4 Numbers of cluster pairs and cluster groups

As the selection criterion for binary cluster candidates we chose a maximum angular separation of ${\le} 1\farcm4$ corresponding to a projected distance of 20 pc (assuming a distance modulus of 18.5 mag) between the centres of a proposed cluster pair. This is nearly the same value that was used by Bhatia & Hatzidimitriou (1988), Hatzidimitriou & Bhatia (1990), and Bhatia et al. (1991). According to Bhatia (1990) and Sugimoto & Makino (1989), binary clusters with larger separations may become detached by the external tidal forces while shorter separations may lead to mergers.

Out of 491 clusters in the bar region, 228 objects can be found in double or even multiple systems. This amounts to $\approx$46% of all bar clusters. We counted in total 166 pairs. However, two or more pairs may form a larger group, e.g., three star clusters may form up to three pairs if each cluster is seen within a projected distance of less than 20 pc from each other cluster. This means that the 166 pairs do not consist of 334 different single clusters but only of the 228 objects mentioned above. Hence we call only an isolated pair a possible binary system. In the bar 59 isolated pairs, 22 triple clusters and 9 larger groups with up to six members can be found.

The area surrounding the bar, $E_{\rm bar}$, is roughly half as densely populated with star clusters as the bar region itself. The percentage of clusters found in potential binary and multiple systems is still high, $\approx$35% (306 objects), forming in total 207 pairs.

The cluster density in the northern region, $E_{\rm north}$, is nearly the same as in $E_{\rm bar}$, and approximately the same percentage of clusters ($\approx$31% or 117 objects) can be found in 88 pairs which form 36 binary, 5 triple, and 6 larger systems.

In the remaining inner LMC region ( $E_{\rm inner}$) the cluster density is lower by an order of a magnitude; however, still $\approx$26% (371) of the clusters appear in potential binary and multiple systems.

In the outskirts of the LMC, the cluster density is the lowest, as is the number of clusters involved in pairs and groups: 93 "outer'' clusters, i.e., $10\%$, form in total 55 pairs (40 binary, 3 triple and 1 quadruple systems).

The distribution of all cluster groups found in each selected area is summarized in Table 4 and illustrated in Fig. 6. The percentage of all clusters involved in the groups is indicated in Fig. 6, e.g., $24\%$ (or 118) of all clusters can be found in 59 binary systems in the bar.

Table 4 also lists the sum of all clusters and cluster pairs which result if the values for the different regions are added up. The last line of Table 4 gives the group statistics for the whole LMC without a division into separated areas. As can be seen, the sum of the individual group statistics differs from the statistics found for the total LMC. This is due to the fact that some multiple cluster candidates are located at or across the borders of the selected areas, so that they get divided into smaller groups or might even disappear as a cluster group through the division into different regions.

We caution that this statistical approach so far does not take into account possible age differences between clusters (which are mainly unknown). Also, we do not have any other information about the actual three-dimensional separation between the clusters.