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5 The colour-magnitude diagram morphology and
parameters of NGC 6553

\includegraphics [width=14cm]{7410f6.eps}\end{figure} 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

5.1 Duration of the RGB-bump phase

Figure 7 shows the differential luminosity function of the GB branch derived from the field star subtracted sample of the cluster. There are two peaks marked in the histograms. The higher peak contains the HB stars while the smaller contains the stars belonging to the RGB-bump which is a clump of stars along the RGB evolutionary phase. This clump is due to a temporary reversal in the star path that is ascending the RGB, the star stops and goes toward slight fainter magnitudes for some time and then starts again ascending the RGB. In the V, (V-I) diagrams of the Galactic bulge clusters, which have nearly solar

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).

\includegraphics [width=8.8cm]{7410f7.eps}\end{figure} 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 $0.17~\pm~0.05$ which is not too different from the value of $0.19~\pm~0.03$ 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.

5.2 Morphology of the horizontal branch (HB)

A very interesting feature in the lower V, (V-I) diagram (Fig. 6) is the position of HB. It is very red, elongated, tilted, and even overlaps with the RGB. Such tilted and elongated HBs have been repeatedly reported for metal-rich clusters located towards the Galactic centre (see Ortolani et al. 1997; Grebel et al. 1995). Armandroff (1988) proposed differential reddening as the cause, because the slope of the tilted feature resembles in the most striking cases the reddening vector. For Terzan 5, Grebel et al. (1995) showed that differential reddening is present, derived a reddening map, and dereddened the initially diagonal HB, which became clumpy and lost its diagonality almost entirely. Also the RGB became much narrower. A small amount of "diagonality'' still remained, which may indicate that some of it is an intrinsic property of HB evolution as indicated by theoretical HB tracks. For the first time, it was shown directly that most of the diagonality is indeed caused by differential reddening. In order to understand the cause in the case of NGC 6553, we carried out following analysis:
In order to derive an extinction map, we divided the observed cluster region into boxes of $\sim$ 200 $\times$ 200 pixels2, as indicated in the Table 4 and identified the HB stars located in the box. The star is considered as a HB star if its brightness is 16.35 < V < 17.55 and the colour is 1.85 < (V-I) < 2.35. Theoretical models indicate that all HB stars have an (almost) equal luminosity but have range in temperature due to different shell mass. This fact is used to derive the extinction value for a box from the mean apparent brightness of its HB stars. For this, we used the results given by Guarnieri et al. (1998) that the apparent brightness of the HB stars of the cluster ($V_{\rm HB} = 16.92$) corresponds to Av = 2.34. The value of Av and the number of HB stars found in the box are listed in the table. Generally more than 5 HB stars are present in a box, except in the boxes with $X \ge$ 800. The standard deviation ($\sigma$) of the mean V value of the HB stars in a box is generally $\sim$ 0.2. One finds that the values of Av change smoothly along a column and randomly along the row with the minimum vaues in the row with Y=350 to 550. This indicates presence of strong differential extinction in the north south direction of the cluster region. It is in agreement with the obscuration observed on the sky survey plate and also with the observations of Ortolani et al. (1990).
In order to study variaton in shape and width of the HB and RGB across the cluster face, we plotted in Fig. 8 the V, (V-I) values of the HB and RGB stars located in the six cluster regions. It clearly shows that both scatter as well as tilt of the HB differ from one region to other. Both the HB and RGB sequences in a region are narrow and well defined. This indicates that most of the scatter present in (V-I) colour of the cluster RGB sequence (see Figs. 5 and 6) is due to presence of differential extinction across the cluster face. However, the HB of a region is always tilted and elongated. Presence of differential interstellar extinction across the face of a box (size $\sim$ 66$^{\prime\prime}$$\times$ 66$^{\prime\prime}$)can not be ruled out, as radio studies indicate very small scale (a few AUs) patchy absorption in the Galactic disk. It may not be strong as its effect on the RGB (see Fig. 8) of a region in the form of scatter is not very large. This may indicate that presence of differential extinction across the cluster face may not explain the observed elongation of the cluster HB sequence. Further studies are desired for understanding them.

In order to quantify the extent of differential extinction present across the cluster face, we plotted mean loci of the HB and GB sequences of the different cluster regions in Fig. 9. Average slope of the HB seems to be not too different from the normal slope of interstellar reddening. However, extent of elongation of the HB differs from one strip to other. The mean loci of the GB sequences of the regions with Y=150 to 360; 350 to 550 and 550 to 750 are almost identical. However, the mean locus of the GB sequence of the region with Y=750 to 950 is clearly shifted towards red side. This indicates that extent of differential reddening amounts to $\Delta E(V-I)\sim$ 0.2 mag and $\Delta A_v \sim$ 0.5 mag. This agrees very well with the results derived from the brightness of the HB stars (see Table 4). Ortolani et al. (1990) observed slightly smaller extent of differential extinction across the cluster region.
\includegraphics [width=14cm]{7410f8.eps}\end{figure} 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

\includegraphics [width=12cm]{7410f9.eps}\end{figure} 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.

