by H. Richer and R. Buonanno within a wider collaborative program, using a 2,048 [FORMULA] 2,048 pixels detector with field of view of [FORMULA] 7' [FORMULA] 7'. The observations consisted of two sets of BVI frames reported in Table 1. The short exposures were specifically taken to survey the very inner regions, avoiding strong saturation effects. Since the detector had a very poor response in the blue, Ferraro et al.  (1993-F93) used the deepest V and I exposures to get a first hint on the BSS population in the cluster central regions ([FORMULA] 2').


[TABLE]

Table 1. Observation log of the BVI CCD data


Fig. 1 shows the position of the area surveyed in the present study (the full square) overlapped to the map of the regions considered in the photographic study (PH94). For sake of clarity, the individual stars measured on the plates in the PH94 bright (crosses) and faint (small dots) sample are respectively plotted.

[FIGURE] Fig. 1. Map of the regions of M 3 covered with the photographic survey (PH94). The full square reproduces the field covered by the present CCD-observations. Crosses indicate stars included in the PH94 bright sample, while dots indicate stars membering the photographic faint sample. In the map, North is up and east is to the right; the scale-unit is in arcsecond.

To give a global overview of the planned survey, we report in Fig. 2 also the size and location of the three WFPC2 fields we observed with GO 5496. As it can be seen, there is a useful overlapping between the photographic, CCD, and HST  considered areas. For comparison, we have also reported in the same figure (dashed squares) the fields covered by other recent photometric studies on M 3, namely those by Bolte et al.  (1995; hereinafter BHS), Guhathakurta et al.  (1994; hereinafter GYBS), and Burgarella et al.  (1995) using the WFPC of HST  before refurbishment.

[FIGURE] Fig. 2. Global overview of the fields observed in the photographic, CCD, and HST  surveys that will compose our overall photometric data-set in M 3. The full square represents the contour of the CFHT field. The dashed squares are the fields surveyed by Bolte et al.  (1995; label B.) and Guhathakurta et al.  (1995; label G.), respectively. Note that the FOC-field observed by Burgarella et al.  (1995) would be represented here by just a "central dot". The annulus (2.0' [FORMULA] 3.5'; thin solid lines) is the region of M 3 where the "complete" sample considered in the photographic study has been obtained (PH94). The small full circle represents the central region (with [FORMULA]) where crowding makes unfeasible any meaningful photometry on the deep CCD-frames taken at the CFHT.

2.2. Data reductions

The data analysis was performed in Bologna and Rome using ROMAFOT (Buonanno et al.  1979, 1983), whose standard procedures have been reported in other papers (see for references Ferraro et al.  1990, F93). No special requirement has been involved either in the searching phase or in measuring the instrumental magnitudes.

Since the only wide set of standard stars available in the M 3 field we observed were those measured with the photoelectric photometer by Sandage (1953, 1970), later revised by Sandage and Katem (1982), we put some effort to obtain an independent CCD-calibration. As a matter of fact, neither BHS (they only presented instrumental magnitudes) nor GYBS (who ultimately referred their magnitudes to Auriere and Cordoni 1983 and F93) obtained an independent calibration. The photometry of Auriere and Cordoni (1983) in the central regions was linked to star profiles (King 1966) and cannot be used for calibration. The data presented by Scholz and Kharchenko (1994) are referred to Sandage (1970). Finally, Paez et al.  (1990) in their CCD-study of the outer regions (at about 5 arcmin from the cluster center) did not get any independent calibration but referred their data to 41 stars in common with Sandage and Katem (1982).

In PH94, we used the sequence of photoelectric standards from Sandage (1970) to calibrate the photographic magnitudes to the standard [FORMULA] Johnson system. In F93, the CFHT data were calibrated using two standard fields observed during the same nights in NGC 4147 and M 67, with the well known problems related to the difficult handling of calibrated stars in crowded standard fields. Eventually, we concluded that a new independent CCD-calibration was necessary starting from a proper set of primary standards.

