1 Introduction

Globular clusters (GCs) are among the oldest stellar objects in the Milky Way. Due to the total luminosity from the large number of stars, they can be observed far away. They play very important rôles in the study of the structure and evolution of the Galaxy. For instance, with GCs as a new constraint, Dauphole & Colin (1995) studied the mass distribution in our Galaxy, re-calculated the model potential and obtained a better consistency with the observations. The formation of the Galaxy was studied by Eggen et al. (1962; hereafter ELS), which were in favour of a pressure supported rapid collapse model (ELS model), while Searle & Zinn (1978; hereafter SZ) proposed an accretion model of Galaxy formation (SZ model). Their model is based on the fact that the globular clusters could be considered as relics of some sub-systems merging with the Galaxy, these relics still having different kinematics and metal abundances. Geffert et al. (1995) and Dauphole et al. (1996), using a sample of 26 GCs with absolute proper motion data, found a correlation between the apogalactic distances and the metallicities in support of the ELS model.

Kinematic parameters of globular clusters may provide important information for the understanding of the formation of the Galaxy. The reliability of their determination, however, depends of the quality of the proper motion measuring. In fact, the accuracy of radial velocities of the GCs, at present, is better than $\pm1$ km s^-1 and the accuracy of distance determination is better than $10\%$. On the other hand, if the proper motion accuracy were $\pm1$ mas/yr -a typical value for a recent proper motion determination- it would lead to an uncertainty of 50 km s^-1 for the tangential velocity of an object with a distance of 10 kpc. Moreover, proper motions should be linked to an inertial reference system and this correction itself might have larger uncertainties that could result in errors worse than $\pm1$ mas/yr.

To avoid such errors from the corrections, Brosche et al. (1983) have determined the proper motions of reference stars in the fields of globular clusters relative to a large number of extragalactic objects, using the Lick plates taken for the NPM program. They so reduced the data directly to an inertial system. Using the above method, Brosche et al. (1985) obtained absolute proper motions of 42 stars in the globular cluster NGC 4147 and found the mean absolute proper motion of $\mu_{\alpha}\cos\delta=-2.7\pm0.6$ mas/yr, $\mu_{\delta}=+0.9\pm0.6$ mas/yr (in 1991, they recalculated the both errors as $\pm1.3$ mas/yr). One problem in their work is, that the number of observed stars is too small and no photometric data are given. Since also the proper motion accuracy of individual stars is poor, membership cannot be estimated reliably and only three field stars in the sample were found. Another problem is that Brosche et al. (1985) used the AGK3 Catalogue to determine the positions of reference stars so that their results still unavoidably contain systematic differences from an inertial system. Now we can fortunately use the Hipparcos Catalogue, which is the best optical realization of the International Celestial Reference System, to minimize such a difference.

The colour-magnitude diagram of the globular cluster NGC 4147 was given earlier by Sandage & Walker (1955) and was studied by Friel et al. (1987) later. Aurière & Lauzeral (1991) presented the BV CCD photometry of this cluster and presented a CMD of 532 stars up to V = 21 within a $100\hbox{$^{\prime\prime}$ } \times 160\hbox{$^{\prime\prime}$ }$ area. In the CMD, they found a red giant 25 $\hbox{$^{\prime\prime}$ }$ away from the cluster center, which was about 1 mag brighter and 0.4 mag redder than other red giants in the cluster. The giant is located on the extension of the red giant branch (RGB) of the cluster CMD but it may also be a field star. The proper motion data of this star may provide a clarification of its membership.

In the present work more accurate absolute proper motions for more stars in the cluster NGC 4147 region are determined. With the proper motion result, the membership probabilities of the stars are estimated using the maximum likelihood method. Meanwhile, multi-colour photometry was made of stars in the cluster. The proper motion membership probability is used to purify the CMDs. Then, with this member sample, a more reliable mean absolute proper motion of the cluster is deduced.