Table 4: Variation of extinction Av across the face of the cluster NGC 6553. The number of HB stars observed in a box is given in brackets

{c c c c c c } \\  \hline
 Range in $Y$\space pixels& \multicolu...
 ...ce ~950 & 2.50(3)~&2.48(4)~&2.59(5)~~&2.38(7)~ & 2.50(2) \\  \hline\end{tabular}

5.3 The morphology of the giant branch and cluster parameters

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 $\sim$ 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.

Table 5: The fiducial sequence for the RGB and HB of NGC 6553

{c c c } \\  \hline
 $(V-I)$\space & $V$\space & Sequence \\  \h...
 ... \\  1.99 & 16.64 & HB \\  2.07 & 16.77 \\  2.16 & 16.98 \\  \hline\end{tabular}

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 $(V-I)\sim$ 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).

5.3.1 Metallicity and reddening

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, $\Delta V$. 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 $\Delta V$ 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, $\Delta V=1.5~\pm~0.1$. 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 $\Delta V$ and [Fe/H] using theoretical isochrones given by Bertelli et al. (1994) for [Fe/H] = 0.4, 0.0, -0.4 and -0.7.

\begin{displaymath}[{\rm Fe/H}]
= (-0.57 \pm 0.03) \cdot \Delta V + (0.74 \pm 0.04). \end{displaymath}

This yields a value of $-0.1~\pm~0.1$ 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 $M_{\rm bol}$ and $T_{\rm eff}$ 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 $2.15~\pm~0.1$, indicating a value of $0.95~\pm~0.15$ 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.

5.3.2 Distance

For distance determination, we have used the following empirical relation between HB brightness and metallicity given by Salaris & Weiss (1998)

M_V = 0.17* [{\rm Fe/H}] + 0.78.\end{displaymath}

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 $V = 16.7~\pm~0.2$ (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 $\sim$ 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).

5.4 Parameters of the field population

The V, (V-I) diagram for the brighter field stars (V < 21) is shown in the upper part of Fig. 6. Some stars belonging to the cluster population are also present, but they will not affect the results. The blue MS of Galactic disk stars and the bulge RGB and HB stars dominate the diagram, and the cluster sequence is too sparse to be identified. The CMD is very similar to that of Baade's window and those of the other fields near the Galactic centre published recently by Paczynski et al. (1994) and earlier by Terndrup (1988). In order to estimate reddening, distance and age of the relatively narrow and well defined MS, we fitted Bertelli et al. (1994) isochrones for solar metallicity and found $(m-M) = 14.1~\pm~0.3, E(V-I)=0.9~\pm~0.05$ and age $= 800~\pm~200$ Myr. Paczynski et al. (1994) have also observed this population almost at the same distance of $\sim$ 2 kpc. At this distance, along the line of sight, the scale height of the thin disk corresponds to a distance of $\sim$ 100 pc. All these indicate that the foreground stars are in the Galactic disk and they are concentrated at a single distance of $\sim$ 2 kpc. The dispersed but clearly defined RGB and the tilted and elongated ($\Delta (V-I)$ > 0.7 mag) HB are in part caused by depth effects along the line of sight and probably also by differential interstellar extinction within the field region. The slope of the HB tilt is $\sim$ 2.5. The RGB of the bulge populations also turns over just like the NGC 6553 population. In Fig. 6, a theoretical isochrone from Bertelli et al. (1994) is overplotted for apparent distance modulus of 17.2 and reddening E(V-I) = 1.1. The isochrone has Z=0.02 and an age of 12 Gyr. The fits of theoretical isochrones in Fig. 6 cannot account for the bright stars with $(V-I) \geq 4.5$ as seen also in the cluster population. There are about 10 such stars.

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 $\Delta V$, the magnitude difference between the HB level and the top (brightest) of the RGB in V is $1.5~\pm$ 0.2 indicating nearly solar metallicity for most of the bulge populations. The location of the HB where it joins the RGB is about $1.5~\pm~0.4$ mag fainter in V and about $0.3~\pm~0.2$ 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 $\sim$ 7 kpc with reddening $E(V-I) \geq 1.2$. These estimates agree fairly well with the values derived from the isochrone fitting.

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