Online material

Appendix A: Orbit calculations

The Milky Way potential that we used in the simulations is the analytical 3-component bulge-, disk-, and halo-potential used to model the orbits of satellites in Johnston et al. (1995), Dinescu et al. (1999), and Koposov et al. (2010). The potential of each cluster was approximated by a Plummer sphere using currently measured half-light radii and masses. The calculation of the tidal radii was done assuming constant rotation curve (e.g Milky Way enclosed mass is proportional to radius).

Since the true Galactic potential is not accurately known and the results of our simulations may depend significantly on the assumed parameters, we also run the simulations with masses of the disk and bulge perturbed by 10% Gaussian variations and see how it affects the probabilities of the star being associated

with one of the clusters. As an additional test, we also run our backwards orbit integration to 2 Gyr instead of 5 Gyr to see how it affects our results. While the individual probabilities for the clusters do change, the overall picture does not, e.g. ω Cen is always ranked within the top three.

We further note some important limitations of our calculation: we ignore the dynamical friction of the GCs, which is expected to bring the GCs closer to the Galactic centre. We also ignore the fact that all the GCs were likely to be bigger in the past and have tidally lost some of that mass, which reduces the absolute probabilities we find. Finally, we ignore secular changes in the Milky Way potential over time, which are expected although the Galaxy had a quiet recent accretion history.

© ESO, 2015