tokens: for eccentric and radial orbits in the case M g = 3.2 × 10 11 M ⊙ . In the case e = 0.7, it is worth noting that at every passage at pericentre some stars are stripped away from the GC and tend to move on precessing ellipses whose semi-major axes increase with the number of passages at pericentre. On the other hand, when the GC experiences a ‘head-on’ collision with the SMBH, stars are scattered backwards at different velocities, depending on the impact parameter that characterizes each star–SMBH interaction. This peculiar interaction leads to the formation of a wake behind the former GC, with a structure similar to the propagation of a wave on a water plate. Figure 4. Snapshots at different times (labelled) of the cluster on an eccentric orbit in the case M g = 3.2 × 10 11 M ⊙ . The central black dot represents the BH with mass M BH = 5 × 10 8 M ⊙ . The x–y plane is the GC orbital plane. Figure 5. Same as in Fig. 4 , but for a cluster on a radial orbit. Therefore, although it is quite difficult to identify the ‘core’ of the GC, the interaction between an SMBH and an infalling GC produces debris that hides much informations about the initial orbital parameters of the GC. However, due to the fact that it is almost impossible to identify a centre for the cluster in these cases, we limited our analysis to the estimate of the amount of GC mass which remains confined to an inner region of the galaxy, around the SMBH. When considering the simulations with M g ≥ 10 11 M ⊙ , we found that eccentric and radial orbits allow a more efficient transport of mass, towards the Galactic Centre, than circular orbits do. On these orbits, the GC can carry about 20 per cent of its initial mass to the Galactic Centre, while, on circular orbits, such percentage is limited to few per cent. On the other hand, for lower galaxy masses, M g 10 11 M ⊙ , we found that the major contribution to the deposited mass comes from GC on circular orbits. We will deepen the discussion about these results in Section 4 . 4 DISCUSSION In this paper, we have presented several N -body simulations to study the interaction between a single GC and an SMBH in the Galactic Centre. The results shed light on the actual mechanisms of mass accumulation in the central region of a massive galaxy ( M g ≥ 10 11 M ⊙ ). Fig. 6 shows the GC cumulative mass profile as a function of the distance from the SMBH after the orbital decay process, for all the orbits considered and in the case of M g = 10 10 M ⊙ and M g = 3.2 × 10 10 M ⊙ . Considering our lightest galaxy model, we found that circular and radial orbits are both efficient in the transport of mass towards the Galactic Centre. In such cases, the mass left to the Galactic Centre exceeds 80 per cent of the initial mass of the GC. On the other hand, in heavier galaxy models, only GCs moving on initial nearly radial orbits deposit a non-negligible amount of their mass (∼20 per cent of the initial mass of the GC) in the inner 20 pc of the galaxy.
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