6 The proper motion of NGC 6528 and the velocity dispersion in the Bulge

The measured proper motions can be used to find the mean proper motion of NGC 6528 relative to the Galactic bulge, and the bulge and cluster velocity dispersions.

As discussed above, it appears that the bright blue stars contain a Galactic disk component. Therefore we use the bright (V< 19), red (V-I> 1.6) sample to get the final values for cluster and bulge velocity dispersion and proper motion given in Table 6. This then gives us a cluster proper motion relative to the bulge of $<\mu_l>$ = 0.006 and $<\mu_{b}>$  = 0.044 arcsec/century.

 

 

Table 6: Final values for velocity dispersion and mean proper motion. An error of 0. indicates that that particular parameter was kept fixed during the fitting procedure. All values are in arcsec century^-1.

	$\sigma_{l}$	$\sigma_b$	$<\mu_l>$	$<\mu_{b}>$
Bulge	$0.327\pm0.027$	$0.254\pm0.017$	- $0.030\pm0.026$	- $0.063\pm0.021$
Cluster	$0.089\pm0.007$	$0.089\pm0.$	- $0.024\pm0.007$	- $0.019\pm0.008$

The velocity dispersion for the cluster, 0.08 arcsec per century, translates to 24-30 km s^-1 for the upper and lower distance limits to NGC 6528 of 6.5 kpc and 8 kpc (Richtler et al. 1998). (The distance found by Ortolani et al. (1992) is 7.5 kpc.)

Globular clusters in the Galaxy have measured velocity dispersions that range from a few km s^-1 to $\sim$20 km s^-1, see Pryor & Meylan (1993) and Dubath et al. (1997). In M 31 at least two globular clusters have measured velocity dispersions >20 km s^-1, Dubath & Grillmar (1997). Zoccali et al. (2001) found $\sigma =$ 28 km s^-1 for NGC 6553. This result is very similar to ours. Since most globular clusters in the Galaxy have significantly lower velocity dispersion they concluded that their measured $\sigma_{\rm cluster}$ was dominated by measurement error. This is most likely also the case for NGC 6528.

Assuming the cluster velocity dispersion in NGC 6528 is dominated by errors, we deconvolve this from the measured velocity dispersion for the bulge to find the true bulge velocity dispersion. Using the data for the red sample (Table 5 with $V_{\rm 555}<19$) we get $\sigma_{l~{\rm bulge}}= 0.33\pm 0.03$ and $\sigma_{b~{\rm bulge}}= 0.25\pm0.02$ arcsec per century. These numbers are in good agreement with the results for bulge giants found by Spaenhauer et al. (1992), $\sigma_{l~{\rm bulge}}=~0.32\pm~0.01$ and $\sigma_{b~{\rm bulge}}= 0.28\pm0.01$arcsec per century for their full sample of 429 stars.

These numbers give a $\sigma_{\rm l}/\sigma_{b}=1.32\pm0.16$, which is identical, within the error estimates, to the 1.33 predicted for the coordinates of NGC 6528 by the model of kinematics in the Galactic bulge in Zhao (1996).

In their study of NGC 6553 Zoccali et al. (2001) derived $\sigma_{l~{\rm bulge}}= 0.26 \pm 0.03$ and $\sigma_{b~{\rm bulge}}= 0.21 \pm 0.02$arcsec per century giving $\sigma_l/\sigma_b=1.24\pm0.17$. These values are lower than found here, however, NGC 6553 is situated further out from the Galactic centre than NGC 6528 and we should thus expect $\sigma_{l~{\rm bulge}}$ to be a factor $\sim$0.86 lower than for the coordinates of NGC 6528, see Zhao (1996) Table 6. $\sigma_{b~{\rm bulge}}$ should remain roughly the same. Specifically the model of Zhao (1996) predicts a $\sigma_{l}/\sigma_{b}=1.32$ at l=1, b=-4 and $\sigma_{l}/\sigma_{b}=1.09$ at l=5, b=-3, which is consistent, within the errors, to the values found here and in Zoccali et al. (2001) for the bulge stars observed in the fields of NGC 6528 and NGC 6553 (which are situated close to the coordinates for which Zhao's model makes its predictions).

We may thus conclude that these two new studies of the proper motions of Galactic bulge stars confirm the predictions by models of the kinematics in the Galactic bulge. To our knowledge the current work and that of Zoccali et al. (2001) are the first studies to address the velocity dispersion, measured by proper motions, of bulge stars below the horizontal branch.

We can use the measured proper motions ( $<\mu_l>\,=\,\sim$+0.006 and $<\mu_b>\,=\,\sim$+0.044 arcsec per century) of the cluster relative to the Galactic bulge along with a radial velocity of 210 km s^-1 (Carretta et al. 2001), cluster distance of 7.5 kpc (Ortolani et al. 1992), solar peculiar velocity relative to the local standard of rest of ( $u_{\odot},~v_{\odot},~w_{\odot})=(10,~5.25,~7.17)$ kms^-1 (Dehnen & Binney 1998) and the rotational velocity of the local standard of rest of 239 km s^-1 (Arp 1986) to calculate the absolute space velocity components of NGC 6528. These are ( $\Pi,~\Theta,~W)=(-220,~17.4,~16.1$) kms^-1 ($\Pi$ points radially outwards from the Galactic centre towards the cluster, $\Theta$ is oriented in the direction of Galactic rotation, and W points towards the north Galactic pole, and we have made the simplifying assumption that the cluster is at (l,b)=(0,0)).

In an attempt to estimate the internal errors on the derived velocities we varied the proper motions for the cluster according to the errors derived when fitting the histograms and we find that the $\Pi$ velocity is unaffected by the errors while $\Theta$varies between $\sim$8 and $\sim$27 km s^-1 and W between $\sim$8 and $\sim$23 km s^-1. These should represent maximal internal errors in our analysis and thus we can conclude that the velocities derived are fairly robust.