After several unfruitful runs (due to bad weather, telescope failures etc.), our new calibration is based on an observing run carried out at the 1.23 m telescope at the German-Spanish Astronomical Centre, Calar Alto, Spain. BVI CCD-frames of M 3 and of several Landolt CCD standard areas were acquired under photometric conditions in the night of April 2, 1995, using a thinned 1024 [FORMULA] 1024 Tektronix chip (24 µ pixels, 0.50 arcsec/pixel), with Ar-coatings. The I filter is in the Kron-Cousin system, centered at 8020 Å.

The calibration of the CFHT CCD magnitudes was thus performed in two steps. First, we used 18 stars in 7 CCD standard areas (Landolt 1983) to link the Calar Alto instrumental magnitudes to the standard Johnson system. The final equations we adopted for the B,V,and I filters are reported below and plotted in Fig. 3:

[EQUATION]

([FORMULA] 0.029),

[EQUATION]

([FORMULA] 0.020),

[EQUATION]

([FORMULA] 0.026),

where b,v,i, are the instrumental magnitudes. 1 The atmospheric extinction terms in each colour have been derived by observing the same standard field at different airmass during the night.

[FIGURE] Fig. 3. Calibrating Landolt CCD standard stars used to transform the instrumental Calar Alto magnitudes to the Johnson standard system. Different symbols refer to stars in different standard areas.

In the I calibration we have used only the measurements having a sufficient S/N. In particular, this has led to exclude two of the bluest standard. because of this, we could exclude the existence of residual colour terms for the I band.

These equations have been used to calibrate the instrumental magnitude of a sample of [FORMULA] 100 isolated, unsaturated stars in the Calar Alto frames for which the aperture photometry has been performed. This set of stars has been used to correct the CFHT magnitudes (previously calibrated with the NGC 4147 and M 67 standard fields, see F93). The relations linking the "old" CFHT calibration system to the new standard system (CCD96) are:

[EQUATION]

[EQUATION]

[EQUATION]

Following the above procedure we linked the whole CFHT-CCD data set to the Johnson system. In the next section we find the relation to transform the photographic data set to the new standard system here adopted.

In this respect, it is important to note that, after completion of our reductions, we became aware of the existence of a new independent photometric study of a very wide sample of M 3 stars (about 23,700) carried out by K.A. Montgomery (1995 - M 95) as part of his Ph.D. dissertation, based on 2048 [FORMULA] 2048 (T2ka) CCD-frames taken with the 0.9-meter telescope at KPNO. Since with the f/7.5 secondary, the telescope produced an image scale of 0.68 arcsecs/px and a field of view of 23.2 arcminutes, and moreover 2 [FORMULA] 2 mosaics of images were made with the centers offset by 10 arcminutes in both right ascension and declination, the total field covered by Montgomery fully overlaps both our field and the outer field independently observed by Stetson and Harris (1988), which being located outside the region we observed could not be used in our photometry. We will discuss in detail the results of the comparisons with this new data-set at Sect. 2.4 and 2.5.

2.3. Photographic [FORMULA] CCD photometry; magnitudes and positions for the global sample of M 3

More than 900 stars have been found in common between the CCD96 and PH94 (bright and faint) sample. However, due to the limited performances of the used CCD detector in the blue band, the photometric internal errors in the B band are large and reduce the reliability of the transformations. For this reason only 532 bright ([FORMULA]) stars in common have been used to derive the relations linking the photographic photometric system to the standard system here adopted. The final relations correcting the V magnitude and the [FORMULA] colours are:

[EQUATION]

[EQUATION]

These corrections have been applied to the whole (bright + faint) PH94 sample. A small residual non-linearity in the photographic data (probably due to the original plate transformation) has been corrected using a polynomial fit of [FORMULA] order (to yield [FORMULA] and [FORMULA] for the V and B filter, respectively). This additional correction is properly determined only for bright stars ([FORMULA], [FORMULA]).

