The inefficiency of satellite accretion in forming extended star clusters

The distinction between globular clusters and dwarf galaxies has been progressively blurred by the recent discoveries of several extended star clusters, with size (20-30 pc) and luminosity (-6 <Mv <-2) comparable to the one of the faint dwarf spheroidals. In order to explain their sparse structure, it has been suggested that they formed as star clusters in dwarf galaxy satellites that later accreted on to the Milky Way. If these clusters form in the centre of dwarf galaxies, they evolve in a tidally compressive environment where the contribution of the tides to the virial balance can become significant, and lead to a supervirial state and subsequent expansion of the cluster, once removed. Using N-body simulations, we show that a cluster formed in such an extreme environment undergoes a sizable expansion, during the drastic variation of the external tidal field due to the accretion process. However, we show that the expansion due to the removal of the compressive tides is not enough to explain the observed extended structure, since the stellar systems resulting from this process are always more compact than the corresponding clusters that expand in isolation due to two-body relaxation. We conclude that an accreted origin of extended globular clusters is unlikely to explain their large spatial extent, and rather favour the hypothesis that such clusters are already extended at the stage of their formation.