Context :

Aims : In this study we use multi-epoch near-infrared observations from the VISTA survey of the Magellanic Cloud system ( VMC ) to measure the proper motion of different stellar populations in a tile of 1.5 deg ^ { 2 } in size in the direction of the Galactic globular cluster 47 Tuc .
We obtain the proper motion of the cluster itself , of the Small Magellanic Cloud ( SMC ) , and of the field Milky Way stars .

Methods : Stars of the three main stellar components are selected from their spatial distribution and their distribution in colour-magnitude diagrams .
Their average coordinate displacement is computed from the difference between multiple K _ { \mathrm { s } } -band observations for stars as faint as K _ { \mathrm { s } } = 19 mag .
Proper motions are derived from the slope of the best-fitting line among 10 VMC epochs over a time baseline of \sim 1 yr. Background galaxies are used to calibrate the absolute astrometric reference frame .

Results : The resulting absolute proper motion of 47 Tuc is ( \mu _ { \alpha } \cos ( \delta ) , \mu _ { \delta } ) = ( +7.26 \pm 0.03 , -1.25 \pm 0.03 ) mas yr ^ { -1 } .
This measurement refers to about 35000 sources distributed between 10 ^ { \prime } and 60 ^ { \prime } from the cluster centre .
For the SMC we obtain ( \mu _ { \alpha } \cos ( \delta ) , \mu _ { \delta } ) = ( +1.16 \pm 0.07 , -0.81 \pm 0.07 ) mas yr ^ { -1 } from about 5250 red clump and red giant branch stars .
The absolute proper motion of the Milky Way population in the line-of-sight ( l = 305.9 , b = -44.9 ) of this VISTA tile is ( \mu _ { \alpha } \cos ( \delta ) , \mu _ { \delta } ) = ( +10.22 \pm 0.14 , -1.27 \pm 0.12 ) mas yr ^ { -1 } and results from about 4000 sources .
Systematic uncertainties associated to the astrometric reference system are 0.18 mas yr ^ { -1 } .
Thanks to the proper motion we detect 47 Tuc stars beyond its tidal radius .

Conclusions :