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.
