The probability of close encounters between star clusters leading to a tidal capture is considered to be relatively small or even very unlikely (Bhatia et al. 1991). However, van den Bergh (1996) suggested that it becomes more probable in dwarf galaxies like the Magellanic Clouds due to the small velocity dispersion of the cluster systems. Furthermore, Vallenari et al. (1998) proposed that interactions between the LMC and SMC might have increased the formation of star clusters in large groups in which the encounter rate and thus the formation of bound binary clusters is higher. This scenario is capable of explaining large age differences between cluster pairs which Leon et al. (1999) refer to as the "overmerging problem''. In this section, we will determine the cluster encounter rates in our selected areas.
Inside the chosen regions we find 491 clusters in the bar, 863 in the remaining parts of , 372 objects in , 1439 clusters in (without and ), and 924 remaining entries in the outer region of the LMC. Assuming a distance modulus of 18.5 mag to the LMC, 1 pc corresponds to units in our cartesian system. This leads to a length of 2710 pc and a width of 591 pc for the bar, and thus to a cluster density of clusters . For , the semi major axis corresponds to 2250 pc and its semi minor axis to 1000 pc, resulting in clusters . Cluster densities for the other selected areas follow in an analogous manner: clusters for , clusters for (without the northern ellipse and the region surrounding the bar), and clusters for the outer ring . Please note that, assuming an outer ring with limited boundaries and semi axes corresponding to 5000 pc and 6750 pc, the number of objects in amounts to 911. However, this does not alter the value of the outer cluster density.
The cluster density is highest in the innermost part of the LMC, the bar region, and it drops off by an order of magnitude towards the outer region. According to Vallenari et al. (1998), cluster pairs can be formed by close encounters which result in the tidal capture of two clusters. The higher the cluster density, the higher the probability for close encounters, and thus the probability for the formation of cluster pairs or groups.
The cluster encounter rate can be determined following Lee et al. (1995):
All results are summarized in Table 3.
The probabilities for cluster encounters are already very low. In addition, the
probability of tidal capture depends on further conditions which will
not be fulfilled during every encounter. Whether a tidal capture takes place
or not depends strongly on the velocities of the two clusters with respect
to each other, on the angle of incidence, whether sufficient angular
momentum can be transferred, and whether the clusters are sufficiently
massive to survive the encounter. Since only very few of these rare
encounters would result in tidal capture, it seems unlikely that a
significant number of young pairs may have formed in such a scenario.
|Region||a [pc]||b [pc]|
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