7 The colour-magnitude diagram and the proper motions

Our new colour-magnitude diagram is presented in Fig. 1. It contains all the photometry from both long and short exposures, as described in Sect. 3.

Clearly visible is the stubby red horizontal branch. The red giant bump, roughly 0.5 mags below the horizontal branch is less easily isolated but appears to be present. To the left a "plume'' of field stars and/or blue stragglers in the cluster stretches up from the turn-off region. The turn-off region itself is identifiable but appears confused. The exact position of the sub-giant branch is difficult to establish since it is contaminated with field stars from both the disk and bulge. The red-giant branch rises rather vertically but then appear to turn-over heavily to the red. The red-giant branch itself is very wide. This could be an indication of differential reddening and/or large contamination from bulge stars roughly at the same distance modulus as NGC 6528 but with a spread in both age and metallicity.

The question now is whether the broad red giant branch and the fuzzy sub-giant branch are mainly the result of differential reddening, see e.g. Ortolani et al. (1992), or are primarily caused by contamination of the colour-magnitude diagram by bulge stars (Richtler et al. 1998).

7.1 Applying the proper motions to isolate the cluster

The idea is now to use the proper motions to separate the cluster and bulge stars. There are at least two interesting points here. The first is to know how well we can "decontaminate'' the red giant branch of NGC 6528 from bulge stars. Secondly, we want to find out how many of the stars in the "blue'' plume above the turn-off realistically belong to the bulge, to the cluster, or to the foreground disk. Also here we would like to know how well we can clean the turn-off region from contaminating stars. The quality of the turn-off region is a major limitation in the case of NGC 6528 for determining a reliable relative or absolute age.

We use our Gaussian fits to the different regions of the colour-magnitude diagram to estimate the proper motion cuts which maximize the number of cluster stars relative to the number of bulge stars, whilst still allowing enough cluster stars to make a good cluster colour-magnitude diagram. Using different proper motion cuts in different regions of the colour-magnitude diagram will affect the relative numbers of cluster stars in each region but this does not matter for comparison of the observed colour-magnitude diagram with other globular clusters and with isochrones, where all we use is the position of the cluster stars in the colour-magnitude diagram and not their number density.

In Fig. 6, we show the effect of various different proper motion cuts imposed on the WF2 colour-magnitude diagram. We have previously found that the cluster has a $\sigma=0.09$ arcsec per century. In the following we will use this $\sigma$when defining the cuts to clean the colour-magnitude diagram. In a we show the full colour-magnitude diagram for WF2. Plot c and d then shows the resulting colour-magnitude diagram when a cut of $\sqrt {\mu _{l}^2+\mu _{b}^2} < 0.09$and $\sqrt {\mu _{l}^2+\mu _{b}^2} < 0.18$, have been applied respectively. For the most conservative cut the turn-off region becomes clean, although the sub-giant branch remains somewhat confused. The number of stars in the giant branches, however, becomes almost too small for quantitative work. Moreover, as seen in Fig. 4, for the brighter magnitudes the red part of the colour-magnitude diagram, i.e. the giant branches, is dominated by cluster stars and a more generous cut can be allowed when cleaning the colour-magnitude diagram. This is shown in c. Here though the turn-off region again becomes too confused for good work.

Figure 6: Illustration for WF2 of the effect on the colour-magnitude diagram from different cuts in $\sqrt {\mu _{l}^2+ \mu _{b}^2}$. All stars are measured in both the new and old images and satisfy the cuts imposed in $\chi$ and sharpness variables (see Sect. 3). Stars with fitting errors are excluded. a) all stars, d) stars with $\sqrt {\mu _{l}^2+\mu _{b}^2} > 0.18$, i.e. the rejected (mainly bulge) stars, b) stars with $\sqrt {\mu _{l}^2+\mu _{b}^2} < 0.09$, and c) $\sqrt {\mu _{l}^2+\mu _{b}^2} < 0.18$

Our cleaned colour-magnitude diagram, Fig. 7, is finally obtained by imposing the following cuts; $\sqrt {\mu _{l}^2+\mu _{b}^2} < 0.18$, for star with $V_{\rm 555}<19$ and $\sqrt {\mu _{l}^2+\mu _{b}^2} < 0.09$ for the fainter stars.

