7 Summary and conclusions

We investigated the BSDO catalogue and provide a new catalogue of all binary and multiple cluster candidates found in the LMC. The catalogue is presented in Table 6. Age information available in the literature is also given. We found in total 473 multiple cluster candidates. The separations between the clusters' centres are ${\le} 1\farcm4$ corresponding to 20 pc (assuming a distance modulus of 18.5 mag).

We performed a statistical study of cluster pairs and groups. For this purpose we distinguished between regions of different cluster densities in the LMC.

Vallenari et al. (1998) and Leon et al. (1999) proposed that the encounter rate in large cluster groups is higher so that binary clusters can be formed through tidal capture. Such a scenario might explain large age differences between cluster pair components. For each selected region we calculated the encounter rate of star clusters. However, we found that the probabilities for cluster encounters are universally very low. In addition, the probability of tidal capture depends on further constraints which will not be fulfilled during every encounter. Thus we conclude that it seems unlikely that a significant number of young pairs may have formed in such a scenario.

We counted the number of all cluster pairs and groups found in the selected areas. In order to check how many of these multiple cluster candidates can be expected statistically due to chance line-up, we performed Monte Carlo experiments for each region to produce artificial cluster distributions which are compared with the real LMC cluster distribution. For all selected regions, the number of chance pairs in our simulations is much lower than the quantity of cluster pairs found: between $56\%$ (in the bar region) and $12\%$ (in the outer LMC ring) of all detected pairs can be explained statistically. Especially large cluster groups with more than four members hardly occur in the artificial cluster distributions. A significant number of the cluster pairs and groups cannot be explained with chance superposition and thus might represent "true'' binary and multiple clusters in the sense of common origin and/or physical interaction.

We studied the properties of the multiple cluster candidates:

In the distribution of the centre-to-centre separations of the cluster pairs two peaks around 6 pc and 15 pc are apparent. This bimodal distribution is more apparent for cluster pairs in which both components have diameters smaller than 7 pc, but cannot be neglected for pairs consisting of larger clusters. We cannot confirm a uniform distribution of separations for pairs with large clusters as suggested by Bhatia et al. (1991). Around separations of 9-10 pc, the number of cluster pairs is depleted. This dip might be interpreted as a balance between the effects that lead to an increase in the number of cluster pairs towards either smaller (due to projection effects) or larger separations (pairs with larger separations are more easily detected).

The size distribution of the group components shows a peak at $0\farcm45$($\approx$6.6 pc). Most clusters involved in pairs or groups are small and only few clusters have diameters larger than $1\farcm8$ (26 pc). The size distribution for group components is very similar to the size distribution for all LMC clusters. It seems that binary clusters tend to form with components of similar size.

The spatial distribution of the multiple cluster candidates coincides with the distribution of clusters in general.

Only for a fraction ($\approx$27%) of the clusters that form binary and multiple cluster candidates age information is available, and for only 96 groups ages are known for more than one cluster so that the age structure of the specific group can be examined. For 57 groups the members appear to be either coeval or have ages similar enough to agree, within the errors of the age determination, with a common formation in the same GMC, i.e., the age differences are 10 Myr at maximum (Fukui et al. 1999; Yamaguchi et al. 2001). The remaining 39 groups have internal age differences which make a common origin of the components unlikely.

The clusters involved in pairs or groups are found to be predominantly young. The age distribution shows peaks at 4 Myr, 25 Myr and 100 Myr. Our findings differ from Pietrzynski & Udalski (2000b) in a way that the two peaks at the younger ages are missing in their age distribution. This is due to the fact that these authors investigated only a part of the LMC and used also a smaller distance modulus that leads to higher ages in general.

We scrambled the ages of the groups components and then randomly assigned them to the group members. On average, $12.9\pm2.7$ groups with internal age differences $\le$10 Myr can be expected, however, 46 groups with internal age differences $\le$10 Myr can be found in the real distribution (note that the borderline cases are not considered in this number, see Sect. 6.4), a number significantly larger than the expected one. Also, the group age distribution for scrambled member ages is smoother than the real one, and the internal age scatter is significantly larger for the groups with random member ages.

No correlation was found between the groups' ages and their internal mean separation. However, there might be a weak tendency towards larger internal age scatter with larger internal separations (indicating larger groups) but a strong tendency as suggested by Efremov & Elmegreen (1998) cannot be confirmed.

Most multiple cluster candidates are found to be younger than 300 Myr. A larger number of old cluster groups or of groups with different ages for the components are not found. A formation scenario through tidal capture is not only unlikely due to the very low probability of tidal capture (even in the dense bar region), but the few old groups and the groups with large internal age differences can easily be explained with projection effects, especially since the majority of these groups are located in the dense bar region. Thus, we do not see evidence for an "overmerging problem'' as proposed by Leon et al. (1999).

Our findings are clearly in favour of the formation scenario proposed by Fujimoto & Kumai (1997) who suggested that the components of a binary cluster formed together, and thus should be coeval or at least have a small age difference compatible with cluster formation time scales.

Acknowledgements

The authors acknowledge Jörg Sanner, Klaas S. de Boer and Lindsay King for carefully reading the manuscript of this publication. AD thanks Daniel Harbeck for the introduction to the methods of KMM. This paper has made use of the OGLE database of LMC star clusters. We are grateful to the OGLE collaboration for making their data publicly available. This research has made use of NASA's Astrophysics Data System Bibliographic Services, the CDS data archive in Strasbourg, France.