Resting on our own data alone, it would be impossible to check properly the linearity of the fainter PH94 measures. However, by comparing our data with the quite similar data-set obtained by M 95, we can extend the linearity test to fainter magnitudes, as explained in Sect. 2.4. From this last comparison we have obtained further (small) corrections for the fainter stars (see Sect. 2.4) using a similar procedure as adopted for the bright sample.

Then, to avoid any discontinuity at the junction between the bright and the faint PH94 samples, we have imposed coincidence between the corrections computed at the junction [ [FORMULA] and [FORMULA] ] from the two different CCD data-sets. Fortunately, they actually turned out to be almost equal, and this reinforces both the validity of the procedure and the achievement of a good linearity allover the "revised" PH94 sample.

In Fig. 4 and Fig. 5, we present the ([FORMULA]) and ([FORMULA]) CMDs containing only stars outside a radius of 20" from the cluster centre, excluding the variables which are however included in the lists. Due to the low efficiency in the blue of the CFHT CCD-camera we have plotted in Fig. 4 only the objects measured on our B CCD images with [FORMULA]. In particular, the upper part of the [FORMULA] CMD (brighter than [FORMULA]) contains 2227 constant and 154 variable stars taken from the CFHT CCD sample, plus 42 variable stars and 444 constant stars taken from the bright photographic sample outside the CCD field. For magnitudes fainter than [FORMULA], we report the 9339 stars from the faint PH94 sample. The total number of stars in this CMD is therefore 12206. The [FORMULA] colour magnitude diagram contains 9647 stars including 155 variables that have both V and I magnitudes.

[FIGURE] Fig. 4. CCD96 [FORMULA] colour-magnitude diagram for 12206 stars in M 3 with r [FORMULA] 20". Variable stars are not shown; only stars with [FORMULA] from the CFHT sample have been plotted. See text for details.
[FIGURE] Fig. 5. CCD96 [FORMULA] colour-magnitude diagram for 9647 stars in M 3 with r [FORMULA] 20". Variable stars are not included in the plot, see text for details.

All the available data (magnitudes and positions) are available upon request from the authors, and will also be sent to Strasbourg Data Center. As in the PH94 paper, X, Y coordinates (in arcsec) are referred to the cluster centre, taken at [FORMULA] and [FORMULA]. Coordinate transformation to other systems can be easily performed; to help with cross-identification, we note that our bright stars No. 8877, 10052 and 12045 are the stars No. 9, 3842 and 2267, respectively, in the photometric catalogue of GYBS. This allows conversion of our positions to equinox 2000 coordinates, since GYBS's positions are in R.A. and Dec. referred to the equinox 2000.

2.4. Comparison with other studies

We compare here our CCD-calibrated photometry with the data taken from other studies for the stars in common.

[FORMULA] Comparison with Sandage and Katem 1982

The comparison was made using 81 stars from Tables I and II of SK82, cross- identified with our data. The results of this comparison, together with the least squares fits through the data, are shown in Fig. 6.

[FIGURE] Fig. 6. Differences between our calibrated magnitudes and those from Sandage and Katem (1982) for 81 stars (extracted from his Tables I and II). In each panel the equations of the least-squares fits (solid lines) to the data are also reported.

As one can see, the overall agreement is good, but there are also important differences. First, there is a luminosity shift in both B and V, variable with varying the B-V colour. Second, there is a quite noticeable colour term, in the sense that our data are [FORMULA] 0.08 mag redder at [FORMULA] (the bluest point of the HB), [FORMULA] 0.03 mag redder at [FORMULA] (corresponding to the middle of the instability strip), and [FORMULA] 0.08 mag bluer at [FORMULA], [FORMULA] at the termination of the Red Giant Branch (RGB).

[FORMULA] Comparison with Guhathakurta et al.  1995

Fig. 7 shows the results of a similar comparison with the V and I magnitudes of GYBS for 634 stars, almost down to the completeness limit of the survey. GYBS studied the central field of M 3 using the F555W and F785LP bands of the HST/Planetary Camera-1, that are similar to the Johnson V and I bandpasses, respectively.