Figure 7: Colour-magnitude diagram from WF234 for the stars with $\sqrt {\mu _{l}^2+\mu _{b}^2} < 0.09$ for $V_{\rm 555}\geq 19$ and $\sqrt {\mu _{l}^2+\mu _{b}^2} < 0.18$ for the brighter stars.

Figure 8: Colour-magnitude diagram from WF234 for stars rejected as mainly bulge stars due to their proper motions are included, i.e. $\sqrt {\mu _{l}^2+\mu _{b}^2} > 0.18$.

In Fig. 6b, finally, we show the stars that have $\sqrt {\mu _{l}^2+\mu _{b}^2} > 0.18$. These are mainly bulge stars. Compare also the various histograms.

Figure 8 shows the colour-magnitude diagram for the stars that have $\sqrt {\mu _{l}^2+\mu _{b}^2} > 0.18$, i.e. mainly bulge stars. This diagram is now based on all three WFs. This colour-magnitude diagram has large spreads everywhere. Particularly noteworthy is the plume of stars that emanates from the turn-off region as well as the extremely fuzzy appearance of the regions around the horizontal branches, indeed almost a lack of horizontal branch. This colour-magnitude diagram should be compared to that of Baade's window, see e.g. Feltzing & Gilmore (2000) and Fig. 2 in Holtzman et al. (1998). We note also that the red giant stars show a branch that is turning over significantly.

For stars brighter then V $_{\rm 555}=19$ Fig. 9 shows how the stars, included and excluded, from the colour-magnitude diagram are distributed on the sky. The first panel shows the stars that have the highest probability to belong to the globular cluster, i.e. small proper motions and redwards of 1.6 in colour. The second shows the stars that are most likely to belong to either the bulge or to be foreground disks stars. These plots give further support for our definition of cuts in proper motion when defining the stars that belong to the cluster. Figure 9a show a fairly concentrated structure, which tapers of at a certain radius. Note that the detection of stars in the very centre is limited because here we are only using the short exposures since the long were too crowded for good positions. Figure 9b on the other hand shows a much more even distribution of stars.

Figure 9: Positions on the sky for a) stars with $V_{\rm 555}<19$, $\sqrt {\mu _{l}^2+\mu _{b}^2} < 0.09$, and $V_{\rm 555}-I_{\rm 814}>1.6$. This should be predominantly cluster stars. In b) stars with $V_{\rm 555}<19$, $\sqrt {\mu _{l}^2+\mu _{b}^2}\geq 0.18$and for all colours. This selection should primarily give us bulge and foreground disk stars. The sizes of the symbols code the magnitude of the stars.

7.2 Differential reddening towards NGC 6528

We quantify how much of the apparent spread in the colour-magnitude diagram in Fig. 7 is due to differential reddening by fitting the "straightest'' portion of the red giant branch for each chip using a linear least squares fit. This is shown in Fig. 10. In the final panel the fits for the three different WFs are compared. From this it is clear that, in the mean, the reddening differs between the three chips such that WF2 has the smallest reddening and WF3 has the largest. These reddening estimates are obtained only for stars that most likely belong to the cluster, i.e. the same cuts are imposed in all the following plots as we did in Fig. 7.

Figure 10: Colour-magnitude diagrams for WF234 as indicated. Stars used to provide a linear-least square fit to the red giant branch are shown as $\times$. The fits are indicated by full lines for the individual chips and in the last panel with full (WF2), dotted (WF3) and, dashed (WF4) lines.

We also consider below whether differential reddening is significant within each chip.

WF2

The giant branch in the colour-magnitude diagram derived from WF2 is quite tight and well defined. We take this as an indication that the differential reddening over this chip is small and that no correction for differential reddening within the chip is needed.

WF3

We divide the image into four sections and construct the colour-magnitude diagrams for each of them in Fig. 11.

Figure 11: Colour-magnitude diagrams for the four quadrants of WF3. The division of the chip and labeling of the resulting colour-magnitude diagrams are shown to the right.

Figure 12: The effect achieved by correcting the second quadrant of WF3 for differential reddening with respect to the other three quadrants (see Fig. 11). A reddening of $E(V_{\rm 555}-I_{\rm 814})=0.0447$ was applied.

 

 

Table 7: Differential reddening corrections for the quadrants of WF3 to the mean reddening of WF2. In each case the values indicate how much the stars were moved in order for their fiducial line for the red giant branch to coincide with that of the bluest one within the WF. We used the extinction laws and values in Holtzman et al. (1995b).

