4 Colour-magnitude diagrams

4.1 General remarks

Figure 3 shows the V, (V-I) and I, (V-I) diagrams of all 40170 stars that were identified independently in both V and I filters. The CMD shows the difficulties present in the study of cluster NGC 6553. The field population dominates in the fainter stars ($V \ge$ 18) so much that the cluster sub-giant branch, MSTO region and MS itself are not visible at all. In the brighter stars, typical features of the field population in the direction of the Galactic centre and cluster RGB are clearly visible. The RGB of NGC 6553 is marked as cluster sequence in the Fig. 3. It turns over at about V = 15.3, (V-I) = 2.9 in the V, (V-I) diagram. No such turnover is seen in the I, (V-I) diagram. To the blue side of this sequence, the MS of the young Galactic disk stars can be easily identified while the older bulge populations are present towards the redder side. Both cluster and field populations contain a significant number of bright $(I \le 15)$ but very red stars with (V-I) $\ge$ 4.0. These stars should be taken into account in population synthesis when interpreting red integrated colours of Galactic bulge populations.

4.2 Regions of cluster and field populations

Before discussing the features of cluster or field population any further it is essential to determine the regions in sky where one dominates over the other. In order to find out where the field population becomes dominant with respect to the cluster population we determined the radial stellar density profile of the region using stars brighter than V=20 mag. The (X,Y) pixel coordinates of the eye-estimated cluster centre are (440, 645) with an accuracy of few arcsec. The observed stellar density profile up to $\sim$ 7$\hbox{$^\prime$}$ from the cluster centre is plotted in Fig. 4. The stellar densities derived here are not corrected for data incompleteness. They are therefore underestimated for inner regions (upto a radial distance of about 1$^\prime$), as the plot shown by Trager et al. (1995) indicates that data completness could be less than 50% in the central bin and reaches to $\sim$ 100% only at about 1$^\prime$. Since the cluster profiles from star counts are better than those from integrated photometry in the outer regions, we have used the former for determining outer boundary of the dominant regions of the cluster population. The stellar density decreases strongly from cluster centre out to about a radius of 3$^\prime$. Beyond that it becomes asymptotic at a level of about 150 stars arcmin^-2. The profile given by King (1962) fits the observed stellar density profile satisfactorily.

  

Figure 4: This plot shows the observed stellar density (logarithm of stars brighter than V=20 mag per square arcmin) as a function of radius in arcmin. The length of the bar denotes the error in density determination due to number statistics. The solid curve shows a least square fit of the King profile. The cluster population is not dominant beyond a radial distance of about $3\hbox{$^\prime$}$

The above analysis clearly indicates that the population of the cluster NGC 6553 is not dominant beyond a radial distance of $3\hbox{$^\prime$}$ and most of the stars present in that part of the sky represent the field population. We therefore considered stars with Y < 0 pixels (outside the cluster frame; see Fig. 1), i.e., $\ge 215 \hbox{$^{\prime\prime}$}$ from the cluster centre as representative of the field population. In order to maximise the percentage of cluster members in the sample and to avoid the effects of strong stellar crowding on the VI data, we consider only stars lying in an annular region (defined with inner and outer radii of 17 to 100 arcsec respectively) as representative of cluster population. The V, (V-I) diagrams for the representatives of field and cluster populations are shown in Fig. 5. Their respective numbers are about 14250 and 8500. The corresponding areas are about 23.6 and 8.4 arcmin². The dominance of one population over other can be clearly seen in the both diagrams. With these better defined features of the two populations contamination effects in the CMDs stand out more clearly now. The limiting V mag of the field population is about a magnitude fainter than that of the cluster even though the exposure times are similar (see Table 1). This illustrates the effect of crowding on the limiting magnitude of the observations. We will now analyse both populations separately.

  

Figure 5: The V, (V-I) diagram for the representatives of cluster and field populations. The regions from where they were selected are listed. Dominance of one population over other can be clearly seen in these diagrams

4.3 Subtraction of the field population

We have carried out statistical field star subtraction. For this, we consider only stars brighter than V = 20 mag in both cluster and field populations, since the cluster HB and RGB are present there. The field population used in the statistical subtraction has been selected from a rectangular region with coordinates (in pixels) X=0 to 1000 and Y=-725 to -450. Thus the area is equal to that of the cluster region but located at a radial distance of about 7$\hbox{$^\prime$}$ from the cluster centre. At this radial distance, the cluster population will be negligible, as the values of core and tidal radii for the cluster are about 0.6$\hbox{$^\prime$}$ and 8$\hbox{$^\prime$}$ respectively (cf. Trager et al. 1995). There are 3914 and 1317 stars brighter than V = 20 mag in the chosen cluster and field regions respectively. The statistical field star subtraction is done in the following manner. For each star of the field population, the nearest star located within a box of size $\pm$0.5 mag in V and $\pm$0.2 mag in (V-I) from the V, (V-I) position of the field star in the CMD of the cluster region is deleted from the sample. This procedure will remove statistically field stars from the selected cluster region. However, precisely because of this we cannot completely rule out the presence of some field stars in the cleaned sample or oversubtraction in the cluster data. The lower part of the Fig. 6 shows the CMD of the cleaned sample. The RGB and HB are very well defined in the diagram. Some field stars mostly right side of the cluster SGB are still present in the diagram but they will not affect the results.