Kinematic complexity around NGC$\,$419: resolving the proper motion of
  the cluster, the Small Magellanic Cloud and the Magellanic Bridge
  We present $\it{Hubble}$ $\it{Space}$ $\it{Telescope}$ proper motions in the
direction of the star cluster NGC$\,$419 in the Small Magellanic Cloud. Because
of the high precision of our measurements, for the first time it is possible to
resolve the complex kinematics of the stellar populations located in the field,
even along the tangential direction. In fact, the proper motions we measured
allow us to separate cluster stars, which move on average with
($\mu_{\alpha}\cos\delta^{\rm NGC\,419}, \mu_{\delta}^{\rm NGC\,419}$) =
($+0.878\pm0.055$, $-1.246\pm0.048$) mas yr$^{-1}$, from those of the Small
Magellanic Cloud and those belonging to a third kinematic feature that we
recognise as part of the Magellanic Bridge. Resolving such a kinematic
complexity enables the construction of decontaminated colour-magnitude
diagrams, as well as the measurement of the absolute proper motion of the three
separate components. Our study therefore sets the first steps towards the
possibility of dynamically investigating the Magellanic system by exploiting
the resolved kinematics of its stellar clusters.