[FIGURE] Fig. 7. Residuals between CCD96 V and I magnitudes and the corresponding photometry of GYBS in the F555W (V) and F785LP (I) bands of HST /Planetary Camera-1 (see text). The comparison is based on 634 stars in common within the area covered by GYBS.

As explained below, this comparison is actually more useful for checking completeness since, after a first colour transformation from HST instrumental magnitudes, GYBS linked their photometry to the available ground-based data. In particular, their final values include the application of zero-point offsets to the V and I data to match fiducial points of the upper parts of the CMDs presented by Auriere and Cordoni (1983) and F93. The generally good agreement shown Fig. 7 is thus obvious though the F93 CCD calibration was still based on the NGC 4147 and M67 standard areas.

[FORMULA] Comparison with Montgomery 1995, and Stetson and Harris 1988

Concerning the data-set obtained by M 95, we present here the results of the comparisons made using the still preliminary list of magnitudes and colors kindly made available to us by Dr. K. Janes. Since they could still be subject to further analysis and revisions, and will be eventually published in the near future (Janes and Montgomery, 1996), we schematically report on two main aspects which are of interest for the present study: the linearity test and the comparison of the zero-points.

Concerning the linearity test, after carrying out several different procedures, we decided to restrict the sample to a sub-set of the 7,152 stars in common (from the RGB tip down to the faintest magnitude limit), which have unambiguous identifications, no detected companions in both photometries, and sufficiently low and well difined background. This implies that these stars lie mostly in the outer cluster regions and have good internal photometry in both studies.

From the study of the residuals it is confirmed that, while no significant trend is evident after the corrections applied to the bright PH94 stars using our corresponding CCD data (see Sect. 2.3), there is still a small residual non-linearity in the faint photographic PH94 data, quite similar in size and morphology to that detected for the bright stars with respect to our CCD measures. Therefore, we have corrected the faint PH94 measures using again a polynomial fit of [FORMULA] order (computed over [FORMULA] 3,800 faint stars) as done for the bright stars, and imposing coincidence of the (small, [FORMULA] 0.01-0.02 mag) linearity corrections at the junction between the bright and faint samples (see Sect. 2.3).

The comparison of the zero-points has also been made on a special sub-set of about 2,000 stars, chosen within the sample considered for the linearity test but with V [FORMULA] (to avoid low S/N data). The final figures for the differences, in the sense M 95 - Ours, are: [FORMULA], [FORMULA], [FORMULA] mag, respectively. As can be seen, especially for the B-magnitudes, the residuals are quite large and somewhat worrying.

Based on the description reported in Table 2.1 and Fig. 2.3 of his thesis, Montgomery observed Standard Star fields from Landolt (1992) over the six night run at KPNO, securing approximately 250 measurements with internal accuracy in the individual measure better than 0.05 mag. The KPNO run standard deviations of the residuals he quoted were 0.018 in V and 0.024 mag in B, quite comparable with the figures from our own calibration (see eqs. (1)-(2)). It is therefore difficult to explain the differences between the zero-points adopted in the two photometries based just on the formal errors. And it is also difficult to choose which of the two may be correct. To have further insight on this important aspect, we have carried out a further comparison with the data obtained by Stetson and Harris (1988, -SH88).

Since there is no overlap between our surveyed regions and the area observed by SH88, we must use the comparisons (for different sets of stars) between M 95 and SH88 on the one hand, and M 95 and this study, on the other, to provide a link between SH88 and our photometry. So doing, we get that the differences between our data and SH88 (in the sense Ours - SH88) are: [FORMULA], [FORMULA], and [FORMULA] mag. These figures are compatible with the residuals measured by Montgomery with respect to SH88. From Fig. 2.13 and Table 2.3 of Montgomery (1995) one has in fact for the residuals M 95 - SH88 [FORMULA], [FORMULA] mag, based on 27 stars in common with SH88. As a matter of fact, the zero-points of SH88 turn out to be intermediate between the other two photometric calibrations.

