Origin of the system of globular clusters in the Milky Way
  $Context$. The assembly history experienced by the Milky Way is currently
being unveiled thanks to the data provided by the $Gaia$ mission. It is likely
that the globular cluster system of our Galaxy has followed a similarly
intricate formation path. $Aims$. To constrain this formation path, we explore
the link between the globular clusters and the known merging events that the
Milky Way has experienced. $Methods$. To this end, we combined the kinematic
information provided by $Gaia$ for almost all Galactic clusters, with the
largest sample of cluster ages available after carefully correcting for
systematic errors. To identify clusters with a common origin we analysed their
dynamical properties, particularly in the space of integrals of motion.
$Results$. We find that about 40% of the clusters likely formed in situ. A
similarly large fraction, 35%, appear to be possibly associated to known merger
events, in particular to $Gaia$-Enceladus (19%), the Sagittarius dwarf galaxy
(5%), the progenitor of the Helmi streams (6%), and to the Sequoia galaxy (5%),
although some uncertainty remains due to the degree of overlap in their
dynamical characteristics. Of the remaining clusters, 16% are tentatively
associated to a group with high binding energy, while the rest are all on
loosely bound orbits and likely have a more heterogeneous origin. The resulting
age-metallicity relations are remarkably tight and differ in their detailed
properties depending on the progenitor, providing further confidence on the
associations made. $Conclusions$. We provide a table listing the likely
associations. Improved kinematic data by future Gaia data releases and
especially a larger, systematic error-free sample of cluster ages would help to
further solidify our conclusions.
