Figure 3 (click here) shows the CMDs for the cluster stars determined in the four-dimensional space of proper motions and coordinates with membership probabilities according to Eq. (4) in comparison to the two-dimensional membership determinations using only the proper motions (Eq. 5) and only the coordinates (Eq. 6). For the two-dimensional membership determination we applied additional restrictions concerning the coordinates or proper motions of the stars. The fourth CMD represents the field stars located far outside the cluster region.
Table 3: Cluster parameters dependent on membership
probabilities
Comparing the CMDs we see that the membership determination in the four-dimensional space of proper motions and coordinates provides the best results. The ``best'' CMD was selected visually on the basis of the smallest spread of the cluster members along the known lines of globular cluster CMDs. In comparison to the CMD of Arp (1962) who's photoelectric magnitudes were taken as reference in our photographic photometry we obtain cluster members in three ``non-characteristic'' regions:
1) (B-V)>1.1 and V>16.5,
2) (B-V)<0.2 and V>18.0,
3) (B-V)<0.0 and V>16.0.
We checked these stars for their concentration towards the cluster centre. All three groups of stars show a strong concentration so that we conclude they are cluster members.
Table 4: Cluster and field stars parameters in radial zones around M 5