2.5. Error estimates and choice of the zero-points

Since we have only two frames in each colour with quite different exposure times, we cannot use repeated measures of the same star to yield a direct estimate of the internal measuring errors. However, we can get some quantitative hints from the photometric parameters listed for each star within ROMAFOT (which essentially trace the quality of the fit) and from the comparison of the morphology of the individual branches in the CMD (at different magnitude levels) with those obtained in previous studies. In particular, using also as reference the error estimates discussed in PH94, we are fairly confident that the internal errors in the present photometry are [FORMULA] 0.02-0.03 mag at [FORMULA], and [FORMULA] 0.05 at the TO region.

Concerning the systematic errors, we have already discussed the problems related to the zero-points and the colour transformations. There are now three independent calibrations referred to observations of Landolt's (1992) standards. They are in marginal agreement, but it is difficult at the present stage to choose which is the best.

Since the calibration here adopted seems to be compatible with that obtained by Stetson and Harris (1988) (they actually show a systematic difference of 0.04 both in B and V, yielding however no colour difference), we decided to keep using our calibration.

To be conservative and taking into account the size of the uncertainties, we conclude however that we still cannot exclude errors as high as 0.05 mag in the absolute values, both in magnitude and in colour (particularly at the blue and red extremes).

Such a conclusion is quite disappointing in particular for what concerns the specific study of the RR Lyrae variables (Cacciari et al.  1996), and further efforts to improve the absolute calibrations are urged.

2.6. Completeness of the CMDs

Besides the comparisons in colour and magnitude discussed above, the BHS, GYBS, and M 95 samples can be also used to test in a quantitative way the degree of completeness actually achieved in the present photometric data set. These checks can be performed on different subsets, depending on the regions and the magnitude range covered in the different studies.

[FORMULA] Comparison with Bolte et al.  1993

Of particular interest is the comparison with the BHS's samples, since they were obtained with the same CFHT telescope, " under apparently photometric conditions and with excellent seeing". A careful check is feasible using all stars brighter than [FORMULA] 16.75, the limit in V used by BHS for the reference population in order to study the blue stragglers distribution (see below). The result of this check is plotted in Fig. 8 that compares the (V, [FORMULA]) CMD we have obtained from surveying the same area as BHS (see Fig. 2) with their (V, [FORMULA]) diagram. Note that their instrumental V magnitudes have been transformed to our system by using the brightest (12.5 [FORMULA] 17.0) 544 stars in common.

[FIGURE] Fig. 8. Comparison of the upper part of our CMD (b) with that of BHS (a) in the region covered by their study, for stars brighter than [FORMULA] 16.75. Instrumental v magnitudes of BHS have been shifted to match our own calibrated V system. Variable stars are here included and this explains the "fatness" of the HB (see text).

In the region in common between the two samples, BHS have found 801 stars while we detected 828 objects, at [FORMULA]. Among these, 775 stars were successfully cross-identified, whereas 26 stars from BHS and 53 stars from our survey had no mutual correspondence. However, we must note that most of these residual stars lie on the faint RGB, just above the threshold ([FORMULA]) adopted to carry out the comparison. Therefore, the difference in the samples essentially depends on small variations in the arbitrary offset necessary to match the two data-sets in V and on photometric errors. Since the stars plotted in the CMD of Fig. 8 are the same and the observing conditions of the BHS run were excellent, the overall appearance of the two CMDs confirms also the good internal quality of our photometry. Note that the width of the red HB (in particular) is due to the inclusion of randomly phased measures of the variable stars.

