Milky Way Globular Clusters: close encounter rates with each other and with the Central Supermassive Black Hole

Using the data from Gaia (ESA) Data Release 2 we performed the orbital calculations of globular clusters (GCs) of the Milky Way. To explore possible collisions between the GCs, using our developed highorder {\\phi}-GRAPE code, we integrated (backwards and forward) the orbits of 119 objects with reliable positions and proper motions. In calculations, we adopted a realistic axisymmetric Galactic potential (bulge + disk + halo). Using different impact conditions, we found five pairs of the GCs that likely experienced collisions: Terzan 3 - NGC 6553, Terzan 3 - NGC 6218, Liller 1 - NGC 6522, Djorg 2 - NGC 6552 and NGC 6355 - NGC 6637. We analyzed the GCs interaction rates with the central supermassive black hole. Assuming the maximum 100 pc distance criteria for separation between them we estimated 11 close encounter events. From our numerical simulations, we estimate the close interaction rate as at least one event per Gyr with the impact parameter less than 30 pc; and one event per Myr with the impact parameter less than 60 pc. Our calculations show one very close encounter of NGC 6121 with the central SMBH near 5.5 pc (practically direct collision). Based on the extended literature search for the possible progenitor of our selected 11 GCs, we found that most of them have a Milky Way main bulge origin