The globular cluster M 5 is one of the clusters investigated within our programme of determining mean absolute proper motions and Galactic orbits of globular clusters (Scholz et al. 1993, 1994; Scholz et al. 1996). This programme is based on Schmidt plates with epoch differences between 20 and 40 years. The main aim of the programme is to measure accurate mean absolute proper motions of globular clusters directly with respect to an extragalactic reference frame represented by large numbers of background galaxies. For this purpose the Schmidt plates are measured by the Automated Plate Measuring System (APM) (Kibblewhite et al. 1984) in order to fully extract all the information available on the plates.
Accurate membership determinations of many globular clusters based on
proper motions have been obtained by Cudworth and coworkers (e.g.
Cudworth 1979).
In their investigations they used refractor plates with a good astrometric
scale (
10 arcsec/mm) taken over a baseline of
more than 70 years so that they obtained very high accuracies in the relative
proper motions (of the order of several 100 
as/yr).
Due to the smaller epoch difference and the much larger
scale factor of the Schmidt plates (
50 arcsec/mm) we can only
achieve proper motion accuracies for single stars on the level of several
mas/yr. On the other hand, the Schmidt plates go much deeper and cover the
whole cluster region in comparison to the known membership studies, which are
usually restricted to the bright cluster stars (V < 16) and the central
cluster region (r < 10 arcsec). For the globular cluster M 3 we have
already demonstrated the possibility of extending membership investigations
to the faint stars and to the outer cluster regions by using Tautenburg
Schmidt plates (Scholz & Kharchenko 1994).
The globular cluster M 5 presents a rich outer halo cluster in the special state of a close encounter near the Galactic center. This conclusion may be drawn from the high space velocity resulting from the combination of the present heliocentric distance, the radial velocity and absolute proper motion results. A large absolute proper motion of M 5 had already been mentioned by Cudworth (1979) converting the mean relative proper motion of the cluster to an absolute one via the secular parallax of faint field stars in the cluster vicinity. Cudworth & Hanson (1993) used the more accurate relative proper motion results of Rees (1993) confirming an unusually high space velocity of the cluster. Although the new absolute proper motion of M 5 measured directly with respect to more than 1000 reference galaxies (Scholz et al. 1996) is somewhat smaller than given by Cudworth & Hanson (1993) the space velocity remains large (420 km/s). The resulting orbit of M 5 on the basis of the Galactic model of Allen & Santillan (1991) leads through the outskirts of the Galaxy with an apogalacticon of about 60 kpc. (With the former velocity values from Cudworth & Hanson (1993) the apogalactic distance of M 5 would even rise to 140 kpc.) The large absolute proper motion of M 5 allows to distinguish the proper motion distribution of the cluster from that of the field stars even if we plot the results from the Schmidt data in a vector-point proper motion diagram (see Fig. 4 (click here)a in Scholz et al. 1996).
Here we use the proper motion results of Scholz et al. (1996) in membership determinations in a four-dimensional space of proper motions and coordinates with the maximum likelyhood method. The results are compared with the membership determination from two-dimensional distribution functions including only the proper motions or only the coordinates and with the colour-magnitude diagram (CMD) obtained from a B,V photographic photometry using two of the Tautenburg plates. The membership probabilities of the brighter cluster stars in the central cluster region obtained by Rees (1993) on the basis of proper motions with an order of magnitude better accuracies than ours provide a good external check of the reliability of our membership determinations.
Palomar Schmidt plates have already been used for star counts in many globular clusters, including M 5, by King et al. (1968). First attempt to use automated measuring machines for that task were made by Herzog & Illingworth (1977). Irwin & Trimble (1984) measured the southern globular cluster M 55 on plates of the 150'' telescope of the Anglo-Australian Observatory with the APM measuring machine. Recently, Grillmair et al. (1995) examined the outer structure of 12 Galactic globular clusters using star counts on UK Schmidt plates scanned with the APM.
Tautenburg Schmidt plates measured with the APM were used in an investigation of the density profiles and luminosity functions of the globular clusters M 3 and M 92 (Scholz & Schmidt 1992). APM scans of different Schmidt plates with seven other globulars included in the absolute proper motion programme were also used for star counts applying a crowding correction in the central cluster region based on the area of crowded images and the luminosity function in the outer cluster region (Lehmann 1996). Here we discuss the tidal radii of M 5 obtained from fitting King profiles to the counts of all objects on single plates and to the counts of the cluster members. Member counts had already been used by Tucholke (1992) in order to improve the determination of tidal radii of the globular clusters 47 Tuc and NGC 362.
