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In this study we use multi-epoch near-infrared observations from the VISTAsurvey of the Magellanic Cloud system (VMC) to measure the proper motion ofdifferent stellar populations in a tile of 1.5 deg sq. in size in the directionof the Galactic globular cluster 47 Tuc. We obtain the proper motion of thecluster itself, of the Small Magellanic Cloud (SMC), and of the field Milky Waystars. Stars of the three main stellar components are selected from theirspatial distribution and their distribution in colour-magnitude diagrams. Theiraverage coordinate displacement is computed from the difference betweenmultiple Ks-band observations for stars as faint as Ks=19 mag. Proper motionsare derived from the slope of the best-fitting line among 10 VMC epochs over atime baseline of ~1 yr. Background galaxies are used to calibrate the absoluteastrometric reference frame. The resulting absolute proper motion of 47 Tuc is(mu_alpha cos(delta), mu_delta)=(+7.26+/-0.03, -1.25+/-0.03) mas/yr. Thismeasurement refers to about 35000 sources distributed between 10 and 60 arcminfrom the cluster centre. For the SMC we obtain (mu_alpha cos(delta),mu_delta)=(+1.16+/-0.07, -0.81+/-0.07) mas/yr from about 5250 red clump and redgiant branch stars. The absolute proper motion of the Milky Way population inthe line-of-sight (l =305.9, b =-44.9) of this VISTA tile is (mu_alphacos(delta), mu_delta)=(+10.22+/-0.14, -1.27+/-0.12) mas/yr and results fromabout 4000 sources. Systematic uncertainties associated to the astrometricreference system are 0.18 mas/yr. Thanks to the proper motion we detect 47 Tucstars beyond its tidal radius.

The VMC survey - XVII. The proper motion of the Small Magellanic Cloud and of the Milky Way globular cluster 47 Tucanae