|Figure 6: The V, (V-I) diagrams for the cluster and field stars are presented. The cluster population is for stars brighter than V = 20 mag. The sample has been cleaned statistically for the field star contamination. The field stars brighter than V = 21 are plotted. Theoretical isochrones from Bertelli et al. (1994) for solar metallicity are overplotted for indicated apparent distance modulus, reddening and age. The solid curve is the RGB while the dotted one traces the AGB. The dashed curve is the isochrone fitted to the disk population of the galaxy. The eye-estimated fiducial points for the RGB and HB are plotted by open triangles and squares respectively|
metallicity, the RGB-bump is located below the HB (cf. Lanteri Cravet et al. 1997) and the same is observed for NGC 6553 in Fig. 7. This indicates that the cluster metallicity is nearly solar which is in agreement with the morphological features present in the V, (V-I) diagram of the cluster (see discussions below).
|Figure 7: The differential luminosity function of the GB. The peaks due to the HB stars and RGB-bump are marked as HB and SGB respectively|
The ratio of duration of the RGB-bump phase relative to the life time of the star during the HB phase for clusters having characteristics of the Galactic bulge clusters is 0.2 (cf. Lanteri Cravet et al. 1997 and references therein) and is equal to the ratio of number of stars present in the corresponding evolutionary phases. In order to carry out the star counts in the two evolutionary phases, we used the linear interpolation (see dotted line in the Fig. 7). We obtained the ratio of numbers in the RGB-bump and the HB phases as which is not too different from the value of obtained by Lanteri Cravet et al. (1997) for the cluster. Considering the uncertainty, one can say that the value is in good agreement with the theoretical predictions of 0.2.
|Figure 8: The V, (V-I) diagrams of the stars brighter than V = 19 mag located in the six rectangular strips of the central part of the cluster. The X and Y pixel coordinates of the strips are marked. The HB and RGB stellar sequences are clearly visible in all the diagrams|
|Figure 9: The V, (V-I) diagrams of the mean loci of the HB and GB sequences observed in different strips of the cluster region. Open squares, crosses, open triangles and open circles denote the fiducial points in the strips with Y=150 to 350; 350 to 550; 550 to 750 and 750 to 950 respectively in the cluster region. The arrow indicates the direction of normal interstellar reddening vector|
The above analysis indicates that presence of differential extinction across the cluster face can explain most of the scatter present in the RGB sequence of the cluster population. However, it may not explain more than a magnitude elongation observed in the V magnitude of HB stars of NGC 6553. Ortolani et al. (1990) suggest that blanketing effect can also produce tilting and extension in the HB of the cluster.
The lower part of Fig. 6 shows the presence of a well defined but broad RGB in the diagram. Eye-estimated fiducial points for the RGB and the HB are plotted in the figure and listed in the Table 5. Presence of differential extinction across the cluster face has been considered in this process. An error of 0.03 mag in (V-I) of the fiducial points of RGB is expected. The RGB is extended and curved down, characteristic of a nearly solar metallicity population, like that of the globular clusters NGC 6528, Terzan 5, Terzan 6, and Baade's window.
A theoretical isochrone from Bertelli et al. (1994) is overplotted in Fig. 6 for an apparent distance modulus of 15.7 and reddening E(V-I) = 0.9. The isochrone has Z=0.02 and an age of 12 Gyr. From the fitting of the theoretical isochrones in Fig. 6, one may say that the redder bright stars, if they are indeed cluster members, are on the AGB rather than in the RGB stage of stellar evolution. However, the evolutionary status of the red stars with a (V-I) colour in the range of 3.5 to 5 is not clear as the isochrones for both AGB and RGB merge. The theoretical isochrone fits the shape of the observed RGB very well up to 4.5 and starts to deviate for redder colours. Similarly the theoretical isochrones cannot explain the location of the bright red stars observed in the V, (V-I) diagram of NGC 6528 (see Richtler et al. 1998). This red extension of the AGB/RGB stars must be taken into account when modelling spectra of elliptical galaxies (see Bruzual et al. 1997, and references therein for a detailed discussion).