[FORMULA] Comparison with Guhathakurta et al.  1995

A similar check has been carried out with the GYBS data. Fig. 9 presents the CMDs for the stars independently detected and measured in the common area covered by the two studies (see Fig. 2, [FORMULA] 1'). In this region, we have found 340 stars while GYBS list 339 objects. Of them, 15 and 16 stars in the GYBS and in our subsamples, respectively, do not have cross-identification. As for BHS, they mostly lie near the faint limit of the selected subsets, and the difference is thus due to the selection bias induced by the photometric scatter.

[FIGURE] Fig. 9. Comparison of the upper part of the CMD by GYBS (a) with our data (b) in the spatial region in common to both studies. The dashed line reports the Horizontal Branch and bright Red Giant and Asymptotic Branch limit as adopted in Fig. 7 of GYBS.

By inspecting Fig. 9, it is also interesting to note the difference in photometric quality achieved in the two samples. Since the GYBS data have been obtained using the HST WFPC1, the larger internal scatter is most likely due to the difficulty of measuring "aberrated" stars in the inner crowded region. On the other hand, the excellent agreement in the total numbers of selected objects confirms the very high degree of completeness achieved in our ground-based survey (note that the searching phase is almost "perfect" for the bright objects also with HST WFPC1).

The comparisons discussed above can be considered as external independent checks of the degree of completeness actually achieved in our searching phase, at least as far as the upper part of the CMD is concerned. The results of the comparison have shown that completeness is close to [FORMULA] even using the HST sample as reference. Since this comparison refers to the innermost regions of the cluster, where completeness is most problematic, we are confident that a similar very high degree of efficiency has been guaranteed by our searching routine in the more external fields. Additional tests made adopting the usual "artificial star" procedure fully confirm this conclusion.

[FORMULA] Comparison with Montgomery, 1995: the bright sample

The availability of the new catalog compiled by Montgomery (1995) has offered the opportunity to carry out a preliminary check of completeness allover our observed field as his observations fully overlap our considered regions. Since the limiting magnitudes of the two surveys vary with the cluster regions, we have separated the analysis of the bright sample from that of the faint one.

Fig. 10 shows the CMDs obtained from the two photometries down to B [FORMULA], considering just the overlapping area. As can be seen, apart from a slightly larger scatter in M 95 data, the overall morphology is very similar and also the total number of stars is comparable. This evidence by itself confirms that the degree of completeness achieved in the two studies is also similar and high. We have detected 2841 stars while M 95 lists 2750 objects. However, to have quantitative hints of the completeness of our sample it is useful to check the number and properties of the objects which are present only in the M 95 sample, as they could have been missed in our search.

[FIGURE] Fig. 10. Comparison of the upper part of the CMD by M 95 (a) with our data (b) in the spatial region in common to both studies. Only stars with [FORMULA] have been plotted. Variable stars are here included.

Fig. 11 shows the CMD (panel a) and the map (panel b) of the objects M 95 detected on our field and we apparently missed. It is quite evident that they are mostly located in the very central regions where the resolving capability of the two surveys is different, our own being much better. A careful interactive analysis of a subset of these objects has shown that most of them are actually blended images which we resolved into two (or more) separated stars with off-center positions with respect to the blend. If we increase the size of the box (from 0.5 to 1.0 arcseconds) we get multiple identifications with the individual components.

[FIGURE] Fig. 11. V, [FORMULA] CMD (a) and map (b) of the stars detected by M 95 on our area and not cross-identified with objects detected by ourselves. Coordinates are in arcsec with respect to the cluster center (see Section 2.3).

The few bright stars located at the outskirts of the considered field are lacking in our samples as they are "field" stars according to Cudworth (1979) or because they are highly saturated standards.

To summarize the comparisons and to give a further insight on the mutual completeness of the four considered samples, we have plotted in Fig. 12 the ratios between the number of stars measured by BHS (panel a), GYBS (panel b), and M 95 (panel c), respectively, and the number of stars we measured per bin of 0.5 mag in V. The comparison is obviously made on the areas in common between each quoted study and our own survey. Error bars have been computed by simply taking the inverse of the square of the total number of stars in each bin. As can be seen the bright samples are substantially the same especially considering the effect of binning over CMDs which have slightly different calibrations and local morphologies.