Quadrant	$\Delta({\it V}_{\rm 555}-{\it I}_{814})$	$\Delta {\it V}_{555}$
1, 3, 4	-0.106	-0.273
2	-0.151	-0.388

Again stars on the cleanest portion of the giant branch are selected and fitted with a straight line. First we fit it to all the stars on the chip (full line). Then for each quadrant of the image (dashed lines). From this it is clear, although the number statistics are low, that quadrant 1, 3, and 4 all are close to the mean value, while quadrant 2 has a larger reddening than the rest. As the scatter around the fitted line for that part of the image is small we do not further divide the image into smaller sections but will correct stars in quadrant 2 according to this shift, see Table 7. First we found the shift in $V_{\rm 555}-I_{\rm 814}$. Then we used Holtzman et al. (1995b) Table 12 to find the corresponding $\Delta V_{\rm 555}$ that should be applied to remove the colour difference. Figure 12 shows the WF3 colour-magnitude diagram corrected for differential reddening.

WF4

The colour-magnitude diagram for this chip has the largest spread on the giant branch. Figure 13 shows the result for the four subsections.

For quadrant 3 on the chip nothing can be said since the number statistics is too low. Quadrant 2 appears to be well lined up with the mean value for the chip and quadrant 4 has somewhat larger reddening than quadrant 2. The colour-magnitude diagram for the first quadrant, however, has a remaining large scatter and we further subdivide this quadrant into four sub-quadrants, Fig. 14. This shows that the largest scatter emanates from sub-quadrant 3 and that the three remaining sub-quadrants have a reddening that is less than the mean reddening for the first quadrant. However, because of the complexity found for the differential reddening we will omit WF4 from further discussions.

Our full final colour-magnitude diagram, using data from WF2 and WF3 corrected for differential reddening, is shown in Fig. 15.

We observe that the red giant branch is more pronounced when the reddening corrections have been applied (see also Richtler et al. 1998). The red subgiant branch bump, even though it is not a strong feature in our colour-magnitude diagram, appears more rounded and well-defined. Heitch & Richter (1999) used the lumpiness of this feature to assess the quality of their differential dereddening. Thus we take the improvement in our corrected colour-magnitude diagram of this feature as an indication that the differential reddening that has been applied is the correct one.

7.3 The tilt of the HB and the curved asymptotic giant branch

For a long time it has been known that one of the characteristics of metal-rich globular clusters in comparison with the metal-poor clusters is the presence of a strongly curved red asymptotic giant branch in the optical. This effect is caused by the extra line blanketing provided by the numerous molecular lines, e.g. TiO, present in the spectra of cool metal-rich giant stars. The complexity of such spectra is illustrated by e.g. Fig. 2 in Ortolani et al. (1991). In Ortolani et al. (1992) the optical colour-magnitude diagram for NGC 6528 shows just this curved structure. Richtler et al. (1998) were able to define a sample of NGC 6528 stars extending all the way out to $V-I\sim 6.5$, showing an exceptionally curved red giant branch and asymptotic giant branch (AGB) which after $V-I\sim 4$ progressively deviates from the predictions from stellar evolutionary tracks (see their Fig. 7).

Figure 15 shows the full extent of our AGB. There are a few red stars that are fainter than the majority of the AGB. These stars could be members of the bulge, but could also, obviously belong to the cluster and be in a region which has a larger differential reddening which is on such a small scale that our previous investigation could not detect it.

An upper envelope for the AGB has been found, but since we here are only using material from two WFPC2 chips the field of view is small we are content with saying that our results agree well with those of Richtler et al. (1998) for the upper envelope, see their Fig. 7. They also find a number of stars with $V-I>\, \sim$4. We find no such stars in our proper motions selected sample. The reason for this could either be that the stars are saturated in our I-band images or that they happen to be outside our field of view. We are not in a position to be able to further distinguish between these possibilities.

Figure 13: Colour-magnitude diagrams for the four quadrant of the WF3 image. The division of the chip and labeling of the resulting colour-magnitude diagrams are shown to the right.

Figure 14: Colour-magnitude diagrams for the four sub-quadrants of the first quadrant of WF4 image. The division of the chip and labeling of the resulting colour-magnitude diagrams are shown to the right.