7 Discussion

The space velocity and the orbital parameters of NGC 4147 in Table 10 are quite different from those given by Dauphole & Colin (1995), but are in good agreement with the values given by Odenkirchen et al. (1997). The major difference to the work of Dauphole & Colin (1995) lies in the velocity component $\Theta$, where our values change the cluster's prograde rotation of Dauphole & Colin (1995) into a retrograde motion. Since the inclination angle of the cluster orbit is close to 90 degree, small changes in the proper motion may change the sign of $\Theta$. Both of the absolute proper motion results from this paper and from Odenkirchen et al. (1997) are based on the Hipparcos reference frame and should have a better reliability. However, large proper motion errors of the single stars exist in the previous work while the proper motion reduced in the present work should be better due to deeper first epoch plates. From the relationship between apogalactic distance $R_{\rm a}$ and metallicity [Fe/H] of 26 globular clusters, Dauphole et al. (1996) proposed the existence of a metallicity gradient among the halo globular clusters and they took this as a support to the rapid collapse model of the Galaxy (ELS). It seems that such a metallicity gradient is present in their Fig. 4. NGC 4147 is one of the two clusters, which do not fit very well to the proposed relation. As for NGC 4147, according to Dauphole & Colin (1995), its apogalactic distance is 52 kpc, while its metallicity [Fe/H] = -1.80. If the metallicity gradient is true for the halo clusters, NGC 4147 should have an apogalactic distance smaller than 40 kpc. Using $R_{\rm a}$calculated here or from Odenkirchen et al. (1997), the apogalactic distance of NGC 4147 will fit better to the apogalactic relation of distance and metallicity and NGC 4147 will be then a "normal'' cluster. Among the smaller sample of 15 clusters with proper motions based on Hipparcos reference stars in Odenkirchen et al. (1997) the relation between $R_{\rm a}$ and [Fe/H] is hardly seen. What can be inferred from their work is that the more metal-rich clusters are concentrated towards the galactic center and that the group of clusters with retrograde orbits (including NGC 4147) is in general chemically quite homogeneous, with [Fe/H] between -1.5 to -2.0. This conclusion is to a certain extent in favor of Searle & Zinn's (1978) accretion model, but it not necessarily excludes the ELS model. Our results support the conclusion of Odenkirchen et al. (1997). Obviously more accurate absolute proper motion data of globular clusters should be obtained before we can make definite conclusion on the existence of the metallicity gradient and which of the ELS and SZ models would be the most favorable scenario for the formation of our Galaxy.