[FIGURE] Fig. 12. Comparison of the number of stars we included in the bright samples with the corresponding lists by BHS (a), GYBS (b) and M 95 (c). The ratios of the numbers of stars we found to those measured by BHS, GYBS, and M 95, respectively, are presented over 0.5 mag bins in V.

In conclusion, based on the tests here carried out and on those already reported for the outer samples considered in PH94, we can say that most likely all the objects brighter than [FORMULA] have now been detected and measured in a circular annulus with 0.3' [FORMULA] 7' in M 3.

[FORMULA] Preliminary comparison with our own HST-data: the bright sample

The considerations made above are sufficient to assess the degree of completeness necessary in determining the populations of the bright RGB and AGB (down to [FORMULA] mag below the HB). However, further discussion is required concerning the completeness of the faint, blue HB tail which plays a rôle in the computation of the various population ratios we are going to discuss later.

Since we have specifically taken deep UV exposures with HST to study this aspect and a detailed paper is in preparation, we simply anticipate here the essence of the results. The preliminary reductions of the HST data confirm that their is no significant population in the HB blue tail fainter than [FORMULA] (for [FORMULA]) except for the objects we have detected with the present BVI CCD-survey and the old PH94 study.

In particular, in the area in common between the present sample and the HST survey, we have detected 8 objects in the CCD frames lying at [FORMULA], [FORMULA] and 8 objects in the HST frames. Although the detected population is small and the membership to the HB blue tail is somewhat uncertain given the photometric scatter, this ensures that the loss of candidate faint HB stars should be small and in any case quite negligible in the computation of the global population ratios (see Sect. 3.5).

Outside [FORMULA], where HST-data are not availabe at present, we rest on the tests for completeness carried out on the photographic plates used in PH94. On the other hand, with decreasing significantly the degree of crowding, the degree of completeness raises quite steeply.

In conclusion, from the available data there is no evidence that the stellar counts of the HB (down to [FORMULA], with [FORMULA]) and the AGB and RGB (down to [FORMULA]) are affected at any significant level from incompleteness. Hereinafter, we will refer to this subset as the Bright Complete Sample (BCS) to be used for computing useful population ratios (see Sect. 3.5).

[FORMULA] Comparison with Montgomery, 1995: the global sample over the annulus with [FORMULA] arcmin

In PH94 we presented a CMD including all the stars we measured within the annulus with [FORMULA] arcmin. The degree of completeness of that sample was checked using various techniques, but it was impossible at that time to make any comparison with similar observations in the same field. We have now the opportunity to directly compare our data with the M 95 sample over the same annulus and get some useful information.

Fig. 13 presents the CMDs for the objects measured in the two surveys in the considered annulus. As already noticed for the bright samples, they are very similar and consistent. Of course, the total numbers of measured objects are different mostly because the limiting magnitude we reached is deeper.

[FIGURE] Fig. 13. Comparison of the upper part of the CMD using data from M 95 (a) and from the present work (b). This comparison is limited to the annulus between [FORMULA] and [FORMULA] arcmin.

To make a quantitative comparison it is therefore useful to compute the population ratios over magnitude bins large enough to avoid small number fluctuations. Fig. 14 shows the distribution of the observed ratios as a function of the V magnitudes. As can be seen, down to V [FORMULA] 18.5 the two samples are essentially identical and, presumably, "truly" complete. For fainter magnitudes, our own sample clearly outnumbers the M 95 list.

[FIGURE] Fig. 14. Ratios of the stars detected by M 95 and in the present work over the completeness annulus ([FORMULA] arcmin) defined above. Data are binned in 0.5 mag bins in V.

In conclusion, this comparison adds further confirmation that the samples we secured on the various regions of M 3 we observed are sufficiently complete to be used for testing the ecvolutionary models.

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Online publication: June 30, 1998
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