A number of spectroscopic analyses indicate that metallicity of the cluster NGC 6553 is close to solar. The [Fe/H] values range from -0.1 to -0.4 (see Rutledge et al. 1997; Origlia et al. 1997; Bruzual et al. 1997 and refernces therein). In order to check the consistency with these, we used the present photometric indicators for estimating the metallicity of NGC 6553. The morphology of the RGB can be used to estimate the metallicity and reddening of the cluster. Ortolani et al. (1991) used the slope of the RGB to determine abundances of the metal-rich globulars and found that the metallicity of NGC 6553 is similar to solar. Another indicator of the metallicity is the V magnitude difference between the HB level and the top (brightest) of the RGB, . Its value decreases with increasing metallicity of the cluster. Use of such relations avoids the otherwise required a priori knowledge of reddening for the determination of the metallicity of a cluster. Barbuy et al. (1997) find that the value of is 3.1 for NGC 7099 ([Fe/H] =-2.1), 2.3 for 47 Tuc ([Fe/H] =-0.7), 2.1 for NGC 6356 ([Fe/H] =-0.4) and 1.4 for NGC 6528 ([Fe/H] =-0.2). For NGC 6553, . This would place NGC 6553 with a nearly solar metallicity similar to NGC 6528 (cf. Barbuy et al. 1998).
Heitsch & Richtler (1999) have derived the following empirical relation between and [Fe/H] using theoretical isochrones given by Bertelli et al. (1994) for [Fe/H] = 0.4, 0.0, -0.4 and -0.7.
This yields a value of for [Fe/H] of NGC 6553. This agrees very well with our above estimate as well as with earlier metallicity determinations for the cluster (see Bruzual et al. 1997; Rutledge et al. 1997; Origlia et al. 1997; Guarnieri et al. 1998).
Richtler et al. (1998) have derived empirical relations between (V-I)0,g (intrinsic (V-I) colour of the RGB at the magnitude level of HB in the CMD) and [Fe/H] using the (V-I) theoretical isochrones given by Tripicco et al. (1995) and by Bertelli et al. (1994) for old and metal-rich clusters. We have used these to derive a (V-I)0,g value for the metallicity of NGC 6553. For (V-I)0,g the relation based on Tripicco et al.'s (1995) isochrones yields a value of 1.1 while the relation obtained using Bertelli et al. (1994) isochrones gives 1.3. A similar difference was found for NGC 6528 also (Richtler et al. 1998). This shows the uncertainty involved in the determination of (V-I)0,g using appropriate published theoretical isochrones which depends on the opacities and composition used in the models (see Salaris & Weiss 1998; Alonso et al. 1997, for a detailed discussion). There is growing evidence that alpha elements in the bulge are significantly enhanced in comparison to the values used in the theoretical stellar evolutionary models. Also, the transformations from the theoretical and to the observational visual magnitudes and colours are very uncertain at the low temperatures of the giant and subgiant stars in an old metal rich population. All these seem to be responsible for the observed 0.2 mag difference between the (V-I)0,g values derived from the isochrones of Bertelli et al. (1994) and Tripicco et al. (1995). In the present analysis, we have therefore used the mean 1.2 as a value for (V-I)0,g. The observed value of this parameter in Fig. 6 is , indicating a value of for the colour excess E(V-I). This agrees fairly well with the value of E(V-I) = 0.9 obtained by us by fitting the theoretical isochrones to the shape of the RGB and with most of the earlier estimates of the reddening (see Barbuy et al 1998; Guarnieri et al. 1998 and references therein). We therefore adopted a value of E(V-I) = 0.95 in our further analysis.
This relation is consistent with the HIPPARCOS-based distance measurements and yields a value of 0.76 mag for MV of NGC 6553. The mean brightness level for the HB stars of NGC 6553 is at (see Fig. 7). This gives 13.7 as a value for the true distance modulus of NGC 6553, assuming a normal value of 2.37 for the ratio AV/E(V-I). However, if one takes into consideration that the absorption depends on the temperature, surface gravity and metallicity of the star considered, as was studied recently by Grebel & Roberts (1995), then the value of the ratio becomes 2.6 and a slightly lower value of 13.5 mag is derived for the true distance modulus of the cluster. Considering all these uncertainties, one can say that the cluster is located at a distance of about 5 kpc from us and 3 kpc from the Galactic centre at the outer fringe of the bulge. The present distance estimate agrees very well with the values given recently by Ortolani et al. (1995) and by Guarnieri et al. (1998).
The location of the HB and the morphology of the RGB have also been used to estimate distance, reddening and metallicity of the bulk of the bulge populations present in the direction of the cluster. For this, we have used NGC 6553 as a reference. The value of , the magnitude difference between the HB level and the top (brightest) of the RGB in V is 0.2 indicating nearly solar metallicity for most of the bulge populations. The location of the HB where it joins the RGB is about mag fainter in V and about mag redder in (V-I) than the corresponding location of NGC 6553 in the V, (V-I) diagram. It means that most of the bulge stars in the direction of the cluster are background stars located at distances larger than 7 kpc with reddening . These estimates agree fairly well with the values derived from the isochrone fitting.
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