Merging timescales and merger rates of star clusters in dense star cluster complexes

Interacting galaxies like the famous Antennae (NGC 4038/4039) or Stephan's Quintet (HCG 92) show considerable star forming activity in their tidal arms. High resolution images (e.g. from HST-observations) indicate that these regions consist of up to hundreds of massive stellar clusters or tidal dwarf galaxies (TDG). In this paper we want to investigate the future fate of these clusters of massive star clusters (in this work called super-clusters). We simulate compact super-clusters in the tidal field of a host-galaxy and investigate the influence of orbital and internal parameters on the rate and timescale of the merging process. We show that it is possible that such configurations merge and build a dwarf galaxy, which could be an important mechanism of how long-lived dwarf satellite galaxies form. A detailed study of the merger object will appear in a follow-up paper.